A new class of $(2+1)$-d topological superconductor with $\mathbb{Z}_8$ topological classification

Details A new class of $(2+1)$-d topological superconductor with $\mathbb{Z}_8$ topological classification A new class of $(2+1)$-d topological superconductor with $\mathbb{Z}_8$ topological classification

2012-02-17

arxiv.org/abs/1202.3983v2

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages main text and 3 pages appendix. 1 figure

Scientific paper

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.

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