Exact Exchange: a pathway for a Density Functional Theory of the Integer Quantum Hall Effect

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. \textit{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 $\nu$; \textit{ii)} an analytical solution is found for the magnetic-field dependent EE potential, in the one-subband regime; \textit{iii)} as a consequence of \textit{i)}, the EE potential display sharp discontinuities at every integer $\nu$; and \textit{iv)} the widely used Local Spin Density Approximation (LSDA) is strongly violated for filling factors close to integer values.

References in corpus (19)

• Pseudospin Anisotropy Classification of Quantum Hall Ferromagnets
• Resistance spikes and domain wall loops in Ising quantum Hall ferromagnets
• Two-subband quantum Hall effect in parabolic quantum wells
• Ensemble density functional theory of the fractional quantum Hall effect
• Multiple Phases with the Same Quantized Hall Conductance in a Two-Subband System
• Kohn-Sham Exchange Potential for a Metallic Surface
• Landau Level Anticrossing Manifestations in the Phase Diagram Topology of a Two Subband System
• Exact-exchange density-functional theory for quasi-two-dimensional electron gases
• NMR Probing Spin Excitations in the Ring-Like Structure of a Two-Subband System
• Density functional theory of the fractional quantum Hall effect
• Probing Quantum Hall Pseudospin Ferromagnet by Resistively Detected NMR
• Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas
• Hysteretic resistance spikes in quantum Hall ferromagnets without domains
• Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit
• Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry
• Many-body effects on the ${\rho }_{xx}$ ringlike structures in two-subband wells
• Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field
• Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets
• Exact and approximate relations for the spin-dependence of the exchange energy in high magnetic fields

Cited by in corpus (1)

• Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit