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Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moir\'e materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the…
We propose a new mechanism for quantum anomalous Hall (QAH) effect in the AB stacked MoTe$_2$/WSe$_2$ system. Based on the observation that the inter-layer tunneling is suppressed in the AB stacking, we consider a model with two layers…
Recently Chern insulators with Chern number $C=1$ and $C=2$ in zero (or very small) magnetic field have been observed in two moire graphene systems: twisted bilayer graphene and ABC trilayer graphene, both aligned with a hexagonal…
The ground states of twisted bilayer graphene (TBG) at chiral and flat-band limit with integer fillings are known from exact solutions, while their dynamical and thermodynamical properties are revealed by unbiased quantum Monte Carlo (QMC)…
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct…
Moir\'e network formation in graphene bilayers breaks stacking symmetry, giving rise to domain walls that host topologically protected one-dimensional states. Here we show that these systems undergo an additional symmetry breaking at the…
The physics of phase transitions in low-dimensional systems has long been a subject of significant research interest. Long-range magnetic order in the strict two-dimensional limit, whose discovery circumvented the Mermin-Wagner theorem, has…
We theoretically investigate the magnetic excitations in the quantum anomalous Hall insulator phase of twisted bilayer MoTe$_2$ at a hole filling factor of $\nu=1$, focusing on magnon and domain wall excitations. Using a generalized…
Moir\'e systems provide a highly tunable platform for engineering band structures and exotic correlated phases. Here, we theoretically study a model for a single layer of graphene subject to a smooth moir\'e electrostatic potential, induced…
Chern insulators, which are the lattice analogs of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices. To date, integer Chern…
Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom -- charge, spin,…
The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states through either sweeping the magnetic field or tuning the carrier density. The recent…
Imposing incommensurable periodicity on the periodic atomic lattice can lead to complex structural phases consisting of locally periodic structure bounded by topological defects. Twisted trilayer graphene (TTG) is an ideal material platform…
The recent prediction, and subsequent discovery, of the quantum anomalous Hall (QAH) effect in thin films of the three-dimensional ferromagnetic topological insulator (MTI) (Cr$_y$Bi$_x$Sb$_{1-x-y}$)$_2$Te$_3$ has opened new possibilities…
The quantum anomalous Hall (QAH) effect - a macroscopic manifestation of chiral band topology at zero magnetic field - has only been experimentally realized by magnetic doping of topological insulators (1 - 3) and delicate design of Moire…
We prove the existence of higher-order topological insulators with protected chiral hinge modes in quasi-two-dimensional systems made out of coupled layers stacked in an inversion-symmetric manner. In particular, we show that an external…
Magnetically doped topological insulators (TIs) exhibit two distinct phases: the quantum anomalous Hall (QAH) phase when the Fermi level resides within the surface gap, and a metallic phase outside the gap. The QAH phase hosts…
The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect…
Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when $ \pm 1,…