相关论文: Localization of generalized Wannier bases implies …
We introduce a universal formulation of the generalized real space interactions with translational invariance, when projected into a single Landau level, can be equivalent to density-density interaction projected into any Chern bands (e.g.…
Using the non-commutative Kubo formula for aperiodic solids [1-3] and a recently developed numerical implementation [4], we study the conductivity $\sigma$ and resistivity $\rho$ tensors as functions of Fermi level and temperature, for…
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
Considerable efforts have recently been devoted to the experimental realization of a two-dimensional Chern insulator, i.e., a system displaying a quantum anomalous Hall effect. However, existing approaches such as those based on magnetic…
We study two models for spinless fermions featuring topologically non-trivial bands characterized by Chern numbers $C=\pm1$ at fractional filling. Using exact diagonalization, we show that, even for infinitely strong nearest-neighbor…
We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum…
Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved,…
Topological band insulators are classified using momentum-space topological invariants, such as Chern or winding numbers, when they feature translational symmetry. The lack of translation symmetry in disordered, quasicrystalline, or…
We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass,…
Recent discoveries of zero-field fractional Chern insulators in moir\'e materials have attracted intensive research interests. However, most current theoretical and experimental attempts focus on systems with low Chern number bands, in…
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…
Moir\'e materials with opposite non-zero miniband Chern numbers in time-reversal-partner valleys are two-dimensional topological insulators at band filling $\nu=2$. We explore the possibility that in this class of moir'e materials…
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories…
Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These…
We apply ideas from $C^*$-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological…
Quantum Hall (QH) states are arguably the most ubiquitous examples of nontrivial topological order, requiring no special symmetry and elegantly characterized by the first Chern number. Their higher dimension generalizations are particularly…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…