Patent ID: 12247998

DETAILED DESCRIPTION

The present disclosure relates to scattering-type scanning near-field optical microscope for use at cryogenic temperatures (cryogenic s-SNOM or cryo-SNOM).

In one embodiment, there is provided a cryogenic s-SNOM or cryo-SNOM suitable for use in systems for studying low energy excitations in quantum materials. The use of a cryo-SNOM according to embodiments herein can meet the simultaneous demands such as: vibration isolation, low base temperature, precise nano-positioning, and optical access involved in such studies.

The cryo-SNOM in the embodiments herein use gold-coated Akiyama probes (“A-probes”) available from NanoAndMore USA Corp., where the cantilever tapping motion is detected through a piezoelectric signal. This configuration of an Akiyama-probe-based cryo-SNOM attains high spatial resolution, good near-field contrast, and is able to perform imaging with a significantly more compact system compared to other cryo-SNOM techniques. Measurement results firmly establish the potential of s-SNOM based on self-sensing piezo-probes, which can easily accommodate far-infrared wavelengths and high magnetic fields. Use in magnetic fields of up to 7 Tesla (T) has been demonstrated and the Akiyama-tip is good for up to 12 T. While use in a low temperatures environment of 18° K with a base temperature of 1.7° K has been demonstrated, the embodiments herein can be used in environments below 100 mK.

As defined herein, near-field imaging refers to imaging of a sample surface in the proximity of, such as under, the AFM tip at such a region where the tip interacts with the sample. Performing near-field imaging relies on being able to enhance and scatter the near field at the sample surface such that sufficient contrast for features with differing optical properties can be obtained.

Further, as referred to herein, near-field photocurrent measurements refer to the focusing of light upon the sample surface and obtaining current generated by the tip-focused light through electrodes patterned on the sample surface.

Further, as referred to herein, self-sensing, or self-actuating tip in the context of an s-SNOM apparatus refers to the ability to obtain a topographic property of a sample using a piezo-electric cantilevered probe tip including a tuning fork, wherein a probing is accomplished without using an optical signal (light) but rather using an electrical signal to read and excite the piezoelectric tip. In an embodiment herein, this is accomplished with a cantilevered piezo-electric probe tip, an Akiyama-probe or “A-probe” where a laser focused onto the tip results in a charge distribution induced across the tip, which leads to an enhanced near-field directly under the tip. This near-field enhancement can be understood by the point-dipole model, where the tip is approximated as a polarizable sphere in an electric field.

A self-probing tip refers to the ability of a piezo-electric cantilevered probe tip including a tuning fork where the cantilevered probe tip is for probing the vibration of the amplitude of the tip by measuring the electrical signal rather than an optical signal wherein as the amplitude of the tip changes a voltage that is generated in the tuning fork and that voltage is proportional to the tapping amplitude.

Further, as referred to herein, a cryostat is a device used to maintain low temperatures of samples or devices mounted inside it.

FIGS.1A and1Bdepict respective embodiments of a scattering-type scanning near-field optical microscope apparatus that include an Akiyama probe. The Akiyama probe-based s-SNOM apparatus10such as the one shown inFIG.1Ais configurable for use at room temperature (RT) and, as shown inFIG.1B, the Akiyama probe-based s-SNOM apparatus75is configured for use at cryogenic (low) temperatures (LT).

As shown inFIGS.1A and1B, the scattering-type scanning near-field optical microscope apparatus10, for use at respective room temperature or low temperature, includes an Akiyama probe12. The A-probe is constructed from a piezoelectric material (e.g., quartz) tuning-fork15with a sharp micromachined Si cantilever20glued to its prongs17that includes a high-end sharp silicon tip22. This combination renders a compact and stable tip with a relatively soft spring constant (˜5 N/m, orders of magnitude smaller compared to bare tuning forks) that can be excited either electrically or mechanically. With the A-probes, a room temperature and cryogenic s-SNOM system can be built that is more compact and simpler to use than traditional systems. The resulting apparatus is capable of performing s-SNOM imaging and near-field photocurrent measurements with high spatial resolution and a good signal-to-noise ratio (S/N). In an embodiment, the length of the A-probe is about 28 μm, and the A-probe's Si tip radius can range from between 10-15 nm.

As an alternative to cantilever-based AFM, a tungsten wire (not shown) can be attached to the tuning fork15to realize a piezo-probe. However, good mechanical coupling and substantial shaking power are required to achieve a tapping amplitude, e.g., of 50-100 nm, which is usually required to effectively modulate the near-field interaction.

As shown inFIG.1A, the apparatus10includes two main components: an atomic force microscope (AFM) platform30, and an asymmetric optical interferometer40. The AFM30provides a platform for probing the light interaction with the sample11(light-sample interaction) in the near-field regime. In this manner, using focused light at the A-probe tip22, the s-SNOM can not only probe the sample topography, but also the optical properties of the sample at the nanoscale. By focusing a laser beam onto the AFM tip, the apparatus collects the light scattered off the tip which encodes the local optical properties of the sample11. The Michelson interferometer40enables phase-sensitive detection of the scattered near-field signal. To suppress the background scattering off the tip shank and sample surface, the tip20is operated in tapping mode, oscillating harmonically close to its mechanical resonance frequency. The detected scattered signal is demodulated at higher harmonics of the tip tapping frequency to filter out any undesired far-field background.

In the AFM platform30ofFIG.1A(andFIG.1B), all s-SNOM image sampling operations employ two electrical connections61to the A-probe tuning fork via a Printed Circuit Board (PCB) (not shown) upon which the A-probe12is mounted. As shown in the configuration of the apparatus10for LT optical image sampling shown inFIG.1A, one of the electrical connections61connects to an AFM controller60through drive circuitry66including, but not limited to: pre-amplifier circuits, oscillator circuit/electronics for self-oscillation, and a phase-locked-loop (not shown). This drive circuitry66can provide a drive signal (i.e., an oscillating voltage signal at a particular frequency/amplitude) to the A-probe via one of the electrical connections61to the tuning fork. In an embodiment, by applying a drive signal to the A-probe12, which is a cantilever20attached to a piezoelectric tuning fork15, the driving voltage generates in-plane oscillations of the tuning fork prongs17, which translates to out-of-plane z-axis motion for the cantilever. For example, as described in the reference to Akiyama et al. entitled “Symmetrically arranged quartz tuning fork with soft cantilever for intermittent contact mode atomic force microscopy”, Review of Scientific Instruments 74, 112 (2003),FIG.2Ashows a cantilever tip response25A to a portion of an applied oscillation signal in which the tuning fork prongs17move in respective opposite directions indicated by arrows “A” to generate a first z-axis deflection30A whileFIG.2Bshows a further cantilever tip response25B to another portion of the applied oscillation signal in which the tuning fork prongs17move in respective directions toward each other indicated by arrows “B” to generate a second z-axis deflection30B. In turn, the tip22is brought into contact with the sample, the cantilever deflection translates to mechanical deformation of the tuning fork that generates a piezo voltage proportional to this deflection. This piezo voltage proportional to this deflection can be measured directly from the piezoelectric signal generated by the tuning fork15received at preamplifier circuitry63using the other of the electrical connections61.

In an embodiment depicted in bothFIGS.1A and1B, the asymmetric optical interferometer40is a Michelson interferometer that includes a configuration of mirrors31,33,37and39, optical filters (polarizers)23,27, and includes a beam splitter42, e.g., a ZnSe beam splitter, that splits the incident light by a specified ratio that is independent of the light's wavelength or polarization state in the IR regime. In an embodiment, the Michelson interferometer40is optimized for the mid-IR but can be adapted to be used in the THz frequency range. A coherent light source28, such as a gas, e.g., CO2, laser source, emits coherent light29of a defined wavelength, e.g., 9 μm-11 micrometers, that is coupled via fiber to an in-plane polarizer23(functioning as an optical filter to filter out light polarized in a direction not in-plane to the tip) where it becomes polarized parallel to the tip shank35. The use of polarizer23is optional in the cryo-SNOM apparatus75ofFIG.1Bdepending upon the light source used. The polarized light beam35is reflected off first mirror31to hit the beam splitter42surface. The beam splitter42is partially reflective and reflects (in the reflection arm) a smaller percentage of the input beam, i.e., beam36, towards the A-probe tip, and transmits a majority of the beam, i.e., beam38, towards a transmission or reference arm. In a non-limiting embodiment, the beam splitter42reflects 40% of the beam towards the A-probe tip22and transmits 60% of the beam towards the reference arm. In the reflection arm, the reflected light beam36gets focused onto the A-probe tip22through an aspherical lens45as shown inFIG.1A. In the embodiment ofFIG.1B, the reflected light36gets focused onto the tip through an off-axis parabolic (OAP) mirror65. Whether an OAP mirror65or aspherical lens45is used depends on the light source and operating environment/temperature; the OAP mirror65has the advantage of being wavelength independent while the aspherical lens45provides for easier alignment. The enhanced scattered signal32is collected through the same lens45, in the embodiment of RT apparatus10shown inFIG.1Aor is collected via the OAP65in the embodiment of LT apparatus75shown inFIG.1B. In each embodiment, this enhanced scattered signal32is recombined with the reference arm, and the resulting signal32′ is focused onto a Mercury-Cadmium-Telluride (MCT) detector50for homodyne detection thereof. That is, the transmitted light portion38through the reference arm that is transmitted through the beam splitter42to the mirror33is further reflected by a piezo adjustable mirror39for homodyne detection with the information from the enhanced scattered light signal32reflected from the sample at the AFM30through lens45(or OAP mirror65). In an embodiment, the interferometer is used to collect phase information between the incoming reference arm signal and the scattered light from the sample for the optical imaging of the sample. The enhanced scattered light32′ is filtered using polarizer37prior to detection by the MCT detector50and then sent to a lock-in amplifier to measure the near-field signal. The combined signal is then demodulated at a frequency that is the integer multiple of the tapping frequency of the probe tip to see what optical signal is modulated by the tapping of the tip to capture the genuine near-field region information of the sample.

To perform AFM measurements requires measuring the probe's tapping amplitude and frequency. In the A-probe based systems ofFIG.1A,1B, the tapping amplitude and frequency are measured directly from the piezoelectric signal generated by the tuning fork15since the A-probe is self-sensing. This piezoelectric signal is generated by the tuning fork and received for processing at the AFM controller via connections61. This eliminates the need for separate optical alignment and detection schemes for the cantilevered tip22. As shown in RT s-SNOM apparatus ofFIG.1A, the sample11is mounted on a micro-precision positioner or scanning platform45which can orient a position of the sample in three-dimensions (e.g., XYZ piezo stages) for sample scanning. A focusing lens45for focusing the received probe light signal from the interferometer40is also mounted on a similar XYZ micro-precision positioning platform or scanning stage46that can modify the orientation of the lens45in three-dimensions for optical alignment. In the RT s-SNOM apparatus ofFIG.1A, the A-probe (cantilever/tip and tuning fork) is fixed in orientation with respect to the sample11and the focusing lens45that sits on XYZ piezo stages is adjusted for optically aligning the received light beam36to the A-probe tip. Fixing the tip position increases the overall mechanical stability of the A-probe based s-SNOM system. In the LT cryo-SNOM apparatus ofFIG.1B, the A-probe (cantilever/tip and tuning fork) is mounted on XYZ piezo stages47and the tip is adjusted for optical alignment with the incident light beam36. The XYZ piezoelectric stages in each embodiment include a piezoelectric motor driven scanner in a closed loop operation.

Thus, when an AC signal is sent to the piezoelectric tuning fork17, e.g., quartz, the tuning fork will oscillate and generate an electric signal in response. This allows one to find the resonance frequency of the tuning fork by measuring the electric signal generated as the driving frequency is swept across the resonance. The Akiyama probe is configured to lie perpendicular to the sample surface. The AC signal is transmitted to the tip, and by sweeping the frequency there is found the tuning fork's resonance. Once resonance is found, the driving signal at this frequency is locked using a phase-locked loop (PLL). The tip is then brought into contact with the sample using XYZ piezo stages. Next, a laser is focused onto the tip using either a lens or parabolic mirror for near-field enhancement. The location of the beam spot is then optimized by either scanning the length of the lens with piezo stages or using a visible beam. The light that gets reflected off the tip and sample is collected by the focusing lens or mirror, mixed with the original un-scattered light, and the intensity of the resulting signal is measured by a liquid nitrogen cooled MCT detector.

In operation, p-polarized light29from a CO2laser (e.g., at a wavelength of 10.4 μm) or light from a THz source is coupled via an optic fiber to the Michelson interferometer40for homodyne detection of the s-SNOM signal. The reflected light path is focused onto the AFM tip by the lens42in the RT S-SNOM apparatus10ofFIG.1A. In this embodiment, when the reflected light path36is focused onto the AFM tip, the location of the beam spot is optimized by scanning the lens45via XYZ piezo stages46. As the tip scans the sample surface, the tip scattered light32is collected, and recombined with the reference arm. The intensity of the resulting signal32′ is measured by liquid nitrogen cooled MCT detectors. This signal32′ is then sent to a lock-in amplifier55for demodulation at higher harmonics of the tip tapping frequencies.

In an embodiment, two (2) feedback loops are used to maintain a constant tip-sample distance: frequency and amplitude feedback. Both feedback loops are controlled using an AFM controller60, e.g., an RHK R9 AFM controller (available from RHK Technology, Inc. Troy, MI) which controls the AFM operations. For frequency feedback, the lock-in amplifier55is used to monitor the phase between the tip driving signal and the tip oscillation and keep it at zero degrees. After selecting a desired frequency shift for the tip as it goes into contact with the sample, this feedback loop will maintain this frequency shift as the tip is scanned across the sample surface. Thus, if the tip frequency shifts, the phase difference between the two signals will change and the sample position in the z-direction will be modified. The amplitude feedback loop is used to maintain a constant tapping amplitude by altering the tip driving voltage as the tip is scanned across the sample surface. In general, the AFM controller60is used to control the AFM.

FIGS.3A and3Beach show an actual image of the RT s-SNOM and LT cryo-SNOM systems, respectively.

InFIG.3A, the close-up image shows the lens42, sample11, and A-probe12for the room temperature s-SNOM apparatus ofFIG.1A(UHV compatible). InFIG.3A, arrow labeled32,36indicates the light path through the aspherical lens42(the lens passing infrared range light). The sample11sits on piezo (XYZ) stages45and is scanned to generate an s-SNOM image. The lens45sits on a XYZ piezo stage while the probe tip is fixed in place. The A-probe tip inFIG.3Asits on a PCB48which is attached to a wedge block58. The wedge block58can be angled at about 25 degrees, however, can be fixed at an angle 24-degree with respect to a horizontal. The wedge block58is held in place by a magnetic mount59and does not move throughout a measurement.

InFIG.3B, the close-up image shows the parabolic mirror65, sample11, and A-probe12for the cryo-SNOM apparatus ofFIG.1B. In the embodiment ofFIG.3B, the A-probe tip11sits on piezo stages47while the OAP reflected light beam remains stationary. The sample is scanned to generate an s-SNOM image.

FIG.3Cdepicts resonance curves71,72for both frequency and phase, respectively. The resonance curves71,72are generated by sweeping the frequency of the excitation voltage of the Akiyama probe. In an embodiment, to maximize the s-SNOM signal in the RT apparatus10, the lens45is scanned until a beam hotspot74of 10 μm in diameter is found such as the focused beam hot spot74shown inFIG.3Dobtained by the detector50while scanning the lens in a beam alignment procedure.

FIG.4depicts a beam alignment procedure80for aligning the beam hotspot at the A-probe tip in the fixed OAP configuration of the cryo-SNOM apparatus ofFIG.1B. A first step83is applying a visible “pilot” laser, e.g., a HeNe laser, and the IR (CO2) laser beam spot in a vicinity of the A-probe tip. The HeNe laser is used as a guide beam to focus the CO2laser onto the tip. Then, at85, using temperature sensitive liquid crystal sheets, the method adjusts the visible pilot HeNe laser to achieve a colinear alignment of a visible pilot laser with the IR (CO2) laser. A determination is made at86to determine whether a colinear alignment of the pilot and IR beam is achieved. If colinear alignment is not achieved, the method proceeds to87to adjust the visible pilot laser light until colinear alignment is achieved. Once, colinear alignment is achieved, a further step88involves precisely aligning and focusing of the pilot laser on the very apex of the A-probe tip20. To realize this, there is provided a preliminary positioning of the tip20in the vicinity of the pilot, as shown inFIG.3E. In an embodiment, a microscope (not shown) above the cryostat is used to view the tip so that the sample can be brought into contact without crashing the tip and also focus the HeNe spot on the cantilever. This can be done by first focusing on the tip and then defocusing the camera slightly below the tip, allowing the sample to be brought into focus and close to the tip. A second function of a microscope camera is to locate the regions of interest on the sample where it is desired for measurement. The third function is to view the location of the HeNe and its spot size on the cantilever. In particular,FIG.3Edepicts an image of the Akiyama probe12under an optical microscope and of a focused pilot laser HeNe beam spot74used to align the probe with the IR beam. After preliminarily positioning of the tip20in the vicinity of the pilot, this is followed by high resolution direct tip imaging on a CCD camera (not shown) by inserting a flip-mirror in the light collection path after the beam-splitter. This procedure usually allows for the detection of the true near-field signal during a first tip-sample approach. Further improvement in the SNOM signal can be achieved by fine tuning the position of the IR beam.

Referring toFIG.5A, it is the case that the geometry of the tip shank21of the A-probe long (e.g., 28 μm) is longer than conventional AFM probe tip designs. It is well known that the tip-antenna effect is closely related to the tip shank length, therefore, the A-probe exhibits a good near-field scattering signal for longer incident light wavelengths. To verify this, the system first performs a full-wave numerical simulations using the method of moment (MoM) technique. Compared to other full-wave numerical algorithms MoM is especially suitable for such a simulation because only the tip surface needs to be discretized. This offers a monumental advantage in terms of computer memory and computation time.

In an embodiment, an A-probe tip22is imaged using a scanning electron microscope (SEM) as shown inFIG.5Ato precisely determine its geometry. Then a tip geometry model is constructed accordingly as shown inFIG.5B.FIG.5Cshows the amplitude of the scattered field spectra76demodulated at the second harmonic (S2) when the tip22is placed on top of a metallic surface. The simulation is carried out in a broad frequency range from 1 terahertz (THz) to near-IR. As shown, in the mid- and near-IR spectral range, the A-probe exhibits significantly stronger scattering at longer wavelengths towards the THz regime.

For the numerically simulated S2amplitude spectra using the method of moment (MoM) for the Akiyama probe, the calculation considers the demodulation of tip position as well as finite incident angle and collection angles. The scattered field E(ω, θi, θc) is simulated for all the permutations of θi=40°, 45°, 50°, . . . , 80° and θc=40°, 45°, 50°, . . . , 80°, where θiis the incident angle and θcis the collection angle with respect to sample surface normal. The total collected signal is the average over all E(θi, θc). The dashed line78indicates the length of the A-probe.

This simulation result demonstrates that the A-probe is ideal for far-IR s-SNOM imaging, e.g., with an incident wavelength A in the range of ˜20 to ˜100 μm. In the spectra76shown inFIG.5C, multiple peaks are observed, which is attributed to the antenna resonances.

To characterize the signal-to-noise (S/N) and near-field contrast of the s-SNOM measurements at room temperature (e.g., 300° K) and 15° K,FIGS.6A-6Cprovide a nanoimaging of a test sample such as a standard 20 nm SiO2/Si test sample from commercial companies NT-MDT LLC. (RT system) and NanoAndMore USA Corp. (LT system).

FIG.6Aparticularly depicts room temperature AFM topography image101and S3(third harmonic) image103of a first semiconductor structure sample including SiO2on Si taken with the RT and LT apparatus ofFIGS.1A,1B, respectively. InFIG.6Aeach structure's corresponding horizontal line profiles102,104are shown taken through the middle of the images.FIG.6Bdepicts room temperature AFM topography image105and S3(third harmonic) image106of a second semiconductor structure sample including SiO2on Si taken with the RT and LT apparatus ofFIGS.1A,1B, respectively. InFIG.6B, further shown at the bottom of each topographical image105,106are each structure's corresponding horizontal line profiles107,108taken through the middle of their respective images.

FIG.6Cdepicts the topography image110and S3image111of the same sample structure shown inFIG.6B, acquired at 15° K using the LT apparatus ofFIG.1Bwith each structure's corresponding horizontal line profiles112,114shown taken through the middle of the images.

In particular, as shown inFIG.6A, it is found that the S/N of S3is greater than 30 for the RT system. For the LT-SNOM, the S/N at 300° K is about a factor of two larger than at 15° K (FIGS.6B and6C). This is because, at room temperature, the Q-factor of the A-probe is more than an order of magnitude lower than at low temperatures, allowing for faster rastering and easier optimization of AFM feedback parameters. The near-field contrast between the SiO2and Si, S3(SiO2)/S3(Si), with about a 10 μm incident light has a consistent value of about 0.7 throughout the experiments.

The following presents two case studies of the application of the A-probe system to two-dimensional materials. The first case study, shown inFIGS.7A and7B, is a near-field photocurrent measurement using the RT setup ofFIG.1A.FIG.7Ashows an example sample in the form of a semiconductor device structure90having closely placed source electrode92and drain electrode94of gold (Au) on top of a bilayer graphene channel95formed on a Si substrate. The system (e.g.,FIG.1B, is configurable for measuring near-field photocurrent, which probes the tip-induced thermoelectric, thermovoltaic, or photovoltaic effects down to 20 nm length scale. Photocurrent measurements at low temperature and 7 T magnetic fields are demonstrated in the graphene sample.

In a first case study, as shown inFIG.7A, the A-probe tip-enhanced IR light36creates a local temperature gradient96which can induce a directional photocurrent with the presence of local inhomogeneities (and thus, local variations of the Seebeck coefficient). Instead of gathering the scattering signal, the system detects the near-field photoinduced current97between the two closely placed electrodes92,94on top of the bilayer graphene sample95. The near-field photocurrent signal (Pn)97is amplified by a preamplifier100and demodulated at higher harmonics (n≥2) of the tip tapping frequency. InFIG.7B, there is shown the AFM topography and inFIG.7Cthere is shown the detected third harmonic signal P3. A good signal-to-noise ratio of 20 is found for P3(third harmonic) with approximately 13 mW incident power and an applied −20 V back-gate voltage at 300° K. It is observed that the strongest signal is in the vicinity of the electrodes, as expected, and observed fringes close to suspected line defects as shown inFIG.7C. The fact that the signal is strongest and reversely signed at the two electrodes suggests the observing of the Seebeck effect.

A second case study shown inFIGS.8A-8Cdemonstrates AFM topography (FIG.8B) and the detected fourth harmonic S4image of λ=10.6 m SNOM data (FIG.8C) taken at ambient conditions in commercially available polycrystalline graphene.FIG.8Ashows the same semiconductor structure sample ofFIG.7Aincluding the two closely placed Au contact electrodes92,94on top of the bilayer graphene sample95. The A-probe tip-enhanced IR light36creates polariton excitation and modulation91.FIG.8Cdepicts the line defects97in graphene at ambient temperature, revealed by the plasmon polariton fringes due to scattering at grain boundaries and topographic features. The line defects are not identified in AFM image shown inFIG.8B.

It is the case that the scans ofFIGS.8B,8Creveal information beyond the typical optical contrast between graphene and the (probably insulating) islands associated with defects/adsorbates. There is observed ‘halos’ 93 and line defect ‘highways’ 97 surrounding and connecting topographic features which arise from efficiently damped plasmonic scattering at grain boundaries or defect structures. A good S/N can be achieved routinely up to the 4thharmonic of the tapping frequency as shown inFIG.8C.

These case studies demonstrate the particular strength of using a tuning fork-based Akiyama probe for room temperature s-SNOM and cryo-SNOM. The nano-imaging capability at room and low temperatures demonstrate its potential for near-field photocurrent mapping. In principle, this method is not limited to mid-IR and can be extended to near- and far-IR, as demonstrated using the full-wave simulation.

Using the A-probe tip with the AFM obviates the need for complex AFM sensing circuitry that requires two different light beams for measuring topography and optical properties of the sample which requires excess space. The use of the A-probe system provides for a compact system that facilitates integration into a cryo-chamber providing low-temperature and magnetic field environment. That is, due to the much-simplified experimental layout, the Akiyama probe s-SNOM is used for a cryo-SNOM system that can be used in high magnetic fields.

The piezo-based cryo-SNOM system described herein thus is a compact and high-resolution near-field microscope system that can be incorporated into many systems of varying sizes with greater ease. Existing instruments may be fitted (or retro-fitted) with the piezo-based probes described herein.

FIG.9depicts an exposed cross-sectional view of a cryostat200including a chamber201for housing a cryo-SNOM system250such as the LT s-SNOM system shown inFIG.1B, to provide infrared range nanoimaging capabilities at cryogenic temperature and under magnetic fields up to 7 Tesla. In an embodiment,FIG.9depicts a closed-cycle cryostat200housing an AFM sample stage220and off-axis parabolic mirror stage240of the cryo-SNOM system. Further shown inFIG.9is the location of the fixed A-probe tip230and the OAP mirror260mounted on OAP scanning stage for providing s-SNOM light beam to a sample to be probed.

As shown inFIG.9, the cryostat200includes a cryogenic vacuum chamber201(e.g., OptiCool® from Quantum Design, Inc. San Diego, CA). This cryostat is a closed cycle system with four superconducting magnets202,204,206,208operable to generate up to 7 Tesla magnetic field210at the center of the chamber201. The cryostat chamber201can maintain a vacuum pressure of about 10−6Torr and the base temperature, with no extra hardware, is 1.6° K. To get to 10° K, helium gas is compressed by a pulse tube cryocooler. To go below 10° K, 4° K liquid helium is expanded to get 1.6° K liquid helium, which is sent to a 4 K° plate and sample column where the Cryo-SNOM hardware sits. Further provided is a window providing a CCD camera275or like imaging device access to a sample being probed.

As shown inFIG.9, mounted within chamber201are the AFM stage220and a piezo-actuated OAP stage240of the cryo-SNOM system and their 3-dimensional scanning stages and positioners. Such sample scanning and positioning stages are from Attocube (models ANSxyz100/LT/UHV and ANPxyz101/LT/UHV, respectively). The mechanical noise of the s-SNOM tested by the PI is less than 0.5 nm in z-axis direction and less than 20 nm in xy direction (resolution limited) at 100 K. In an embodiment, the AFM has a spatial resolution of about 15 nm and a scan area of 50×50 μm2at room temperature. The accessible temperature range of the scanning probe system is about 28 K-350 K. A CO2laser centered at ˜11 μm and a QCL laser centered at 6.4 μm are used for the photocurrent and s-SNOM imaging. The laser power before entering the Opticool chamber is around 10 mW-15 mW. The laser is focused onto the tip with a spot size ranging from approximately 10-20 μm. A self-homodyne detection scheme is implemented which yields a stable scattering signal detection and a good signal contrast.

FIG.10shows a sample pod300used to mount the cryo-SNOM hardware inside the cryostat vacuum chamber201. This sample pod300includes brass walls, pod flanges303and a brass mounting plate302configured to accommodate the mounting of the cryo-SNOM hardware inside cryostat chamber201and facilitate all connections needed for cryo-SNOM operations. The pod consists of a brass ring with circuit boards305, which allows the pod to be screwed into the chamber and establishes electrical connections to outside of the chamber.

FIG.11depicts a sample pod300placed inside the cryostat chamber201. Two wiring paths321,322from the pod300to outside the chamber are shown. Further depicted is a region350representing the usable volume inside the chamber201. As shown in the embodiment depicted inFIG.11, the total distance from the bottom of the sample pod to the magnetic field center line351is about 90 mm.

FIG.12shows a self-contained non-magnetic housing unit400for enclosing the cryo-SNOM system ofFIG.1Bminus the interferometer. Housing unit400includes a bottom base plate401including a portion402upon which is situated a first cylindrical-shaped vessel420within which is situated the 3-dimensional sample positioning components include three sample stages and three piezo-positioners for the AFM devices to provide XYZ positioning of the sample to be scanned, a sample scanner device and precision drive circuitry410operable for scanning the sample, and a sample holder platform415for holding the sample to be scanned. In an embodiment, all piezo-positioners are rated for use at 4° K and up to 12 T. In an embodiment, the sample mounting plate has a diameter of about 59 mm. Situated in close proximity above the sample holder415is a tip holder425for holding the PCB including the A-probe of the cryo-SNOM system in a fixed position relative to the sample holder415. In an embodiment, the sample plate to tip distance is about 5 mm. The tip holder425is mounted on a top plate structure430and extends downward at an angle (e.g., 24 degrees with respect to the horizontal) so the A-probe tip is situated at a corresponding angle with respect to the sample.

The self-contained housing unit400and attached components for housing the cryo-SNOM system ofFIG.1Bas depicted can be made of a non-magnetic material, e.g., Aluminum, Titanium, and is designed to provide increased mechanical stability by minimizing vibrations. The enclosure exhibits low mechanical noise (reduces AFM noise), is space efficient, and can achieve a lower operating temperature.

FIG.13depicts a side view450of the tip side and the first cylindrical vessel420. In an embodiment, as shown inFIG.13depicting the tip side view450of the housing400ofFIG.12, the top plate430includes an opening452to view the A-probe tip and sample with a microscope from outside the chamber. As seen in the corresponding tip side view450ofFIG.13, the enclosure400includes a front wall406and a back wall407connecting top plate430to bottom plate portions402and403.

Referring back toFIG.12, the bottom plate401of the self-contained housing unit400for housing the cryo-SNOM system250ofFIG.9includes a second base plate portion403upon which is situated a second cylindrical enclosure or vessel440within which is provided mirror positioning devices and associated three piezo-positioners445for providing the 3-dimensional XYZ positioning of the near-field optics including the OAP mirror470. Due to the location of a window used for light coupling, the parabolic mirror is mounted on the positioners for XYZ positioning. Located above the vessel440is the parabolic mirror mount460for mounting the parabolic mirror470guiding light to the mounted A-probe tip during sample probing operations.FIG.14depicts a corresponding mirror side view475of the housing400ofFIG.12. As seen in the corresponding mirror side view475ofFIG.14, the enclosure400includes a front wall406and a back wall407connecting top plate430to bottom plate portions402and403. Although not shown inFIGS.13,14, ceramic spacers are situated between the top plate and side walls to provide some thermal isolation for the tip to reduce the Q-factor.

FIG.15shows the top view of the s-SNOM system enclosure including the top plate430and showing the opening452for enabling visualization of the sample and A-probe tip.

FIG.16shows a front view of the self-contained housing unit400including the front wall406attached to the top plate430and attached to the base plate401using connectors480, e.g., screws. The front wall406includes an opening455enabling access to the A-probe mount425and sample holder415. A series of holes485in the front wall is further provided for wire organization.FIG.17shows a corresponding back view of the self-contained housing unit400including the back wall407attached to the top plate430and attached to the base plate401using attachment connectors481. The back wall407includes an opening465enabling access to the A-probe mount425and sample holder415and OAP mirror mount460. A series of holes488in the back wall is further provided for wire organization. In embodiments, these holes488are dimensioned to accommodate wiring paths for connecting the various AFM and OAP components, the wires including but not limited to: twisted pair wires for the three positioners and three scanners; two coax cables for the tip driving and output signals; five wires for the tip preamp: input, output, +/−7.5V preamp power and ground; one coax cable for sample photocurrent measurements; and a wire for sample gating.

As further shown inFIG.16, front wall406includes inwardly tapered portions476near respective base plate connection portions480. Similarly, as shown inFIG.17, back wall407includes inwardly tapered portions477near respective base plate connection portions481. The inward tapered portions476,477of the respective front wall and back wall decrease the overall footprint of the lower portion of cryo-SNOM system housing enclosure400while not sacrificing mechanical stability. The decreased footprint of the base portion of the enclosure400for housing the cryo-SNOM system250ofFIG.9enables the fitting of the cryo-SNOM system into the cryostat sample pod300used to mount the cryo-SNOM hardware inside the cryostat vacuum chamber201.FIG.18shows a top view of the cryo-SNOM system housing enclosure400fitted in the sample pod300for incorporation in the cryostat chamber.

FIG.19depicts an elevation view of the cryo-SNOM system housing enclosure400fitted within the sample pod300for incorporation in the cryostat chamber. In the embodiment shown inFIG.19, a copper braid428is provided to create a thermal link to the sample pod.

It is the case that subwavelength confinement, chiral sensing, and programmable manipulation of infrared light at the nanoscale are highly desirable for photonic and optoelectronic applications of quantum materials. By breaking the time-reversal symmetry, magnetic fields enable novel light-matter interactions with important real space features such as chiral magnetopolaritons, unidirectional edge photocurrent, and nonreciprocal light propagation at magnetic interfaces. These novel phenomena are inherently related to the electronic states at the edges of two-dimensional materials via quantum state transitions.

As known, a magnet changes the trajectory of electrons but does not usually have a strong interaction with light. However, by coupling to confined light at the nanoscale, for example through polariton excitations or photo-induced Hall edge currents, the magnetic field can interact strongly with light-initiated collective excitations. One canonical example of an intrinsic magnetic field-induced optical excitation is the inter-Landau level transition (‘LL transition’), which is of paramount importance for studying bulk and edge states in two-dimensional electronic systems. In graphene, the LL transition, which is inherently a quantum transition, can be observed even at close to room temperature in a high magnetic field, e.g. 7 T.

In a further embodiment, the cryo-SNOM system ofFIG.1Bemployed in a cryostat environment ofFIG.13using light at infrared (IR) or terahertz (THz) frequencies and used in conjunction with high magnetic fields up to 7 Tesla renders a magneto scanning near-field optical microscope (m-SNOM) system that can be used to visualize the generation of Dirac magnetoplasmons due to LL transitions (‘Landau plasmons’) in near charge-neutral monolayer graphene. By on-resonance excitation of the LLs, there can be observed a clear magnetic field-tuned plasmon polariton signature in real space and a greatly enhanced photocurrent generation at the edges of graphene.

Generally, such an m-SNOM platform (performed under the s-SNOM framework) can be used to study low-energy excitations in quantum material systems with the breaking of time-reversal symmetry. This is especially important at low photon energies (e.g., 1-1000 meV), since a plethora of low-energy magneto-optical phenomena can now be investigated with a spatial resolution down to 10 nm, such as chiral edge plasmons or nonreciprocal polaritons. The m-SNOM platform can be used to directly visualize infrared plasmon polaritons due to the quantized Landau transitions in near-charge neutral graphene. Via resonant inter-Landau level transition, the magnetoplasmon excitations at the edge of graphene can be mapped to associated enhanced edge photocurrent. Generally, the approach using m-SNOM platform is used to study enigmatic quantum effects including, for example, magnetic phase transitions, low-dimensional magneto-plasmon polaritons, and hybrid magnon-phonon polaritons in Dirac and Weyl electron systems.

FIG.20shows a schematic of a sample field effect device consisting of a hBN/graphene/hBN heterostructure500including a monolayer graphene encapsulated between two thin hexagonal boron nibride (hBN) slabs (top and bottom thickness of ˜5 nm and ˜28 nm, respectively) for use in studying low-energy excitations in an m-SNOM platform. This structure500includes gold electrodes502,504fabricated on the two sides of the hBN/graphene/hBN heterostructure and the structure is tuned to be close to the charge neutral point (CNP). Additionally shown is the A-probe12having cantilevered tip20, and incident light36. A fourth harmonic of the tip scattering signal (S4) and tip-modulated near-field photocurrent (I3) signal are measured simultaneously. Most of the results are demonstrated at 200 K, although similar phenomenon has been observed in a wider temperature range (100K to 300K). InFIG.20, both the scattered near-field Snand the tip-modulated photocurrent Inare demodulated at higher harmonics (n≥2) of the tip resonance frequency to eliminate the far-field background.

As shown inFIG.20, for near-CNP graphene in a magnetic field, Landau transitions yield resonances of the optical conductivity (σxx) at discrete photon energies En=sgn(n)√{square root over (2eℏvF2|nB|)}, where n is the energy level index, sgn(n) is positive (negative) for electrons (holes), vFis the Fermi velocity, and B is the applied magnetic field520. With an incident photon energy of ˜111 meV (˜11.2 μm, 895 cm−1), the optical transition between the 0thto 1stLandau Levels (LL0→1or LL−1→0) is accessed.

FIG.21Adepicts an m-SNOM image (S4) of the hBN-graphene boundary. The gold electrodes are on the top and bottom sides of the sample, consistent with the schematic inFIG.20.

FIG.21Bdepicts an m-SNOM near-field photocurrent image (I3) of graphene, taken simultaneously with the m-SNOM image (S4) ofFIG.21A. The boundary of graphene is outlined with dashed line530.

FIGS.22A and22Bdepict results of magnetic field tuning of the 0thto 1stLandau Level transition in a near-charge neutral graphene as revealed by m-SNOM shown in successive images inFIG.22Aand as corresponding near field photocurrent imaging inFIG.24B. The incident light has a wavelength of ˜11.2 μm (˜111 meV or ˜900 cm−1) and the sample is sitting at 200K. The dashed lines615inFIG.22Aoutline the edges of the graphene.

FIG.22Ain particular shows the successive experimental m-SNOM scattering images600of the S4(fourth harmonic signals) on monolayer graphene from 0 T to ±7 T. The LL transition manifests itself through increased absorption of the incident light by the graphene sheet, as is evident in the relative near-field scattering contrast (S4) between graphene and hBN. From 0 T to below 5 T, the absorption of the incident light is similar for hBN and graphene, providing little contrast between the two. At |5| T and |6| T, however, shown in image605, the high-frequency tail-end of the first LL transition becomes accessible, leading to increased scattering of the incident light by graphene and thus, increased contrast between graphene and the substrate. At |7| T, shown in image610, the coupling between the incident light and the first LL transition is the strongest, resulting in the increased scattering signal (S4) and therefore a visually bright graphene sheet. A plasmon fringe is also evident at the non-contacted edges of graphene as indicated by the arrow620in the 6T image. Since the graphene is near charge neutral and slightly doped in between LL−1and LL0, it is expected Landau plasmons arise from the partially filled LLs. It is noted that the amplitude and sign of the near-field contrast (S2, S3, or S4) between graphene and hBN can depend very sensitively on the Fermi-velocity and electron scattering rate of graphene and varies from sample to sample. Since a homodyne detection scheme is used for the S4signal, only the relative contrast is meaningful according to: |S4grpahene(B)/S4hBN(B)|≈|S4grpahene(B)/S4graphene(B=0)|.

The tip-initiated near-field photocurrent I3also has a strong dependence on the magnetic field (FIG.22B). At zero field, shown in image660, the signal662,663is localized close to the gold contacts at the respective left and right sides of the graphene. This is because the gold contacts break the inversion symmetry, leading to a tip-induced thermal gradient across the electrodes and, therefore, a directional photocurrent due to the photo-thermoelectric effect. Far away from the electrodes or edges, the net photocurrent induced by the tip in every direction averages out to zero due to inversion symmetry. In the low magnetic field regime (<|1| T), the cyclotron motion of the thermo-electrons due to Lorentz force yields shrinking current ‘hot spots’ at opposite corners of the sample. The behavior of the near-field photocurrent in this low field regime can be explained via the Shockley-Ramo (SR) formalism and assuming a non-zero thermoelectric conductivity αxxand αxy. The inset650at 0 T shows the band structure of graphene with the Fermi energy dashed line652tuned to the CNP. At higher fields (e.g. >|6| T), the current along the non-contacted edges of the graphene sheet manifests a clear photo-Nernst effect, where αxyis peaked near charge neutral. At |7| T, image665, this chiral photocurrent along the free edges of graphene is significantly enhanced compared to the low field values, and the current at the same edge has opposite directions for 7 T and −7 T. The inset670at 7 T shows the inter-Landau level transition being measured. Compared to the current generated using an incident light wavelength of 6.588 μm (188 meV, or 1518 cm−1), where the 0→1 transition is not accessible, it is found that the photocurrent generated on resonance at 11.1 μm yields an enhancement of a factor of at least about 12 fold. This enhanced edge current is attributable to the on-resonance LL transitions. The box675shown in the bottom right corner of the sample at 7 T image shows the region being imaged inFIGS.23A-23C.

FIGS.23A-23Cdepict results700of a detailed study of the magnetic field tuning of Landau plasmons revealed in m-SNOM scattering image ofFIG.23Band near-field photocurrent mapping ofFIG.23Cat the graphene-hBN boundary corresponding to the area outlined at675as shown in the bottom right corner of the sample at 7 T image ofFIG.22B. The incident light has a wavelength of ˜11.2 μm (˜111 meV or ˜900 cm−1) and the sample is sitting at 200K.FIG.23Ain particular depicts the calculated imaginary reflection coefficient, rp, at the same magnetic fields as in the images shown inFIGS.23B,23C, showing changes in Landau plasmon dispersion. The dashed line702indicates the applied laser frequency of 895 cm−1. The dashed line710inFIG.23Bindicates the peak intensity of the plasmon.

In particular,FIGS.23A-23Cshows a detailed study performed at the edge of graphene, where the plasmon is the most evident within the limit of the laser frequencies. Beginning at ≥5T, interference fringes due to Landau plasmon polaritons become evident, for which the spatial extent gets clearly broadened with increasing magnetic field. The plasmon fringe extends from ˜100 nm at 5 T to above ˜200 nm at ±17 T, where the coupling between the incident light and the LL0→1transition is the greatest. This increasing of the plasmon wavelength with B field is also expected from the calculation of the imaginary part of the reflection (lm(rp)) as a function of frequency and in-plane momentum q. From a calculated optical conductivity, the system obtains the Landau plasmon dispersion at different magnetic fields. It can be seen inFIG.23Athat the Landau plasmon dispersion intersects the laser frequency with decreasing momentum as the magnetic field increases. This implies a longer plasmon wavelength at 7 T than at lower fields: ˜400 nm at 7 T and ˜200 nm at 5 T.

The evidence of the Landau plasmon is also seen in the near-field photocurrent images shown inFIG.23Cshowing a fringe like pattern and broadening of the overall photocurrent signal at higher fields. This attests to a plasmon modulated photothermo-effect of graphene at the sample edge. It is noted that at the top of the images inFIGS.23A-23C, there is a gold contact oriented in the horizontal direction (box675inFIG.22B(e.g., at 7 T)). Close to the electrodes at the corners of graphene, the amplitude of the edge photocurrent can be increased or decreased, depending on the orientation of the field. This is consistent with the observation inFIGS.20-22and the interpretation of the combined photo-Seebeck and photo-Nernst effect.

FIGS.24A and24Bshow exemplary magnetic field-dependent Landau plasmon dispersion results800of the photocurrents (FIG.24A) and results850of the s-SNOM line scans (FIG.24B) at the graphene-hBN boundary while sweeping the magnetic field from 7 T to −7 T, respectively. The line scans850clearly show the Landau plasmon effects appearing between |5| T and |7| T and disappearing for magnetic fields in between 0 and |5| T. Note the scan speed is different between |5| T and |7| T.

FIG.24Cshows a simulated s-SNOM mapping of the magnetic field plasmon dispersion using the same parameters as the ones inFIGS.25A-25C.

FIG.24Ddepicts a plot of plasmon wavelength, λp, as a function of the magnetic-field, showing strong agreement between the simulation and experiment. Error bars originate in the standard deviations during Lorentz background fitting and plasmon fringe fitting.

That is, to obtain a magnetic field-dependent dispersion relation for the Landau plasmons, line scans are taken across the graphene/hBN boundary while sweeping the magnetic field from 7 T to −7 T, as shown inFIG.24A-24D. This dispersion clearly shows the onset of the LL transition and Landau plasmons at ±5 T. The curvature of the plasmon fringes (shown as dashed curves815,816inFIGS.24A and24B, respectively) suggests longer wavelengths (or equivalently, lower in-plane momentum q) of the plasmon polaritons at higher fields.

Notably, in the near-field photocurrent scans, a similar field-dependent dispersion is observed, as illustrated by the black dashed curve815inFIG.24A. The longer length scale observed in the photocurrent measurements is consistent with the previous observation that the near-field photocurrent signal I3extends further into the bulk than the scattering signal (S4) due to thermal diffusion. The field-dependent plasmonic features can also be simulated in real space using a commercial finite-element solver given the same parameters used inFIG.23A. The simulated results (FIG.24C) are in qualitative agreement with the experimental observations and suggests a wavelength of plasmon on the order of hundred nanometers and a Q factor larger than 2 at 200K.

To quantitatively reveal the Landau plasmon wavelength change on magnetic field in experiment, line cuts of s-SNOM signal are made along dash lines816inFIG.24B. The oscillating s-SNOM signal corresponding to plasmon fringes can be observed under various magnetic fields, especially the ones after subtracting Lorentz backgrounds. By fitting these plasmon fringes, wavelength of Landau plasmon can be extracted and its magnetic field dependency is shown inFIG.24D. It is shown that the Landau plasmon wavelength increases monotonically from 0.238 um at 5 T magnetic field to 0.405 um at 7 T.

The present disclosure implements the m-SNOM system configured to study infrared magneto-optics at the nanoscale. The m-SNOM system described implements methods demonstrating the generation and imaging of tunable graphene plasmons due to inter-Landau level transitions with subwavelength resolution. These plasmons are evident in m-SNOM images and have properties that are highly dependent on the applied magnetic field. The localized Landau plasmons also greatly influence the photocurrent distribution at the sample edge, leading to interesting current pathways along the sample edge.

The present disclosure implementing the m-SNOM system demonstrates the particular strength of near-field optical microscopy for resolving the magneto-plasmons and edge states in strong magnetic fields. In principle, this method is not limited to probing photo-induced quantum transitions at IR frequencies but can also be applied similarly with THz sources to address magneto-optical effects at much lower photon energies. At lower temperature, the absorption edge of the Landau plasmons can be extremely sensitive to Fermi level and scattering rate, which can be useful for studying many body physics in charge neutral graphene (e.g. Moiré modulated vF).

The m-SNOM system can be further used to investigate at least four key spatial features at tens to hundreds of nanometers simultaneously: 1) field-tuned infrared or terahertz polaritons, 2) magnetic lengths, 3) edge photocurrent, and 4) moiré lattice periodicities. Further experiments on THz near-field microscopy and THz near-field emission spectroscopy can be performed on other Dirac and Weyl semimetals, which are predicted to process many intriguing properties including tunable light confinement, nonreciprocal effect, multi-photonic bands, and polarization conversion in magnetic fields or magnetic interfaces.

The described aspects and examples of the present disclosure are intended to be illustrative rather than restrictive, and are not intended to represent every aspect or example of the present disclosure. While the fundamental novel features of the disclosure as applied to various specific aspects thereof have been shown, described and pointed out, it will also be understood that various omissions, substitutions and changes in the form and details of the devices illustrated and in their operation, may be made by those skilled in the art without departing from the spirit of the disclosure. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the disclosure. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or aspects of the disclosure may be incorporated in any other disclosed or described or suggested form or aspects as a general matter of design choice. Further, various modifications and variations can be made without departing from the spirit or scope of the disclosure as set forth in the following claims both literally and in equivalents recognized in law.