Related papers: Disordered Topological Insulators via $C^*$-Algebr…
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…
The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer $\nu$ multiple of $e^{2}/h$. Here we demonstrate the existence…
A two-dimensional topological insulator may arise in a centrosymmetric commensurate N\'{e}el antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge…
We introduce a ${\mathbb Z}_2$-index for time reversal invariant Hamiltonians with unique gapped ground state on quantum spin chains. We show this is an invariant of a $C^1$-classification of gapped Hamiltonians.
We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry…
Topological phases realized in time-reversal invariant (TRI) systems are foundational to experimental study of the broader canon of topological condensed matter as they do not require exotic magnetic orders for realization. We therefore…
For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
We study the effect of strong disorder in a 3-dimensional topological insulators with time-reversal symmetry and broken inversion symmetry. Firstly, using level statistics analysis, we demonstrate the persistence of delocalized bulk states…
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…
We define a $\mathbb{Z}_2$-valued topological and gauge invariant associated to any 1-dimensional, translation-invariant topological insulator which satisfies either particle-hole symmetry or chiral symmetry. The invariant can be computed…
We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near-field of an atom-chip, which effectively mimics the effects…
We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the…
In light of recent progress in the study of amorphous topological phases, we investigate the effects of structural disorder on the topological properties of a two-dimensional quantum spin Hall insulator modeled by the Bernevig-Hughes-Zhang…
Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This…
We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the…
We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…
The ground state of translationally-invariant insulators comprise bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we…