Supersymmetry and the Superconductor-Insulator Transition

Abstract

We present a theory of supersymmetric superconductivity and discuss its physical properties. We define the supercharges Q and Q † satisfying QψBCS = Q † ψBCS = 0 for the BardeenCooper-Schrieffer state ψBCS. They possess the property expressed by Q 2 =( Q † ) 2 =0 , and ψBCS is the ground state of the supersymmetric Hamiltonian H = E(QQ † + Q † Q )f or E> 0. The superpartners ψg and ψBCS are shown to be degenerate. Here ψg 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 ∆(0)/kBTc, do not hold in the present model.