Advances in Theoretical and Mathematical Physics

Zero Field Hall Effect in (2+1)-dimensional QED

Marianne Leitner

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Abstract

In quantum electrodynamics of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be given by an integer, the Chern number. In our field-free situation, however, the conductivity is ±1/2 in natural units. We fit this half-integral result into the topological setting and give a geometric explanation reconciling the points of view of quantum field theory (QFT) and solid state physics. For quasiperiodic boundary conditions, we calculate the finite size correction to the Hall conductivity. Applications to graphene and similar materials are discussed.

Article information

Source
Adv. Theor. Math. Phys., Volume 12, Number 3 (2008), 475-487.

Dates
First available in Project Euclid: 7 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1210167651

Mathematical Reviews number (MathSciNet)
MR2399317

Zentralblatt MATH identifier
1149.81022

Citation

Leitner, Marianne. Zero Field Hall Effect in (2+1)-dimensional QED. Adv. Theor. Math. Phys. 12 (2008), no. 3, 475--487. https://projecteuclid.org/euclid.atmp/1210167651


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