Session G64: Correlated Electronic States in Low Dimensions

Disorder induced 2D metal-insulator transition in moir´e transition metal dichalcogenide multilayers

We develop a minimal theory for the recently observed metal-insulator transition (MIT) in two-dimensional (2D) moir´e multilayer transition metal dichalcogenides (mTMD) using Coulomb disorder in the environment as the underlying mechanism. In particular, carrier scattering by random charged impurities leads to an effective 2D MIT approximately controlled by the Ioffe-Regel criterion, which is qualitatively consistent with the experiments. We find the necessary disorder to be around 5-10 × 10¹⁰cm^-2 random charged impurities in order to quantitatively explain much, but not all, of the observed MIT phenomenology as reported by two different experimental groups. Our estimate is consistent with the known disorder content in TMDs.   

Metal-Insulator Transition with Charge Fractionalization

It has been proposed that an extended version of the Hubbard model which potentially hosts rich possibilities of correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moiré heterostructures. Motivated by recent reports of continuous metal-insulator transition (MIT) at half-filling, as well as correlated insulators at various fractional fillings in TMD moiré heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges. The charge fractionalization at the MIT will lead to experimental observable effects, such as a large universal resistivity jump and interaction-driven "bad metal" at the MIT, as well as special scaling of the quasi-particle weight with the tuning parameter. These predictions are different from the previously proposed theory for continuous MIT.   

Ground State Conductivity Probes in the One-Dimensional Hubbard Model

Using quantum Monte Carlo simulation, we compute quantum metric tensor and localization length in the ground state of the one-dimensional Fermi-Hubbard Hamiltonian, as probes for conductivity. We compare these values with the exact values of the charge gap of the system as a function of the interaction strength. We perform calculations for lattices with up to 1000 sites, at half-filling, using both periodic and open boundary conditions. We assess and discuss the sensitivity of the probes mentioned above in detecting a metal-insulator phase transition. We suggest data analysis methodologies to deal with the finite-size effects. We will also show preliminary results in two dimensions.   

Nonlinear sigma model with particle-hole asymmetry for the disordered two-dimensional electron gas

 

The nonlinear sigma model is a well-established theoretical tool for studies of transport and thermodynamics in disordered electronic systems. An important application is the description of the metallic side of the metal-insulator transition in the two-dimensional electron gas. The conventional sigma model approach for interacting systems does not account for particle-hole asymmetry. It is therefore not suited for studying quantities that are sensitive to this effect such as the thermoelectric transport coefficient. We derive a minimal extension of the Keldysh nonlinear sigma model tailored for two-dimensional interacting systems. We argue that this model can be used to systematically study the combined effect of interactions and disorder on thermoelectric transport. We use the model to analyze the structure of the heat density-density correlation function and calculate interaction corrections to its static part.    

Quantum melting of generalized Wigner crystals

Recent experimental studies have established that moiré materials consisting of transition metal dichalcogenide bilayers host correlated insulating states at a series of fractional fillings of the moiré superlattice. In order to minimize the long-range Coulomb interaction electrons localize on a subset of moiré sites, giving rise to generalized Wigner crystals with charge orders that depend on the filling fraction. We combine exact diagonalization calculations in momentum space and a description in terms of extended t − J models to investigate the properties of the crystalline phases from the classical lattice gas limit up to the quantum melting regime, where quantum fluctuations start to dominate. We address the absence of particle-hole symmetry in the charge gaps relative to half-filling, and the nature of the states on the metallic side of these metal-insulator transitions.   

Evidence for an Exciton Solid in Double Layer Graphene

Double layer graphene, consisting of two monolayers, separated by a thin Boron Nitride spacer, provides a versatile platform to study long-lived interlayer excitons.  In the quantum Hall regime, a superfluid exciton condensate can be realized when each layer is populated to half filling of the lowest landau level.  In this work we investigate the phase diagram of this superfluid in the extreme dilute limit.  Using a combination of hall bar and edge-free corbino geometries we find evidence for an exciton solid ground state. The solid-fluid phase boundary is mapped in the exciton density-temperature phase diagram.     

Bilayer Wigner crystals in van der Waals heterostructures

A Wigner crystal is the earliest predicted correlated electron state and exhibits intriguing quantum phase transitions. Here we report the observation of bilayer Wigner crystals in an atomically thin transition metal dichalcogenide heterostructure, where two MoSe₂ monolayers are separated by a thin layer of hexagonal boron nitride. We observe optical signatures of robust correlated insulating states when fixing the electron density ratio between the two layers at specific values. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction. Using optical probes, we characterize the phase transitions of the Wigner crystals. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their quantum phase transitions.   

Chirality-dependent topological states in twisted double bilayer graphene

The properties of van der Waals (vdW) crystals and heterostructures depend sensitively on their layer stacking configuration. The twist angle and lattice mismatch between constituent vdW sheets have been shown to be crucial parameters influencing the strongly correlated and topological states of matter in moiré materials. Here, we demonstrate a new approach for controlling these emergent states by altering the stacking chirality of the moiré structure. We study twisted double bilayer graphene (tDBG) in an AB-BA stacking configuration (i.e., with the component Bernal bilayers rotated by nearly 60°) and observe topological and symmetry-broken states that are absent in AB-AB stacked tDBG. Our results motivate future experiments in which the stacking chirality is employed as an important new degree of freedom for controlling the strongly correlated and topological phase diagram of other moiré materials.

    

Correlated electron states in coupled quarter-flux Hofstadter layers under opposite magnetic field

We present a numerical study of a strongly correlated bilayer Hofstadter model, with properties strikingly similar to magic-angle twisted bilayer graphene (MATBG). While experiments on MATBG have revealed a variety of interesting superconducting and correlated insulating phases, a complete description of these states has been inhibited by the size of the moiré unit cell and the resultant complexity of large-scale numerical simulations. Motivated by this, we propose and analyze a lattice model containing the most important symmetries and topological features of MATBG. Namely, we study a spinful bilayer system of quarter-flux Hofstadter lattices subjected to opposite magnetic field, equipped with both local Hubbard interactions and interlayer tunneling. We explore its phase diagram using the infinite density matrix renormalization group method, finding symmetry-breaking correlated insulating states at integer filling of the lowest Hofstadter bands. We conclude by discussing its potential experimental implementation in an optical lattice system.   

Symmetry-broken states at half-integer moire fillings in twisted bilayer graphene-WSe2 heterostructures

Magic-angle twisted bilayer graphene (TBG) has recently become a playground for exploring many correlated phases such as superconductivity, correlated insulators, orbital ferromagnetism, Chern insulators, and nematicity hosted by strongly interacting electrons within the low energy flat bands of the system. The rapid progress in this field has enabled the fine-tuning of several experimental knobs to access the low energy degrees of freedom of the band structure, which favor exotic phases at or near integer number of carriers per moire unit cell. However, experimental demonstration of ordered states at fractional moire band-fillings at zero applied magnetic field B is a challenging pursuit. Engineering the dielectric environment of TBG results in a highly tunable platform to investigate the strong correlations. In this work, we have investigated such a moire heterostructure assembled by placing a tungsten diselenide (WSe2) layer on top of a TBG. We observe symmetry-broken states at half-integer band-fillings of v = 0.5 and 3.5 at B ≈ 0. Further, we observe reset of charge carriers at v = 2 and 3. In addition to magnetotransport, we employ thermoelectricity as a tool to probe the system at B = 0. Our band structure calculations are consistent with a spontaneously broken translational symmetry supercell with twice the area of the original TBG moire cell.  The combined effects of a commensurate density wave potential and spin-orbit coupling terms lead to degeneracy-lifted, zone-folded moire bands with spin-valley isospin ordering anisotropy that describe the states at half-integer fillings observed experimentally. Our results suggest the existence of a spin-charge density wave ground state at half-integer fillings of TBG in the zero B-field limit.   

Spin-valley relaxation dynamics of Landau-quantized electrons in MoSe2 monolayer

Transition metal dichalcogenide monolayers provide a fascinating experimental platform for optical investigations of strongly correlated electronic states. Although the formation of such states has been evidenced in explorations of electronic ground state properties [1], the effects of strong correlations on non-equilibrium dynamics remained elusive. In this talk I will review our recent studies of spin-valley relaxation of electrons in charge-controlled MoSe₂ monolayer under the influence of strong out-of-plane magnetic field that quantizes the electronic bands into Landau levels (LLs) [2]. The electron spins are optically depolarized with excitons injected by a short light pulse and the spin-valley relaxation rate is measured in pump-probe experiments. Our results evidence that the relaxation dynamics at temperatures below 100 mK displays prominent oscillations with the LL filling factor: it speeds up when the electrons form an uncorrelated integer quantum Hall state and slows down at non-integer fillings, when the electronic correlations become more prominent. This observation indicates that spin-valley relaxation dynamics may be exploited to study the effects of strong inter-electron interactions in the electronic ground state of an atomically-thin semiconductor.   

Parent (half)metal and emergent superconductivity in rhombohedral trilayer graphene

Combining mean-field and renormalization group analyses, I shed light on recently observed superconductivity and their parent states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields. I argue that close to the charge neutrality, on site Hubbard repulsion favors layer antiferromagnet, which when combined with the displacement field (inducing layer polarization), produces a spin-polarized, but valley or isospin unpolarized half-metal, conducive to the nucleation of spin-triplet  f-wave pairing. By contrast, at larger doping Kekulé valence bond order emerges as a prominent candidate for isospin coherent paramagent, boosting condensation of spin-singlet Cooper pairs in the conventional s-wave channel, manifesting a "selection rule" among competing orders. Responses of these paired states to displacement and in-plane magnetic fields show qualitative similarities with experimental observation.   

Emergence of Gaussianity in the thermodynamic limit of interacting fermions

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-1/2 chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. 

To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.