Partition functions and stability criteria of topological insulators

Topological String Partition Functions as Equivariant Indices

In this work we exploit the relationship with certain equivariant genera of isntanton moduli spaces to study the string partition functions of some local Calabi-Yau geometries, in particular, the Gopakumar-Vafa conjecture for them [8]. Gromov-Witten invariants are in general rational numbers. However as conjectured by Gopakumar and Vafa [8] using M-theory, the generating series of GromovWitten ...

Topological String Partition Functions as Polynomials

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.

Topological insulators

Topological Insulators and Superconductors

We study theoretical properties of robust low energy electronic excitations associated with topological insulators and superconductors. The bulk materials are described by non-interacting single particle band Hamiltonians with a finite excitation gap. Their topological phases are classifed according to symmetries and dimensions, characterized by discrete bulk invariants, and correspond to topol...

Topological crystalline insulators.

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal sur...