Moiré heterostructures as a condensed-matter quantum simulator

Abstract

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties and the promise that they hold for realizing elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications.

Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene

“…These findings demonstrate the importance of electronelectron interactions for understanding the electronic properties of tBLG [11,12]. The quintessential model for strongly interacting electrons is the Hubbard model, in which electrons only interact when they are on the same "site" (typically assumed to be an atom).…”

“…Since the discovery of superconductivity in proximity to correlated insulator states at half (electron or hole) filling of the flat bands [1,2], there has been great interest in the electronic properties of magic-angle twisted bilayer graphene (tBLG) [3]. Additional experiments [4][5][6][7][8][9][10] discovered correlated insulator phases and superconductivity at other doping levels of the flat bands and revealed a wide range of interesting phenomena [11,12] including strange metal behavior [13,14], ferromagnetic order [15,16], superconductivity without correlated insulators [17][18][19], Chern insulators [20][21][22], and nematic order [6,[23][24][25].…”

Emergence of a noncollinear magnetic state in twisted bilayer CrI3

“…The emergence of two-dimensional (2D) magnetic crystals and moiré engineering of van der Waals materials has opened the door for devising new magnetic ground states via competing interactions in moiré superlattices [1][2][3][4][5][6][7][8][9] . Although a suite of interesting phenomena, including multi-flavor magnetic states 10 , noncollinear magnetic states [10][11][12][13] , moiré magnon bands and magnon networks 14 , has been predicted in twisted bilayer magnetic crystals, nontrivial magnetic ground states have yet to be realized.…”

“…Moiré superlattices built on twisted bilayers of van der Waals materials have presented an exciting platform for studying correlated states of matter with unprecedented controllability [7][8][9] . In addition to graphene and transition metal dichalcogenide moiré materials 17 , recent theoretical studies have predicted the emergence of new magnetic ground states in twisted bilayers of 2D magnetic crystals [10][11][12][13][14] .…”

Quantum anomalous Hall effect from intertwined moiré bands

“…Two-dimensional moiré heterostructures of van der Waals materials present a new paradigm for engineering electron correlation, topology, and their interplay 8,[14][15][16] . In graphene systems, moiré patterns can produce topologically nontrivial bands with valleycontrasting Chern numbers to enforce time-reversal symmetry of the single-particle band structure 14 .…”