Supersymmetry and the Superconductor-Insulator Transition(Condensed Matter and Statistical Physics)

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We present a theory of supersymmetric superconductivity and discuss its physical properties. We define the supercharges Q and Q^† satisfying Qψ_<BCS>=Q^†ψ_<BCS>=0 for the Bardeen-Cooper-Schrieffer state ψ_<BCS>. They possess the property expressed by Q^2=(Q^†)^2=0, and ψ_<BCS> is the ground state of the supersymmetric Hamiltonian H=E(QQ^†+Q^†Q) for E>0. The superpartners ψ_g and ψ_<BCS> are shown to be degenerate. Here ψ_g denotes a fermionic state within the superconducting gap that exhibits a zero-energy peak in the density of states. A supersymmetric model of superconductivity with two bands is presented. On the basis of this model we argue that the system of interest goes into a superconducting state from an insulator if an attractive interaction acts between states in the two bands. There are many unusual properties of this model due to an unconventional gap equation stemming from the two-band effect. The model exhibits an unconventional insulator-superconductor first-order phase transition. In the ground state, a first-order transition occurs at the supersymmetric point. We show that certain universal relations in the BCS theory, such as that involving the ratio Δ(0)/k_BT_c, do not hold in the present model.
理論物理学刊行会の論文
2007-08-25