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Interacting Systems far from EquilibriumQuantum Kinetic Theory$
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Klaus Morawetz

Print publication date: 2017

Print ISBN-13: 9780198797241

Published to Oxford Scholarship Online: February 2018

DOI: 10.1093/oso/9780198797241.001.0001

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Kinetic Theory of Systems with SU(2) Structure

Kinetic Theory of Systems with SU(2) Structure

Chapter:
(p.458) 21 Kinetic Theory of Systems with SU(2) Structure
Source:
Interacting Systems far from Equilibrium
Author(s):

Klaus Morawetz

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198797241.003.0021

Systems with spin-orbit coupling and magnetic fields exhibit a SU(2) structure. Large classes of materials and couplings can be written into an effective spin-orbit coupled Hamiltonian with Pauli structure. Appropriate kinetic equations are derived keeping the quantum spinor structure. It results in coupled kinetic equations of scalar and vector distributions. The spin-orbit coupling, the magnetic field and the vector part of the selfenergy can be written in terms of an effective Zeeman field which couples both distributions. The currents and linear response are derived and the anomalous parts due to the coupling of the occurring band splitting are discussed. The response in magnetic fields reveals subtle retardation effects from which the classical and quantum Hall effect result as well as anomalous Hall effects. As application the dynamical conductivity of grapheme is successfully calculated and compared to the experiments.

Keywords:   spin-orbit coupling, SU(2) symmetry, Pauli structure, spinor parts, normal and anomaly currents, response in magnetic fields, spin-Hall effect, quantum-Hall effect, transport in magnetic fields, graphene

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