相关论文: A New Numerical Method for $\mathbb{Z}_2$ Topologi…

Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly…

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…

Applying a Lindemann-like criterion obtained previously by Kierfeld, Nattermann and Hwa [Phys. Rev. B 55, 626 (1997)], we estimate the magnetic field and temperature for a high-$T_c$ superconductor, at which a topologically ordered vortex…

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…

We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…

In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been…

Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the…

Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their Z$_2$ topological order can be realized at room…

We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The…

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…

In this paper, we investigate the edge-Wiener index, the Szeged index, the edge-Szeged index, and the PI index, which are some of the most studied distance-based topological indices. As the main result we show that for benzenoid systems…

The past decade has witnessed significant progress in topological materials investigation. Symmetry-indicator theory and topological quantum chemistry provide an efficient scheme to diagnose topological phases from only partial information…

This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system…

Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the…

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five…

Odd index pairings of $K_1$-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a…

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic…

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…

Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in $E$-theory. The other type is by module multiplications in $K$-theory, which also yields an…

We investigate the effect of a strong bichromatic deformation to the $\mathbb{Z}_{2}$ topological insulator in a fermionic ultracold atomic system proposed by B. B\'eri and N. R. Cooper, Phys.Rev.Lett. {\bf 107}, 145301 (2011). Large…