Related papers: Variants of the symmetry-based indicator

For a many-body system of arbitrary dimension, we consider fermionic ground states of non-interacting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $\Delta$ between the number of occupied symmetric and…

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological…

Phase-change materials are ubiquitous in technology because of their ability to transition between amorphous and crystalline phases fast and reversibly, upon shining light or passing a current. Here we argue that to fully understand their…

For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of…

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 method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…

Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…

Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…

In this manuscript, we derive symmetry indicator formulas for the filling anomaly on 2D square lattices with and without time reversal, inversion symmetry, or their product, in the presence of spin-orbit coupling. We go beyond previous work…

Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…

In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…

Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…

Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these…

Topological insulators are typically characterized by particularly stable properties, such as global invariants, and can be identified by probing their robust surface states. A recently discovered novel form of band topology, delicate…

Topological materials are characterized by integer invariants that underpin their robust quantized electronic features, as famously exemplified by the Chern number in the integer quantum Hall effect. Yet, in most candidate systems, the…

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…

Topological insulators (TIs) are a recently discovered class of quantum materials that are currently attracting considerable attention. The most interesting aspect of the TIs is, in fact, not that they are bulk insulators but that their…

We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…