Simple Models for All Topological Phases

TL;DR

This paper introduces simple, explicit models that can realize all topological phases of free fermions, encompassing the entire periodic table of topological insulators and superconductors, unifying many known models.

Contribution

It provides a comprehensive framework for constructing explicit models for all topological phases of free fermions, covering all invariants in the periodic table.

Findings

Models realize all nontrivial topological phases

Includes many known topological insulator and superconductor models

Unifies various models into a general construction

Abstract

We construct simple models for all topological phases of free fermions. These explicit models can realize all the nontrivial topological phases (with any possible topological invariant) of the periodic table. Many well known models for topological insulators and superconductors are special cases of our general constructions.