Exact exchange: A pathway for a density functional theory of the integer quantum Hall effect

¹ Centro Atómico Bariloche, CNEA, CONICET - 8400 S. C. de Bariloche, Río Negro, Argentina
² Instituto de Física, Universidade Federal de Uberlândia - Uberlândia, Minas Gerais 38400-902, Brazil
³ Centro Atómico Bariloche and Instituto Balseiro - 8400 S. C. de Bariloche, Río Negro, Argentina

Received: 17 August 2017
Accepted: 13 October 2017

Abstract

It is shown here that the exact-exchange (EE) formalism provides a natural and rigorous approach for a density functional theory (DFT) of the integer quantum Hall effect (IQHE). Application of a novel EE method to a quasi–two-dimensional electron gas (q2DEG) subjected to a perpendicular magnetic field leads to the following main findings. i) the microscopic exchange energy functional of the IQHE has been obtained, whose main feature being that it minimizes with a discontinuous derivative at every integer filling factor ν; ii) an analytical solution is found for the magnetic-field dependent EE potential, in the one-subband regime; iii) as a consequence of i), the EE potential display sharp discontinuities at every integer ν; and iv) the widely used local spin density approximation (LSDA) is strongly violated for filling factors close to integer values.