Related papers: Topological linear response of hyperbolic Chern in…
The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements. Recently, it was predicted that topology can also give rise to a…
It is well known that a nontrivial Chern number results in quantized Hall conductance. What is less known is that, generically, the Hall response can be dramatically different from its quantized value in materials with broken inversion…
We propose the model of layered materials, in which each layer is described by the conventional Haldane model, while the inter - layer hopping parameter corresponds to the ABC stacking. We calculate the topological invariant $N_3$ for the…
Chern insulators are states of matter characterized by a quantized Hall conductance, gapless edge modes but also a singular response to monopole configurations of an external electromagnetic field. In this paper, we describe the nature of…
Physical systems with non-trivial topological order find direct applications in metrology[1] and promise future applications in quantum computing[2,3]. The quantum Hall effect derives from transverse conductance, quantized to unprecedented…
We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…
The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number. The…
We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be…
We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and…
The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant…
Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of…
It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given…
We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group structure, such lattices are associated with a high-dimensional…
We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body…
We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number…
We investigate slow quenches in Chern insulators in ribbon geometry. We consider the Qi-Wu-Zhang model and slowly ramp the parameters (large time of the quench $\tau$) from a non-topological (Chern number = 0) to a topological regime (Chern…
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…