Eur. Phys. J. B (2016) 89: 153
https://doi.org/10.1140/epjb/e2016-70076-8

Regular Article

Berry phases and zero-modes in toroidal topological insulator

¹ Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Brazil
² Instituto Federal de Educação, Ciência e Tecnologia Baiano, 48970-000 Senhor do Bonfim, Brazil
³ Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Santiago, Chile

^a e-mail: jakson.fonseca@ufv.br
^b e-mail: vagson.santos@ufv.br
^c e-mail: winder@ufv.br https://sites.google.com/site/wamouramelo/home
^d e-mail: apereira@ufv.br https://sites.google.com/site/quantumafra/

Received: 1 February 2016
Received in final form: 4 April 2016
Published online: 15 June 2016

Abstract

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.