Title: Atomic-scale Spectroscopic Structure of Tunable Flat Bands, Magnetic Defects and Heterointerfaces in Two-dimensional Systems
Description: Graphene, a single atom thick hexagonally bonded sheet of carbon atoms, was first isolated in 2004 opening a whole new field in condensed matter research and material engineering. Graphene has hosted a whole array of novel physics phenomena as its carriers move at near the speed of light governed by the Dirac Hamiltonian, it has few scattering sites, it is easily gate-tunable, and hosts exciting 2D physics amongst many other properties. Graphene was only the tip of the iceberg in 2D research as researchers have since identified a whole family of materials with similar layered atomic structures allowing isolation into several atom thick monolayers. Monolayer material properties range from metals to semiconductors, superconductors, magnets and most other properties found in 3D materials. Naturally, this has led to making fully 2D heterostructures to study exciting physics and explore applications such as 2D transistors. It has recently been found that not only can you stack these materials at will but you can also tune their properties with an inter-layer twist between layers which at precise twist angles yields on-demand electronic correlations that can be easily tuned with experimental knobs leading to novel correlated phases.

The pioneering techniques towards understanding each 2D material and heterostructures thereof have usually been with transport and optics. These techniques are inherently bulk macroscopic measurements which do not give insights into the nanoscale properties such as atomic-scale features or the nanoscale heterostructure properties that govern the systems. Atomic-scale structural and electronic insights are crucial towards understanding each system and providing proper guidelines for comprehensive theoretical understandings. In this thesis, we study the atomic-scale structural and electronic properties of various 2D systems using ultra-high vacuum (UHV) scanning tunneling microscopy and spectroscopy (STM/STS), a technique which utilizes electron tunneling with an atomically sharp tip to visualize atomic structure and low-energy spectroscopic properties. We focus on three major types of systems: twisted graphene heterostructures (magic angle twisted bilayer graphene and small angle double bilayer graphene), bulk and monolayer semiconducting transition metal dichalcogenides (TMDs), and 2D heterointerfaces (TMD - metal and graphene p-n junctions).

We establish a number of state of the art methods to study these 2D systems in their cleanest, transport-experiment-like forms using surface probes like STM/STS including robust, clean, reliable contact methods and procedures towards studying micronscale exfoliated 2D samples atop hexagonal boron nitride (hBN) as well as photo-assisted STM towards studying semiconducting TMDs and other poorly conducting materials at low temperatures (13.3 Kelvin). We begin with one of the most currently mainstream topics of twisted bilayer graphene (tBG) where, near the magic angle of 1.1◦ the first correlated insulating and superconducting states in graphene were observed. A lack of detailed understanding of the electronic spectrum and the atomic-scale influence of the moir´e pattern had precluded a coherent theoretical understanding of the correlated states up til our work. We establish novel, robust methods to measure these micron-scale samples with a surface scanning probe technique. We directly map the atomic-scale structural and electronic properties of tBG near the magic angle using scanning tunneling microscopy and spectroscopy (STM/STS).

Contrary to previous understandings (which predicted two flat bands with a several meV separation in the system), we observe two distinct van Hove singularities (vHs) in the local density of states (LDOS) around the magic angle, with a doping-dependent separation of 40-57 meV. We find that the vHs separation decreases through the magic angle with a lowest measured value of 7-13 meV at 0.79◦ . When doped near half moir´e band filling where the correlated insulating state emerges, a correlation-induced gap splits the conduction vHs with a maximum size of 6.5 meV at 1.15◦ , dropping to 4 meV at 0.79◦ . We find that more crucial to the magic angle than the vHs separation is that the ratio of the Coulomb interaction (U) to the bandwidth (t) of each individual vHs is maximized (as opposed to the proximity of the individual vHs’s), indicating that indeed electronic correlations are very important and suggesting a Cooper-like pairing mechanism based on electron-electron interactions. This establishes that magic angle tBG is to be understood in a single vHs picture where the band-width of the vHs is minimized.

Spectroscopy maps show that three-fold (C3) rotational symmetry of the LDOS is broken in magic angle tBG, with an anisotropy that is strongest near the Fermi level, and is highly enhanced when the doping is in the vicinity of the correlated gap, indicating the presence of a strong electronic nematic susceptibility or even nematic order in tBG in regions of the phase diagram where superconductivity is observed. We next turn to twisted double bilayer graphene (tDBG), a system that is similar to tBG in phenomenology but turns out to be quite different. Correlated insulating and superconducting states were also found using transport in tDBG at a magic angle of 1.2-1.3◦ and ABC rhombohedral trilayer graphene aligned to hBN (ABC-tLG/hBN) with some stark differences such as displacement field tunable correlated states. We perform the first atomic-scale structural and electronic studies of small-angle tDBG as well as ABCA four layer rhombohedral stacked graphene and compare the findings to tBG.

We first find that the moir´e pattern formed by tDBG is fundamentally different from tBG in that instead of hosting AB/BA Bernal stacking regions, it hosts BABA/ABCA (Bernal/rhombohedral) stacking domains. While we find this for small angle tDBG, these structural arguments will apply at all angles including the magic angle indicating that the flat bands and electron densities in tDBG are likely dominated at the ABCA sites. We use small angle tDBG to study large domains of four-layer ABCA graphene, revealing its displacement field dependent low energy spectroscopic structure and the flat band structure that comes with the four layer rhombohedral stacking which hosts the flattest band measured in any system of a 3-5 meV half-width. Furthermore, we measure the emergence of a 9.5 meV correlated gap in ABCA four-layer graphene at neutrality indicating that even without a hBN moir´e, ABCA graphene will likely host correlated states purely due to a flat band. These correlated states could be insulating or even superconducting in nature and the study thereof could provide crucial insight into whether superconductivity is related to Mott insulator physics as is suggested in the cuprates.

When coupled to an hBN moir´e, these correlated states may be even stronger than that of magic angle tBG, magic angle tDBG and (most cer- tainly) ABC-tLG/hBN. Finally, we show that at Bernal - four-layer rhombohedral domain boundaries, there exists a topologically protected helical surface edge state. We next turn to the semiconducting TMDs. We find that semiconducting MoTe2 and MoSe2 have long range magnetic ordering as measured by muon spin resonance and SQUID at critical temperatures of 40 K and 100 K respectively. Using atomic-resolution STM/STS, we find that the semiconducting TMDs have a variety of intrinsic defects, one of which (a molybdenum substitution for a chalcogen, Mosub) we postulate using DFT is the cause of the long-range magnetism in the semiconducting TMDs which are not expected to host magnetism in their pristine structures. This finding establishes these semiconducting TMDs as magnetically ordered and adds them to the family of potential dilute magnetic semiconductor materials (the uniform robust fabrication of which has been sought-after for decades) which could have applications in spintronics.

We then perform 13.3 Kelvin measurements (for the first time in these materials to our knowledge) on the same crystals using photoassisted STM, a technique that we establish to enable this low temperature measurement. The photo-assisted STM measurements reveal that not only are these defects magnetic but they host localized structural distortions which cover a large areas of the crystal surfaces. We find that these structural distortions are localized charge density waves due to a very high amount of localized doping that comes from the defects, putting the materials into a locally metallic regime and causing a phonon instability (found by phonon DFT). This finding of localized charge density waves in these high-quality semiconducting 2D materials is highly atypical for a semiconductor system and could have implications towards all techniques. The charge density waves could also be related to the measured magnetism as they have a much larger area of coverage in MoSe2 as opposed to MoTe2 which could be related to the critical temperature difference.

We finally turn to two types of heterointerfaces, the first being metal-monolayer MoS2 junctions. We present measurements of the atomic-scale energy band diagram of junctions between various metals and heavily doped monolayer MoS2 using STM/STS. Our measurements reveal that the electronic properties of these junctions, at the fundamental limit of a minimized Schottky barrier, are dominated by 2D metal induced gap states (MIGS). These MIGS are characterized by a spatially growing measured gap in the local density of states (LDOS) of the MoS2 within 2 nm of the metal-semiconductor interface. Their decay lengths extend from a minimum of about 0.55 nm near mid gap to as long as 2 nm near the band edges and are nearly identical for Au, Pd and graphite contacts, indicating that this is a universal property of the monolayer 2D semiconductor. Our findings indicate that even in heavily doped semiconductors, the presence of MIGS sets the ultimate limit for electrical contact. These findings are generally applicable to any 2D semiconductor.

We next look at another type of heterointerface, this time purely electronic in nature, graphene p-n junctions. Graphene p-n junctions should host interesting electron-optical properties such as electron collimation and Veselago lensing. While vague signatures of these have been observed, robust, definitive control of these properties are still lacking. We present the first atomic-scale characterization of state-of-the-art graphene p-n junctions using STM/STS revealing their current imperfections including significant electron-hole asymmetry, nonlinearity, roughness and intrinsic doping. We model the implications thereof and show that these imperfections strongly hinder electron-optical applications. Finally we explore the origin of these imperfections and potential avenues towards realizing better graphene p-n junction devices that may host much improved electron-optical properties.