1996/12/09 by Jean Desbois, J. Desbois, Stéphane Ouvry +1 · 15 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Conductivity #Electron #Graphene research and applications #Hall conductivity #Hall effect #Hamiltonian (control theory) #Kubo formula #Magnetic field #Mathematics #Mechanics #Physics #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Thermal Hall effect #Topological Materials and Phenomena #Vortex #cond-mat.mes-hall #hep-th
paper · pdf · open access · doi:10.1016/s0550-3213(97)00395-7
published in Nuclear Physics B 500(1-3), 486-510 (Elsevier BV) · 28 pages, latex, 2 figures
arxiv created 1996/12/09 · openalex publication_date 1997/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity (P breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like 1/ω2. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.