相关论文: Crystalline finite-size topology

A Z2 topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction driven band inversion. For example, the topological phase in the Bi-Sb system is due to an odd number of band inversions. A related…

We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as…

By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime,…

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a…

Topological phases can not only be protected by internal symmetries (e.g., time-reversal symmetry), but also by crystalline symmetries, such as reflection or rotation symmetry. Recently a complete topological classification of reflection…

We present the exhaustive classification of surface states of topological insulators and superconductors protected by crystallographic magnetic point group symmetry in three spatial dimensions. Recently, Cornfeld and Chapman [Phys. Rev. B…

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry…

Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported…

Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…

We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…

Quantum simulation, as a state-of-art technique, provides the powerful way to explore topological quantum phases beyond natural limits. Nevertheless, a previously-not-realized three-dimensional (3D) chiral topological insulator, and…

Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…

Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory.…

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs…

Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of…

The interplay between topology and crystalline symmetries in materials can lead to a variety of topological crystalline insulator (TCI) states. Despite significant effort towards their experimental realization, so far only…

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground…

In this article, we study quantum critical phenomena in surfaces of symmetry-protected topological matter, i.e. surface topological quantum criticality. A generic phase boundary of gapless surfaces in a symmetry-protected state shall be a…

Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…

Topological phases of matter are classified based on symmetries, with nonsymmorphic symmetries like glide reflections and screw rotations being of particular importance in the classification. In contrast to extensively studied glide…