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The fractional quantum anomalous Hall effect has recently been experimentally observed in zero-field fractional Chern insulators (FCI). However, an outstanding challenge is the presence of a substantial longitudinal resistance $R_{xx}$ (a…
Recent experimental observations of the fractional quantum anomalous Hall effect in spin/valley polarized moir\'{e} systems call for a more expansive theoretical exploration of strongly correlated physics in partially filled topological…
In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…
The fractional quantum anomalous Hall (FQAH) effect was recently discovered in twisted MoTe2 bilayers (tMoTe2). Experiments to date have revealed Chern insulators from hole doping at v = -1, -2/3, -3/5, and -4/7 (per moir\'e unit cell). In…
We consider fractional quantum Hall states in systems where two flat Chern number $C=\pm 1$ bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor $\nu=1$ this setting…
The quantum anomalous Hall effect is a intriguing quantum state which exhibits the chiral edge states in the absence of magnetic field. While the search for quantum anomalous Hall insulators is still active, the researchers mainly search…
As one of the most intriguing states of matter, the chiral spin liquid (CSL) has attracted much scientific interest while its existence and mechanism in crystalline strongly correlated systems remain hotly debated. On the other hand, strong…
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in…
We propose a new mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moir\'e heterobilayers at $\nu=1$ hole filling. We suggest that the…
Quantum spin Hall (QSH) insulators are versatile platforms for exploring exotic quantum phases, especially when combined with high-order van Hove singularities (VHSs) that enhance electron correlations. However, perfect spin Hall…
In parallel to the condensed-matter realization of quantum Hall (Chern insulators), quantum spin Hall (topological insulators), and fractional quantum Hall (fractional Chern insulators) effects, we propose that bilayer flat band (FB)…
Quantum spin Hall insulators (QSHIs), also known as two-dimensional topological insulators, have emerged as an unconventional class of quantum states with insulating bulk and conducting edges originating from nontrivial inverted band…
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged…
We address the question of whether fractionally filled bands with a nontrivial Chern index in zero external field could also exhibit a Fractional Quantum Hall Effect (FQHE). Numerical works suggest this is possible. Analytic treatments are…
The quantum anomalous Hall state with a large band gap and a high Chern number is significant for practical applications in spintronics. By performing first-principles calculations, we investigate electronic properties of the fully…
Fractional Chern insulators (FCIs) showing a transport effect with fractionally quantized Hall plateaus emerging under zero magnetic field, provide a radically new opportunity to engineer topological quantum electronics. By construction of…
Chiral spin liquid (CSL) is a magnetic analogue of the fractional quantum Hall (FQH) liquid. Collective excitations play a vital role in shaping our understanding of these exotic quantum phases of matter and their quantum phase transitions.…
In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in magnetic field or increasing density, we observe multiple transitions of the fractional quantum Hall states (FQHSs) near…
We study the physics of quantum spin Hall (QSH) effect and topological quantum phase transition on the porphyrin lattice. We show that in a special limit the pristine model on this lattice reduces to the usual topological insulator (TI)…
In a bilayer system consisting of a composite-fermion Fermi sea in each layer, the tunnel current is exponentially suppressed at zero bias, followed by a strong peak at a finite bias voltage $V_{\rm max}$. This behavior, which is…