One-dimensional topological insulators with chiral symmetry

 I will talk about the properties of microscopical models of one-dimensional topological insulators in universality classes that possess chiral symmetry.  To construct such models we start with a deformation of the Su-Schrieffer-Heeger chain that breaks time-reversal symmetry, which puts it in the AIII class that has chiral symmetry only. We then couple this model to its time-reversal counterpart to build models in other symmetry classes [1]. This construction is similar to what has been done by Kane and Mele in their construction of Spin Hall insulator by coupling two Quantum Hall planes. I will talk about topological properties of such models, and in particular, will demonstrate that the models that belong to Z classes can be adiabatically deformed into one another without the change of topological invariant as long as chiral symmetry is preserved. This property is general and holds also in three dimensions [2].  I will also discuss how interactions change the topological properties of the constructed models by using bosonisation [3]. 

[1]  P. Matveeva, T. Hewitt, D. Liu, K. Reddy, D. Gutman, and S. T. Carr, Phys. Rev. B 107, 075422 (2023) 

[2] D. Liu, P. Matveeva, D. Gutman, S.T. Carr , Phys.Rev. B 108 (3), 035418 (2023)

[3] P. Matveeva, D. Gutman, and S. T. Carr, Phys. Rev. B 109, 165436 (2024)