Related papers: Dynamical topological invariant for non-Hermitian …
The Chern topological numbers of a material platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green's function method to determine from first…
If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…
In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the ${\mathbb Z}_{2}$ topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry…
Topological phases and topological phase transitions (TPT) are among the most fantastic phenomena in Nature. Here we show that injecting a current may lead to new topological phases, especially new gapless topological metallic phases with…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice…
We study the adiabatic topological charge pumping driven by interlayer sliding in the moir\'{e} superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moir\'{e} pattern flow and a…
Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one…
We investigate the bulk-boundary correspondence for massless Dirac fermion in $\alpha$-${T}_3$ lattice where the Berry phase can be continuously tuned from $\pi $ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
Topological charge pumping represents an important quantum phenomenon that shows the fundamental connection to the topological properties of dynamical systems. Here, we introduce a pumping process in a spin-dependent double-well optical…
The exploration of the Berry phase in classical mechanics has opened new frontiers in understanding the dynamics of physical systems, analogous to quantum mechanics. Here, we show controlled accumulation of the Berry phase in a two-level…
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical…
In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding…
Quantum geometry may enable the development of quantum phases ranging from superconductivity to correlated topological states. One powerful probe of quantum geometry is the nonlinear Hall response which detects Berry curvature dipole in…
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in…
We investigate two kinds of topological structures (sphere and torus) spanned by the controlled parameters of a driven two-level system's Hamiltonian, and consider the connection between the structures and the system's dynamics. We discuss…
We propose a geometric criterion of the topological phase transition for non-Hermitian systems. We define the length of the boundary of the bulk band in the complex energy plane for non-Hermitian systems. For one-dimensional systems, we…
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…