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Superconductivity in the anyon model

1990; American Physical Society; Volume: 42; Issue: 1 Linguagem: Inglês

10.1103/physrevb.42.342

1095-3795

Yutaka Hosotani, Sumantra Chakravarty,

Quantum many-body systems

We analyze a two-dimensional system of electrons or holes, interacting via, in addition to the electromagnetic fields, the Chern-Simons gauge fields (${\mathit{a}}_{\ensuremath{\nu}}$) equipped with the action (\ensuremath{\mu}/2)(${\mathrm{\ensuremath{\epsilon}}}^{\ensuremath{\lambda}\ensuremath{\nu}\mathrm{\ensuremath{\rho}}}$${\mathit{a}}_{\ensuremath{\lambda}}$${\mathrm{\ensuremath{\partial}}}_{\ensuremath{\nu}}$${\mathit{a}}_{\mathrm{\ensuremath{\rho}}}$. For \ensuremath{\Vert}\ensuremath{\mu}\ensuremath{\Vert}=${\mathit{e}}^{2}$N/2\ensuremath{\pi} (N=2,4,6,. . . ), the ground state is unique and a spin singlet, having completely filled Landau levels with respect to the Chern-Simons magnetic fields. For these values of \ensuremath{\mu}, equations are derived that replace the London equations in BCS theory. It is shown that a complete Meissner effect operates at zero temperature. Integer quantum Hall effects in the Chern-Simons fields play a crucial role. The magnetic penetration depth coincides with that in BCS theory as long as N\ensuremath{\ll}1000.