# Simultaneous Observation of the Cyclotron Resonances of Electrons and Holes in a HgTe/CdHgTe Double Quantum Well under “Optical Gate” Effect

Leonid S Bovkun, Sergey Krishtopenko, Vladimir y Aleshkin, Nikolay

Mikhailov, Sergey Dvoretsky, Frédéric Teppe, Milan Orlita, Vladimir I.

Gavrilenko, Anton V. Ikonnikov

► To cite this version:

Leonid S Bovkun, Sergey Krishtopenko, Vladimir y Aleshkin, Nikolay Mikhailov, Sergey Dvoretsky, et al.. Simultaneous Observation of the Cyclotron Resonances of Electrons and Holes in a HgTe/CdHgTe Double Quantum Well under “Optical Gate” Effect. JETP Letters, 2023, 118 (11), pp.867-874. 10.1134/S0021364023603536. hal-04724758

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# Simultaneous Observation of the Cyclotron Resonances of Electrons and Holes in a HgTe/CdHgTe Double Quantum Well under “Optical Gate” Effect

L. S. Bovkun<sup>a,b</sup>, S. S. Krishtopenko<sup>c,d</sup>, V. Ya. Aleshkin<sup>b</sup>, N. N. Mikhailov<sup>e</sup>, S. A. Dvoretsky<sup>e</sup>, F. Teppe<sup>c</sup>, M. Orlita<sup>a</sup>, V. I. Gavrilenko<sup>b</sup>, and A. V. Ikonnikov<sup>d,*</sup>

Received October 13, 2023; revised November 3, 2023; accepted November 7, 2023

Spectral studies of the photoconductivity in the temperature range of $T = 5–70$ K, as well as studies of the magneto-absorption and magnetotransport at $T = 4.2$ K, have been performed in a HgTe/CdHgTe hetero-structure with a double quantum well under an “optical gate” effect. Studies of magneto-absorption spectra under the controlled optical exposure have made it possible to observe absorption lines caused by both the cyclotron resonances of electrons and holes simultaneously. The coexistence of electrons and holes in the HgTe/CdHgTe double quantum well with a relatively large bandgap (~80 meV) indicates the appearance of a strongly inhomogeneous light-induced distribution of charge carriers in the plane of the structure. Experimental results obtained clearly demonstrate disadvantages of the control of the Fermi level positions in heterostructures with HgTe/CdHgTe quantum wells by means of the optical gate.

DOI: 10.1134/S0021364023603536

## 1. INTRODUCTION

HgTe/CdHgTe quantum wells (QWs) demonstrate an enormous variety of physical properties that stem primarily to the qualitative rearrangement of the band structure under the variation of the thickness of QWs [1–3]: from a trivial insulator through the system of two-dimensional (2D) massless Dirac fermions [4–10] to a 2D topological insulator [11–13] and further through a 2D semimetal [14–17] to a three-dimensional (3D) topological insulator [18, 19]. HgTe double quantum wells (DQWs) have an even greater variety of phase states: in addition to the states listed above, they allow the “bilayer graphene” and “double inversion” states [20]. The band gap in the former case can be varied by an electric field, and the latter system can be considered as a higher-order topological insulator [21].

Variety of topological phases, as well as the possibility of affecting the value of the band gap by the applied electric field, provides potentially wide possibility of applications of HgTe/CdHgTe DQWs in electronics and optoelectronics. The possibility of controlling the position of the Fermi level, as well as the concentration and type of charge carriers, is a key

property to use HgTe/CdHgTe DQWs in real devices. In particular, to use quantized conductivities observed in the topological insulator phase [22], the Fermi level must be located in the band gap of bulk states. The position of the Fermi level in HgTe/CdHgTe DQWs is usually controlled by fabricating electric gate structures [23–25]. However, such a fabrication is technologically complex, particularly in the case of small (≤1 µm) structures or large (≥ several millimeters) gates.

A simpler alternative method of changing the position of the Fermi level in structures with HgTe/CdHgTe QWs is based on the persistent photoconductivity effect [26–28]. This method is called the “optical gate” [29, 30] or “optical doping” [8, 31]. The optical gate effect is a light-induced change in the conductivity of the 2D system and the subsequent holding of this new state after the end of illumination. The optical gate effect in most 2D systems can lead only to an increase or a decrease in the charge carrier concentration (see, e.g., [32–37]), but the type of conductivity can also change in some systems, e.g., HgTe/CdHgTe QWs [10, 27, 38]. In particular, as found in [10], the controlled illumination of single HgTe/CdHgTe gap-

<footnote><sup>a</sup> Laboratoire National des Champs Magnétiques Intenses, CNRS-UGA-EMFL-UPS-INSA, FR-38042 Grenoble, France</footnote>

<footnote><sup>b</sup> Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia</footnote>

<footnote><sup>c</sup> Laboratoire Charles Coulomb, UMR CNRS 5221, Université de Montpellier, Montpellier, 34095 France</footnote>

<footnote><sup>d</sup> Faculty of Physics, Moscow State University, Moscow, 119991 Russia</footnote>

<footnote><sup>e</sup> Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia</footnote>

<footnote>*e-mail: antikon@physics.msu.ru</footnote>
less QWs by green light changes the type of charge carriers from holes to electrons. The “identity” of the electric and optical gates was in fact demonstrated in [10]. The illumination-induced change in the type of conductivity was also detected in the HgTe/CdHgTe DQWs with a band gap of about 80 meV [38]. However, only the “dark” state with the hole conductivity and the “illuminated” state with the electron conductivity that is due to long-term illumination were studied in [38]. The possibility of a reversible change in the type of conductivity in HgTe/CdHgTe DQWs irradiated by light with various photon energies was also demonstrated [27]. All these allow one to hope that the use of the optical gate in the structure with HgTe/CdHgTe QWs will make it possible to control the position of the Fermi level, in particular, to fix it at the charge neutrality point by varying the duration of illumination.

The aim of this work is to determine the behavior of the Fermi level under controlled optical action on structures with HgTe/CdHgTe DQWs with a relatively large band gap. We chose this sample because a similar sample had already demonstrated a change in the sign of the conductivity under the optical gate effect [38], and average values of the band gap (~80 meV) in the chosen structure should significantly exceed the scale of fluctuations of the bandgap. One of the most direct methods of studying the band structure of bulk materials and heterostructures with QWs is magneto-absorption spectroscopy, which allows for the direct reconstruction of the band structure in the case of low magnetic fields (cyclotron resonance) at various positions of the Fermi level [7, 17]. The band structure can be reconstructed by comparing theoretical calculations of transitions between Landau levels with the experimentally observed features of magneto-absorption spectra measured in quantized magnetic fields [6, 7, 15, 38–46]. Additional information on the band gap and on its temperature dependence can also be obtained from photoconductivity spectra [47, 48].

In this work, we study magneto-absorption and photoconductivity spectra, as well as transport properties in HgTe/CdHgTe DQWs under the optical gate effect. First, comparing experimental results with model calculations with an eight-band Kane Hamiltonian, we refine the widths of the layers of HgTe/CdHgTe DQW. Second, we study the magneto-absorption and the Hall effect in the HgTe/CdHgTe DQW exposed to the controlled optical illumination by blue light at low temperatures. It is shown that successive illumination results in a change from hole charge carriers to electron ones, which is manifested in both transport measurements and magneto-absorption spectra. At the same time, absorption lines caused by both the electron and hole cyclotron resonances are surprisingly observed in magneto-absorption spectra at a certain intermediate illumination. The coexistence of electrons and holes in the sample with a relatively large band gap of about 80 meV indicates the

appearance of a strongly inhomogeneous light-induced distribution of charge carriers in the plane of the sample under the optical gate effect.

## 2. METHODS

The studied structure was grown by molecular beam epitaxy (MBE) on a 400-µm-thick GaAs (013) semi-insulating substrate [49, 50]. A buffer consisting of a 30-nm ZnTe layer and a 5-µm-thick CdTe relaxed layer was grown on the substrate. The active part of the structure consisted of the 30-nm bottom CdₓHg₁₋ₓTe barrier, two HgTe QWs with the thickness *d* separated by a CdₓHg₁₋ₓTe tunnel barrier with the thickness *t*, and the 30-nm top CdₓHg₁₋ₓTe barrier. A 40-nm-thick CdTe cap layer was grown above the entire structure. The structure was not intentionally doped. The nominal growth parameters of the structure were *x* = 0.64, *d* = 4.5 nm, and *t* = 3.0 nm.

Photoconductivity spectra were studied in the temperature range of 5–70 K using a Bruker Vertex 70v Fourier-transform spectrometer. To this end, strip contacts were deposited on the edges of the 4 × 5-mm sample. We used a Globar as a radiation source and a Mylar Multilayer beamsplitter. The sample was placed in an Oxford Instruments Optistat CF helium-flow cryostat, which had polypropylene and Mylar windows and was placed in the spectrometer so that the sample was in the focus of the radiation beam. A cold black polyethylene filter was placed in front of the sample. The spectral characteristics of all used optical elements and filters allow one to record photoconductivity spectra in the range of 4–120 meV, except for an opaque region of the beamsplitter of 87–92 meV. A spectral resolution was set to 1 meV.

Magnetoabsorption spectra were recorded at Laboratoire National des Champs Magnétiques Intenses (LNCMI-G, Grenoble, France) with a Bruker 80v Fourier-transform spectrometer in static magnetic fields up 11 T and at the Moscow State University with terahertz quantum-cascade lasers under the variation of the magnetic field up to 4.5 T at a temperature of *T* = 4.2 K. In the former case, 5 × 5-mm samples were placed in a waveguide insert in the center of a superconducting solenoid in liquid helium. A light-emitting diode placed near the sample allowed the controlled illumination of the sample by blue light. A black polyethylene or ZnSe filter was placed between the insert and the Fourier-transform spectrometer. Studies were carried out in the Faraday geometry; i.e., the axis of growth of the HgTe/CdHgTe DQW was parallel to the magnetic field and the direction of propagation of radiation. We used a Globar as a radiation source and a Mylar Multilayer or KBr beamsplitter. Radiation transmitted through the sample was detected by a composite silicon bolometer. A signal from the bolometer was fed to the analog-to-digital converter of the Fourier-transform spectrometer. Spectra obtained
with a spectral resolution of 0.5 meV were normalized
to the spectrum in zero magnetic field.

Measurements at the Moscow State University
with terahertz quantum-cascade lasers with frequen-
cies of 2.27 and 3.0 THz, which were used as sources
of monochromatic radiation (pulse duration of 10–
20 µs and a repetition frequency of 19 Hz). Magne-
toabsorption spectra were also recorded in the Faraday
geometry. The sample could also be illuminated by
blue light. A Ge:Ga crystal was used as a detector.
Radiation transmitted through the sample was received
by the detector, a signal from which was amplified and
fed on a boxcar averager. The Hall effect was simulta-
neously measured, which allowed the determination of
the concentration and type of charge carriers. To this
end, point indium contacts were sealed on 4 × 5-mm
samples in the Hall geometry.

To calculate the band structure, Landau levels, and
transition matrix elements in the studied sample, we
used the eight-band Kane Hamiltonian in the axial
approximation for structures with the (013) orienta-
tion [6, 46] and took into account the built-in defor-
mation caused by the difference between the lattice
constants of the CdTe buffer, CdₓHg₁₋ₓTe barriers,
and HgTe QWs. The plane-wave expansion was used
to determine the coordinate dependences of the enve-
lopes of the function in the direction perpendicular to
the plane of QWs. The influence of the magnetic field
was taken into account by means of the Peierls substi-
tution, and the transverse part of envelope functions
was expanded in the wavefunctions of the free electron
in a uniform magnetic field. To numerically calculate
envelope functions and the corresponding energies of
electrons, the structure was considered as a superlat-
tice of weakly coupled quantum wells with the period
such that the interaction between them hardly affected
the energy spectrum of the system. To describe the
effect of the temperature on the band structure of the
HgTe/CdHgTe DQW, the temperature dependences
of the band gap of HgTe and CdHgTe, valence band
offset at the heterointerface, lattice constants of the
layers, and elastic constants were taken into account in
the eight-band Kane Hamiltonian. The calculation
method was described in more detail in [3]. The
dependence of the semiclassical cyclotron mass on the
charge carrier concentration was determined from the
dispersion relation of charge carriers in a particular
band.

3. RESULTS AND DISCUSSION

3.1. Band Structure Parameters

According to the calculations reported in [20], the
studied structure should have a normal band structure
(energies of all electron subbands are greater than any
hole subband). This is also confirmed by our experi-
mental studies. Figure 1a presents photoconductivity
spectra measured at various temperatures. It is seen

that the long wavelength cut-off of the photoconduc-
tivity is blueshifted with increasing temperature. This
certainly indicates that the studied structure has the
normal band structure [48]. Furthermore, these
spectra allow one to estimate the band gap E_g as
(76 ± 3) meV at low temperatures. This value is close
to 77 meV presented in [38] for this structure and is
significantly larger than a value of 31 meV determined
from calculations of the band structure with nominal
growth parameters. All these show that the real
parameters of the DQW layers noticeably differ from
the growth parameters determined by ellipsometry.

Magneto-optical studies also confirmed the made
assumption. Figure 1b shows the magneto-absorption
false-color map obtained with the maximum illum-
nation by blue light (Fermi level in the conduction
band). Figure 1c presents the magneto-absorption
spectrum recorded in a magnetic field of 6.75 T. Two
main lines α and β₁ are primarily seen in the spectra.
The former line corresponds to an intraband transi-
tion, and its extrapolation to zero magnetic field gives
zero energy. The latter line corresponds to interband
(one or several) transitions, and its extrapolation to
zero magnetic field provides a nonzero energy (see,
e.g., [42, 48]), which makes it possible to estimate the
band gap as (76 ± 2) meV, coinciding with the value
estimated from photoconductivity data.

As mentioned above, the calculations of the band
structure using the nominal parameters of the layers
give a band gap of 31 meV; consequently, the adequate
theoretical description of observed magneto-absorp-
tion spectra requires the correction of the parameters
of the DQW used in calculations. A similar correction
was also used in [38, 41], where magneto-absorption
was studied in HgTe DQW grown in the same MBE
setup. Since our sample was grown in the same growth
cycle as the structures with the HgTe/CdHgTe DQW
studied in [41], when correcting the parameters of
DQWs, we also reduced the width of the QWs *d* and
the tunnel barrier *t*, holding the relative content of Cd
in barriers. Nevertheless, to achieve good agreement
between calculations and experimental data, it was
also necessary to enable a nonzero content of Cd *y* in
layers of Hg₁₋ₓCdₓTe QWs. The best agreement with
experimental data was achieved at the parameters
*x* = 0.64, *y* = 0.02, *d* = 4.0 nm, and *t* = 2.8 nm (see
Fig. 1b). At these parameters of the sample, the line α
in magneto-absorption spectra corresponds to the
intraband 0 → 1 transition in the conduction band,
and the line β₁ corresponds to the interband −2 → −1
and −1 → 0 transitions (see Fig. 1d). Moreover, theo-
retical calculations with these parameters well repro-
duce not only the behavior of other lines in magneto-
absorption spectra under the variation of the magnetic
field (see Fig. 1b) but also the temperature depen-
dence of the cut-off of the photoconductivity (see the
inset of Fig. 1a).
<figure><img src="image_2.png" /></figure>

**Fig. 1.** (Color online) (a) Photoconductivity spectra of the HgTe/CdHgTe DQW at various temperatures. The gray band is the opaque region of the used Mylar Multilayer beamsplitter. The inset shows (squares with error bars) the temperature dependence of the cut-off of the photoconductivity and the calculated temperature dependence of the band gap. (b) Magneto-absorption false-color map and (c) the magneto-absorption spectrum of the HgTe/CdHgTe DQW. Darker regions correspond to stronger absorption. Circles are data from [38]. Lines are transitions between Landau levels calculated with corrected parameters. The map and spectrum are composed from two sets of measurements with various filters and beamsplitters: the black polyethylene filter and the Mylar Multilayer beamsplitter were used in measurements for energies below 60 meV, and the ZnSe filter and the KBr beamsplitter were applied for energies above 60 meV. The vertical solid straight line in panel (b) marks a magnetic field of 6.75 T, for which the spectrum is shown in panel (c). (d) Landau levels that are calculated with the corrected parameters of the layers of the DQW. Levels enumerated according to [6, 39, 46]. Arrows mark observed transitions in notation from [39, 41, 42, 46]). The upper −2 Landau level of the valence band is doubly degenerate due to the symmetry of the double quantum well.

## 3.2. Magneto-Absorption at Various Durations of Optical Illumination

After the more accurate determination of the real parameters of the sample layers, it was possible to examine subtle effects, in particular, the transformation of magneto-absorption lines during the transition from hole to electronic type of conductivity when using the optical gate. Figure 2 presents magneto-absorption spectra obtained under dark conditions and after the controlled illumination of samples by blue light. As seen in Fig. 2a, magneto-absorption spectra recorded under dark conditions exhibit three main lines, two of them below 30 meV ($\alpha^*$ and $\delta^-$) and one above 100 meV ($\beta_1$). As mentioned above, the last line corresponds to the interband $-2 \rightarrow -1$ and $-1 \rightarrow 0$ transitions (see Fig. 1d). Calculations of tran-

sition matrix elements show that the leading contribution comes from the $-2 \rightarrow -1$ transition. Interband transitions are much more sensitive than intraband transitions to fluctuations of the parameters of the structures (and to related fluctuations of the band-gap). As a result, the width of the line $\beta_1$ is noticeably larger than the widths of lines $\alpha, \alpha^*, \text{and } \delta^-$ (see Figs. 1c and 2). The last two lines are obviously due to intraband transitions because their energy in the entire magnetic field range does not exceed the bandgap (76 meV).

Measurements of the Hall effect show that the structure under dark conditions has the hole conductivity (see line 1 in Fig. 3a). In addition, it is seen in Fig. 2a that a magnetic field of about 5–6 T, above which the line $\beta_1$ appears, coincides with the magnetic
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** (Color online) Magneto-absorption false-color maps of the HgTe/CdHgTe double quantum well obtained (a) under dark conditions, (b) after the short-term (<1 s) illumination by blue light, and (c) after the long-term (>10 s) illumination by blue light. Darker regions correspond to stronger absorption. Color lines correspond to the calculated transitions between Landau levels. The black polyethylene filter and the Mylar Multilayer beamsplitter were used in the measurements of the spectra. Empty circles in panel (b) mark the positions of magneto-absorption lines measured by quantum-cascade lasers. Panel (c) partially repeats Fig. 1b.</figcaption></figure>

field in which the intensities of the lines $\alpha^*$ and $\delta^-$ drop significantly. Since the leading contribution to the line $\beta_1$ comes from the $-2 \rightarrow -1$ transition, the line $\beta_1$ can be attributed to the appearance of electrons on one of the $-2$ levels (see Fig. 1d), which corresponds to the filling factor $v = 2$ (the corresponding hole concentration is $\sim 2.7 \times 10^{11} \text{ cm}^{-2}$). In this case, the attenuation of the lines $\alpha^*$ and $\delta^-$ will be due to the complete filling of the top 1 level in the valence band with electrons (see Fig. 1d). Therefore, the lines $\alpha^*$ and $\delta^-$ can be attributed to the $0 \rightarrow 1$ and $2 \rightarrow 1$ intraband transitions in the valence band, respectively (see Fig. 1d). Some discrepancy between the positions of the line $\alpha^*$ and the $0 \rightarrow 1$ transition, as well as an incomplete disappearance of the lines $\alpha^*$ and $\delta^-$ in fields above 5–6 T, can be explained by the “mixing” of closely located Landau levels due to the symmetry lowering [42, 45], which was disregarded in this work. The charge carrier concentrations obtained from transport measurements slightly differ from those at which the filling factors of Landau levels discussed above are reached. For the dark case (see line 1 in Fig. 3a), the hole concentration determined from the slope of the Hall curve is as low as $0.8 \times 10^{11} \text{ cm}^{-2}$. This situation is most probably due to the pinning of the Fermi level at the side maximum of the valence band, where holes do not contribute to the quantum Hall effect [25] and, as a result, the concentration in transport measurements in low magnetic fields is lower.

Optical illumination qualitatively changes magneto-absorption spectra due to the persistent photoconductivity effect, which is pronounced in HgTe/CdHgTe DQWs [27]. In particular, after the

long-term (>10 s) illumination by blue light (see Fig. 2c), the lines $\alpha^*$ and $\delta^-$ are replaced by the single intense line $\alpha$ whose position is in excellent agreement with the $0 \rightarrow 1$ transition in the conduction band, which corresponds to electron cyclotron resonance in the quantum limit. In low magnetic fields <2 T, the position of this line linearly depends on the magnetic field and corresponds to the “classical” electron cyclotron resonance line for a cyclotron mass of $0.0127m_0$. From the calculated dependence of the cyclotron mass on the carrier concentration in the conduction band (see the inset of Fig. 3b), the electron concentration can be estimated as $0.45 \times 10^{11} \text{ cm}^{-2}$. This value is close to the value obtained from the concentration estimated by the position of the plateau for the $v = 1$ quantum Hall effect (see line 3 in Fig. 3a). The observation of the electron cyclotron resonance lines after optical illumination is in good agreement with transport measurements (see Fig. 3a), which confirm the illumination-induced change in the type of conductivity (the signs of the Hall effect for lines 1 and 3 in Fig. 3a are opposite).

Of the most interest are magneto-absorption spectra in the HgTe/CdHgTe DQW obtained after the short-term (<1 s) illumination by blue light (see Fig. 2c). The magneto-absorption map in this case qualitatively is a superposition of maps obtained in the dark and maximum illumination cases. Indeed, as seen in Fig. 2b, magneto-absorption spectra simultaneously include the lines $\alpha^*$ and $\delta^-$, which is due to the hole cyclotron resonance, and the electron cyclotron resonance line $\alpha$. Electron and hole cyclotron resonance lines are also simultaneously observed in magneto-absorption spectra obtained with quantum-cas-
under the optical gate effect depending on the optical illumination time is currently absent. However, our experimental results have already demonstrated demerits of the optical gate control of the position of the Fermi level in heterostructures with HgTe/CdHgTe QWs.

## ACKNOWLEDGMENTS

The authors are grateful to Laboratoire National des Champs Magnétiques Intenses (LNCMI-G), member of the European Magnetic Field Laboratory for support.

## FUNDING

This work was supported by the Russian Science Foundation (project no. 22-22-00382).

## CONFLICT OF INTEREST

The authors of this work declare that they have no conflicts of interest.

## OPEN ACCESS

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