相关论文: Topological insulators and K-theory

We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the…

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…

The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the $\mathbb{Z}_2$ invariant found by Kane and Mele. Such invariants protect the topological insulator and give rise to a spin…

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…

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…

Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…

We use a "monodromy" argument to derive new expressions for the ${\bm Z}_2$ invariants of topological insulators with time-reversal symmetry in 2 and 3 dimensions. The derivations and the final expressions do not require any gauge choice…

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological…

This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of…

We study disordered topological insulators with time reversal symmetry. Relying on the noncommutative index theorem which relates the Chern number to the projection onto the Fermi sea and the magnetic flux operator, we give a precise…

We show that the two-dimensional $\mathbb{Z}_2$ invariant for time-reversal invariant insulators can be formulated in terms of the boundary-condition dependence of the ground state wavefunction for both non-interacting and…

We present a general description of topological insulators from the point of view of Dirac equations. The Z_{2} index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic B term in…

We present homotopy theoretic and geometric interpretations of the Kane-Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence…

We apply ideas from $C^*$-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological…

We define a new $Z_2$-valued index to characterize the topological properties of periodically driven two dimensional crystals when the time-reversal symmetry is enforced. This index is associated with a spectral gap of the evolution…

We represent the $\mathbb Z_2$~topological invariant characterizing a one dimensional topological superconductor using a Wess-Zumino-Witten dimensional extension. The invariant is formulated in terms of the single particle Green's function…

Topological crystalline superconductors are known to have possible higher-order topology, which results in Majorana modes on $d-2$ or lower-dimensional boundaries. Given the rich possibilities of boundary signatures, it is desirable to have…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Recent work by Prodan and the second author showed that weak invariants of topological insulators can be described using Kasparov's $KK$-theory. In this note, a complementary description using semifinite index theory is given. This provides…

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…