Eur. Phys. J. B 79, 465-471 (2011)
https://doi.org/10.1140/epjb/e2011-10875-9

Hatano-Nelson model with a periodic potential

¹ INLN, Université de Nice-Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France
² Physics Department, Massachusetts Institute of Technology, 77, Massachusetts Avenue Cambridge, 02139-4307 MA, USA
³ Physics Department, University of California, Davis, 95616 California, USA
⁴ School of Mathematical Sciences, Fudan University, Shanghai, 200433, P.R. China
⁵ Departments of Mathematics and Computer Science, University of California, Davis, 95616 California, USA

Corresponding author: ^a frederic.hebert@inln.cnrs.fr

Received: 14 November 2010
Revised: 11 January 2010
Published online: 16 February 2011

Abstract

We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.