Session F11: Local Characterization of Moirés in Transition Metal Dichalcogenides

Imaging twisted MoTe2 with scanning tunneling microscopy: Part 1

Twisted bilayer molybdenum ditelluride (tMoTe₂) has recently been found to host a variety of strongly correlated and topological states of matter, most notably the fractional quantum anomalous Hall effect arising at partial fillings of the moiré flat band. These states have been characterized using a combination of optical spectroscopy and electrical transport measurements, which necessitate averaging over micrometer-scale regions of samples. Critically, the microscopic mechanisms underlying these novel phases have yet to be directly explored. Although scanning tunneling microscopy and spectroscopy (STM/S) can serve as powerful tools for atomic-scale studies of tMoTe₂, fabricating STM/S-compatible samples presents substantial challenges owing to the high environmental sensitivity of MoTe₂ and difficulties in establishing ohmic contacts at cryogenic temperatures. Here, we summarize our efforts towards creating ultra-clean and gate-tunable tMoTe₂ samples for STM/S characterization. To prevent degradation of the exfoliated MoTe₂ crystals, we fabricate our samples in an argon-filled glove box and use a custom-built transfer suitcase to move the samples directly into the high-vacuum load lock of the STM. Using this technique, we study generations of device designs which steadily iterate towards functional electrical contacts at cryogenic temperatures. We will overview the quality of devices in each generation, leading into a discussion of the details of the atomic-scale electronic properties of tMoTe₂ in the second part of this presentation.   

Imaging twisted MoTe2 with scanning tunneling microscopy: Part 2

Twisted molybdenum ditelluride (tMoTe₂) has recently emerged as an exciting new platform to study strongly correlated topological states of matter. The moiré superlattice that arises from twisting two MoTe₂ monolayers generates flat bands that act as a platform for the fractional quantum anomalous Hall effect. The nature of the correlated ground states and their topology is intimately tied to the moiré lattice. Furthermore, this lattice can be tuned by applying a perpendicular electric field which modifies the layer polarization of charges. Though these effects have been studied macroscopically through electrical transport and optical spectroscopy, they have not yet been investigated on the atomic scale. This is in part due to challenges in fabricating vdW heterostructures with a pristine exposed tMoTe₂ surface, which we will discuss in the first part of this presentation. Here, we present direct visualization of the flat bands in tMoTe₂ with spatially resolved scanning tunneling microscopy and spectroscopy (STM/S) measurements acquired at different energies and band fillings. These measurements elucidate how the low energy states localize on the moiré scale. Our results shed light on the nature of the flat bands that underlie interaction-driven phenomena in tMoTe2 and will inform future studies of its integer and fractional quantum Hall states.   

High-resolution potential imaging using the Atomic SET - Part I

Visualizing electronic states on local scales is becoming an essential tool to understand new quantum states of matter. One central property that can be visualized is electrostatic potential. Its measurement enables local imaging of a variety of key thermodynamic quantities including electronic compressibility, magnetization, and entropy. To date, the best scanning detector of electrostatic potential is the scanning single electron transistor (SET). Its ability to measure on microscopic scales has allowed it to evade disorder prevalent in many quantum materials and unearth exciting new phenomena. However, existing scanning SETs have a critical limitation – with a spatial resolution of ~100 nm, they cannot access the growing list of charge-ordered quantum states that appear on ~10 nm scales, e.g. in moiré lattices. Here, we will showcase a novel scanning probe that improves SET spatial resolution by two orders of magnitude, down to 1 nm. Based on the quantum twisting microscope (QTM), it uses a single atomic defect embedded in a pristine van der Waals interface as the smallest scanning detector of electrostatic potentials. In Part I, I will present the operating principle of this novel probe and how its different modalities expand our toolset for understanding quantum materials.   

High-resolution potential imaging using the Atomic SET - Part II

In part II of this presentation, I will describe our recent ultra-high resolution scanning thermodynamic measurements performed using the Atomic single electron transistor (SET). Many of the electronic systems at the forefront of condensed matter physics have interesting physical phenomena that occur over few nanometer length scales. Examples include edge states in quantum Hall and topological systems, as well as the ordered moiré lattices formed by twisting two van der Waals (vdW) layers with respect to each other or by aligning two vdW layers with a slight lattice mismatch. In all of these systems, electronic charge orders in real space on a characteristic length scale of about 10 nanometers. Visualizing the electrostatic and thermodynamic properties of these states with a spatial resolution better than their characteristic scales provides us with a window into some of their central properties which were so far out of reach. The Atomic SET, a nanoscale charge sensor built upon the quantum twisting microscope (QTM) geometry, is an ideal tool to examine these questions in detail. In this talk, I will present our latest scanning Atomic SET experiments that probe these vdW systems with ultra-high resolution electrostatic imaging.   

Local Characterization of Correlated States in an MoTe2 Twisted Bilayer Moiré Superlattice

Moiré superlattices in transition metal dichalcogenides (TMDs) host a variety of exotic quantum phenomena, such as generalized Wigner crystals, the integer quantum anomalous Hall (QAH) effect, and fractional Chern insulators (FCIs). These topological and correlated phenomena are often accompanied by electronic states having novel signatures at the moiré length-scale that are difficult to probe with conventional optical or transport methods. We have used scanning tunneling microscopy/spectroscopy (STM/S) to examine the local electronic states in gate-tunable twisted MoTe₂ (t-MoTe₂) devices. Our samples include a Si/SiO₂ back gate under the t-MoTe₂ and a monolayer graphene/ hBN sensing layer above the t-MoTe₂ that allow us to separately control the carrier density and electric field in the t-MoTe₂ [1] and to detect the formation of insulating states in t-MoTe₂ through charging/discharging events in the graphene sensing layer [2]. We have performed spectroscopic characterization of t-MoTe₂ at different filling levels and electric fields to locally probe novel correlated and topological states observed previously in optical and transport measurements. 

[1]        H. Li et al., Nature 597, 650 (2021).

[2]        H. Li et al., ArXiv: 2209.12830 (2022).   

Large angle commensurate moiré crystals in twisted bilayer WSe2

Superlattice created by homobilayers at larger twist angles (e.g. 21.8 and 38.2) has unveiled intriguing properties such as sharp conductivity peaks and enhanced excitonic peaks ^[1–3]. These large-angle commensurate moiré crystals, with periodicity of order of 1 nm or less, offer a distinguished platform for investigating Umklapp scatterings and interlayer coherent couplings. Using valley-resolved tunneling spectroscopy^[4] in combination with first-principle calculations, we present direct evidence of robust interlayer and intralayer interactions in large-angle twisted bilayer WSe₂ which reasonably explains the transport phenomena observed in this system. This study shows intricate electronic configurations of large angle commensurate WSe₂, close to the VBM, positioning them as promising candidates for gated, precision-tuned optical and transport studies.

References:

[1] Koren, E. et al. Coherent commensurate electronic states at the interface between misoriented graphene layers. Nat. Nanotechnol. 11, 752–757 (2016).

[2] Zhang, L. et al. Twist-angle dependence of moiré excitons in WS2/MoSe2 heterobilayers. Nat. Commun. 11, 5888 (2020).

[3] Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science 361, 690–693 (2018).

[4] Zhang, C. et al. Probing Critical Point Energies of Transition Metal Dichalcogenides: Surprising Indirect Gap of Single Layer WSe ₂. Nano Lett. 15, 6494–6500 (2015).

 

Influence of atomic relaxations on the moiré flat band wavefunctions in antiparallel twisted bilayer WS2

Twisting bilayers of transition metal dichalcogenides (TMDs) gives rise to a periodic moiré potential resulting in flat electronic bands with localized wavefunctions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image bilayer WS₂ marginally twisted off of antiparallel alignment. Room temperature scanning tunneling spectroscopy reveals the presence of localized electronic states in the vicinity of the valence band onset. However, the experimentally observed electronic structure was found not to agree with first principles density-functional theory calculations, in particular differing on the real-space location of the valence band onset wavefunctions, which are predicted to correspond to a flat band. Agreement with theory is recovered when the calculations are carried out on bilayers in which the atomic displacements from the unrelaxed positions have been reduced, reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.   

Visualizing structure of correlated ground states using collective charge modes

The variety of correlated phenomena in moiré systems is incredibly rich, spanning effects such as superconductivity, a generalized form of ferromagnetism, or even charge fractionalization. This wide range of quantum phenomena is partly enabled by the large number of internal degrees of freedom in these systems, such as the valley and spin degrees of freedom, which interplay decides the precise nature of the ground state. Identifying the microscopic nature of the correlated states in the moiré systems is, however, challenging, as it relies on interpreting transport behavior or scanning-tunneling microscopy measurements. In this talk, we will demonstrate how the real-space structure of collective charge oscillations of the correlated orders can directly encode information about the structure of the correlated state, focusing in particular on the problem of generalized Wigner crystals in moiré TMDs. This discussion builds upon our earlier result that the presence of a generalized Wigner crystal modifies the plasmon spectrum of the system, giving rise to new collective modes. Our analysis focuses on scanning near-field optical microscopy technique (SNOM), fundamentally a charge-sensing-based method, and introduces a regime under which SNOM can operate as a probe of the spin degree of freedom.   

Magnetic imaging of integer and fractional Chern insulators in tMoTe2

Fractional Chern insulators[1-7] are topologically ordered electronic ground states that may occur at partial filling of a lattice band when time reversal symmetry is broken. Crucially, because they occur in lattice bands rather than Landau levels in case of Fractional Quantum Hall Effect, the energy scale of the Coulomb interaction is set by the lattice spacing rather than the magnetic length, potentially enabling higher energy scales. Here, we use nanoSQUID microscopy to measure the local magnetization of tMoTe₂ as a function of the gate-tuned density and electronic displacement field. We see signatures of robust gapped states with large edge state orbital magnetization at fillings -1 and -⅔, consistent with integer and fractional Chern insulators at these fillings. Samples show a high degree of disorder on the sub-micron scale, likely associated with misalignment of the rotationally faulted layers. We use our local probe to measure the thermodynamic energy locally, revealing significantly larger gap sizes compared to those obtained through optical and transport experiments which average over larger spatial areas.

[1] Spanton, E. M. et al. Science 360, 62–66 (2018).

[2] Xie, Y., Pierce, A.T., Park, J.M. et al. Nature 600, 439–443 (2021).

[3] Cai, J., Anderson, E et al. Nature 1–3 (2023).

[4] Zeng, Y., Xia, Z. et al. Nature 622, 69–73 (2023).

[5]  Park, H., Cai, J., Anderson, E. et al. Nature 622, 74–79 (2023).

[6] Xu, F. et al. Phys. Rev. X 13, 031037 (2023).

[7] Lu, Z. et al. arXiv:2309.17436 (2023).   

Chemical potential evolution of a doped Mott insulator in a semiconductor moiré lattice

Intriguing correlated electronic phases arise when electron or hole-like carriers are doped to a Mott insulator, an interaction-driven insulating phase that occurs at half-filling of an electronic band. The emergence of semiconductor moiré materials opens promising new avenues for exploring doped Mott-Hubbard systems, as the doping density of these two-dimensional materials can be precisely controlled through electrostatic gating. In this talk, I will describe direct chemical potential measurements of a prototypical moiré lattice system that realizes a Mott insulating phase at moiré filling factor ν = -1. Using a scanning single-electron transistor, we acquire local information on the chemical potential evolution across the Mott gap as a function of doping, as well as how the gap size depends on experimental tuning parameters such as magnetic field. I will discuss how these thermodynamic measurements inform our understanding of the doped Mott insulators in semiconductor moiré systems.   

Twisted WSe2 as a Candidate Chern Insulator

TMD twisted homobilayers have been proposed to be an ideal platform for studying strong correlation phenomena, as exemplified by the recent discovery of fractional quantum anomalous Hall effect (FQAHE) in twisted MoTe₂^{1, 2}. The K valley position, which needs to be at the valence band maximum, and the layer pseudospin configuration, which needs to include opposite layer polarizations at different points within the moiré unit cell, are the key ingredients needed to support FQAHE states.  The layer pseudospin texture of K valley carriers underlies the moiré pseudomagnetic field (real-space Berry curvature) for realizing the Kane-Mele/Haldane model³.

 

Here we report on experimental evidence that twisted WSe₂ bilayers might be another good candidate. Our constant height scanning tunneling spectroscopies (CHSTS) reveal the moiré potential modulation for G-valley. Using constant current STS, we map out the electronic state of the K-valley within the moiré superlattice revealing that the K-valley states are at the VBM. In addition, K-valley STS mapping reveals opposite polarizations of the wavefunction between the MX and XM sites, establishing the theoretically predicted pseudospin texture.

[1] Park, H.et al., Nature 622, 74–79 (2023).

[2] Nicolás Morales-Durán et al. arXiv:2308.03143

[3] Yu et. al., National Science Review 7, 1, 12–20 (2020)