Session D57: Twisted 2D Heterostructures: Beyond Graphene

Stacking Dependance of optical properties in TMD van der Waal Heterostructure

In our study, we fabricated 3R- and 2H- stacked hBN/WSe₂-WS₂/hBN vdWH and observed an intriguing strong raman quenching behavior on out of plane vibration mode (A_1g) of WSe₂ and significant modulation of out-of-plane vibration mode of WS₂ in the vdWH when excited with most commonly used 532nm CW laser at room temperature. Moreover, we also observed the strong stacking dependance of the ILE emission where the ILE intensity in 2H stacked vdWH is in general 2x or more than ILE in 3R-HS at room temperature and remains the same behavior down to 20K.

We found those results only occur when WSe₂ is in strong interaction with WS₂ in the stacking geometry really close to 3R stacking (0 degree). This WSe₂ A_1g raman mode diminishes from vdWH while all the raman modes from adjacent layer (WS₂) is still in present at room temperature in the vdWH.  Such strong stacking dependance raman behavior has not been reported and this result highly suggesting the strong raman modulation is caused by the strong interaction between WSe₂ and WS₂ in 3R stacking. Excitation energy dependance raman at room temperature reveals this strong raman quenching could possibly due to raman resonance effect and tensile strain in the system.  As similar raman modulation effect by excitation energy could also be found in WSe₂ 3R- vs 2H- homobilayer.

Continuum model for iron-based superlattices

We derive a BM-like continuum model for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (1) a single monolayer experiencing an external periodic potential, and (2) twisted bilayers with long-range Moire tunneling. A symmetry derivation for the inter-layer Moire tunnelling is provided for both the $\Gamma$ and $M$ high-symmetry points. We show the possibility for Moire bands with non-zero topological quantum numbers without breaking time-reversal symmetry.   

Triangular lattice Hubbard model physics at intermediate temperatures

Moire systems offer an exciting playground to study many-body effects of strongly correlated electrons in regimes that are not easily accessible in conventional material settings. Motivated by a recent experiment on $\text{WSe}_2/\text{WS}_2$ Moire bilayers [Y. Tang et al., Nature 579, 353–358 (2020)], which realizes a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice in the regime $t \ll U$ for intermediate temperatures $t < T < U$. Using finite temperature Lanczos calculations, we quantitatively recover the observed trends in the reported Curie-Weiss temperature $\Theta_c$ at various charge densities using the reported value of interaction strength $U/t=20$. In particular, we focus on the large increase of $|\Theta_c|$ on doping away from the half-filled antiferromagnet, with a sign change above half-filling, which signals the appearance of ferromagnetism. Remnants of the underlying zero temperature phase transition, which we explore with ground state DMRG, appear as crossovers at intermediate temperature.

    

Quantum Criticality in Twisted Transition Metal Dichalcogenides

Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behavior that defies the Landau Fermi paradigm. In moiré heterostructures, gate-tunable insulating phases driven by electronic correlations have been recently discovered. In this talk, we use transport measurements to characterize metal–insulator transitions (MITs) in twisted WSe₂ near half filling of the first moiré subband. We find that the MIT as a function of both density and displacement field is continuous. At the metal–insulator boundary, the resistivity displays strange metal behavior at low temperatures, with dissipation comparable to that at the Planckian limit. Further into the metallic phase, Fermi liquid behavior is recovered at low temperature, and this evolves into a quantum critical fan at intermediate temperatures, before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe₂ as a new platform to study doping and bandwidth-controlled metal–insulator quantum phase transitions on the triangular lattice. We also present additional magnetoresistance data to complete the phase diagram.   

Nanoscale Lattice Dynamics in Hexagonal Boron Nitride Moiré Superlattices

Twisted two-dimensional van der Waals (vdW) heterostructures have unlocked a new means for manipulating the properties of quantum materials.  The resulting mesoscopic moiré superlattices are accessible to a wide variety of scanning probes.  To date, spatially-resolved techniques have prioritized electronic structure visualization, with lattice response experiments only in their infancy.  Here, we therefore investigate lattice dynamics in twisted layers of hexagonal boron nitride (hBN), formed by a minute twist angle between two hBN monolayers assembled on a graphite substrate.  Nano-infrared (nano-IR) spectroscopy reveals systematic variations of the in-plane optical phonon frequencies amongst the triangular domains and domain walls in the hBN moiré superlattices.  Our first-principles calculations unveil a local and stacking-dependent interaction with the underlying graphite, prompting symmetry-breaking between the otherwise identical neighboring moiré domains of twisted hBN.   

SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers

We propose moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayer consists of two separate moiré superlattice layers coupled through the inter-layer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term K∼t3U2, we find SU(4) symmetric crystallized phase and an SU(4)1 chiral spin liquid (CSL) at the balanced filling. We also predict two different exciton supersolid phases with inter-layer coherence at imbalanced filling under displacement field. Especially, the system can simulate an SU(2) Bose-Einstein-condensation (BEC) by injecting inter-layer excitons into the magnetically ordered Mott insulator at the layer polarized limit. Smoking gun evidences of these phases can be obtained by measuring the pseudo-spin transport in the counter-flow channel.   

Thickness and twist angle tunable moiré excitons in InSe/GaSe heterostructures

Moiré quantum systems have emerged as a materials framework displaying highly tunable electronic, optical and topological properties with an exquisite level of control. To date, the moiré physics has been constrained mainly by two factors i) the dimensionality, defined by the stacking of monolayers, and ii) the twist angle φ, which unveils novel phases only at quite precise values (e.g. superconductivity, orbital magnetism, correlated insulator states). Here, we overcome these practical limitations through a new class of heterostructures composed of γ-InSe on ε-GaSe that reveal strong evidence for the moiré potential even in thick stacked layers and at arbitrary values of φ. We detect a pronounced interlayer exciton composed of several superimposed emissions that are uniformly spaced in energy ΔE  with pronounced φ-dependence. In the interfacial area, similar behavior is displayed also by the intralayer exciton of GaSe. This strong correlation between φ and ΔE implies the localization of excitations at the moiré potential minima. But in contrast to transition metal dichalcogenides (TMDs), the moiré potential modulates the multi-component interlayer exciton over the entire range of φ due to their direct band-gap at the center of their Brillouin zone. γ-InSe/ε-GaSe interfaces offer an unprecedented level of moiré exciton tunability not yet achieved in any other van der Waals heterostructure. Our results demonstrate clear pathways for quantum optoelectronics while offering opportunities to study electronic correlations over a broad range of moiré periodicities and layer thicknesses.   

Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS2

We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS₂, spin-orbit coupling in the conduction band states from ±K valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number S=±2. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at 1/2-filling into a valley-polarized state, which realizes a correlated quantum anomalous Hall state with Chern number C=±2. Effects of displacement fields are discussed with comparison to nontrivial topology from layer-pseudospin magnetic fields.   

Chiral valley phonons and flat phonon bands in moiré materials

A chiral object is not the same as its mirror image. The chirality of quasiparticles is a critical concept behind many modern developments of condensed matter physics. Some recent examples include Klein tunneling in graphene and the chiral magnetic effect due to chiral fermions in three-dimensional semi-metals. Here, we show that phonons, bosonic collective excitations, in moiré patterns created with WSe2 can be chiral. Furthermore, we observe the flattening of bands near the phononic band-gap edges in these systems. Our findings, which are expected to be generic for moiré materials created with two-dimensional materials that break inversion symmetry, are important in understanding electron-phonon, exciton-phonon scattering, and in designing efficient phononic crystals.   

Flat bands in twisted multilayer transition metal dichalcogenides from ab initio tight-binding calculations

Recently, twisted bilayers of transition metal dichalcogenides (TMDs) have gained interest as a novel and robust platform for simulating quantum phases of matter on emergent 2D lattices. These systems exhibit rich phase diagrams as function of twist angle, carrier density and temperature, including correlated insulating, superconducting and topologically non-trivial phases[1-5]. The emergence of these phases is attributed mainly to strong electron-electron interactions among electrons in flat bands near the Fermi level [6].

Studying the atomic and electronic structure of these systems using first-principles methods is computationally highly challenging because for small twist angles the moiré unit cells contain thousands of atoms. To overcome this problem, we employ a multi-scale approach in which classical force fields are used to find the equilibrium atomic structures and tight-binding calculations are carried out on the relaxed structures to determine electronic band structures [7]. We present results for twisted tri- and quadlayer TMDs and discuss the dependence of the flat bands on the twist angle and the stacking arrangement.

Refs.

[1] Zhang Z. et al., Nat. Phys. 16, 1093–1096 (2020)

[2] Wang L. et al., Nat. Mater. 19, 861-866 (2020); Ghiotto A. et al., Nature 597, 345-349 (2021)

[3] Regan E. C. et al, Nature 579, 359–363 (2020); Xu Y. et al., Nature 587, 214–218 (2020); Huang X. et al., Nat. Phys. 17, 715-719 (2021)

[4] Li H. et al., Nature 597, 650–654 (2021)

[5] Jin C. et al., Nat. Mater. 20, 940–944 (2021)

[6] V.Vitale et al., 2D mater. 8, 4 (2021) 

[7] Park et al., Nature 590, 249-255 (2021)   

Twister: Construction and structural relaxation of commensurate moiré superlattices

The introduction of a twist between layers of two-dimensional materials which leads to the formation of a moiré pattern is an emerging pathway to tune the electronic, vibrational and optical properties. The fascinating properties of these systems are often linked to large-scale structural reconstruction of the moiré pattern. Hence, an essential first step in the theoretical study of these systems is the construction and structural relaxation of the atoms in the moiré superlattice. We present the Twister package, a collection of tools that constructs commensurate superlattices for any combination of 2D materials and also helps perform structural relaxations of the moiré superlattice. Twister constructs commensurate moiré superlattices using the coincidence lattice method and provides an interface to perform structural relaxations using classical forcefields.