Related papers: Topology invisible to eigenvalues in obstructed at…
A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry based classification of condensed matter. Exotic spin transport phenomena such as the…
We first study the importance of the sign of the Berry curvature in the Euler characteristic of the two-dimensional topological material with two bands. Then we report an observation of a character of the topological transition as a…
Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using…
Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…
Topological insulators are bulk semiconductors that manifest in-gap massless Dirac surface states due to the topological bulk-boundary correspondence principle [1-3]. These surface states have been a subject of tremendous ongoing interest,…
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature $\Omega_{kn}$ whose integral on the Brillouin zone is a topological invariant known as the Chern number. The…
We show that a hierarchy of topological phases in one dimension -- a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a…
We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space…
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological…
Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian {topologies that thrive on involving multiple gaps} were studied, unveiling a new horizon {in topological…
Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge connections behave as non-Abelian antisymmetric tensor gauge fields in momentum space and naturally generalize…
The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this…
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the…
We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is a homotopy classification, which enables us to see more topological invariants.…
Obstructed atomic phases, with their realizations in systems of diverse dimensionality, have recently arisen as one of the topological states with greatest potential to show higher-order phenomena. In this work we report a special type of…
While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological…
The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant…
The symmetry-constrained topological invariant fails to explain the emergence of the special edge modes when system does not preserve discrete symmetries. The inversion or chiral symmetry broken SSH model is an example of one such system…
The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane ($\mathrm{RP}^2$) and the appearance of quadrupole…
We show that the $Z_N$ Berry phase (Berry phase quantized into $2\pi/N$) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small…