Properties of an excitonic insulator in the superconducting state

Abstract

The properties of an excitonic insulator with embedded (nondissipative) current are studied using the self-consistent field approximation, in which the wavefunction of the system has the form of the known Bardeen-Cooper-Schrieffer trial function with time-dependent coefficients; the equations for these coefficients are derived. Such a formulation holds for the homogeneous case (in the absence of a coordinate dependence). We consider two problems: (i) time evolution of the system in the case when an embedded current exists at the initial instant; and (ii) the response of the system to an abrupt perturbation (the vector potential changes jumpwise from zero to a certain finite value). In both cases, the state of the system depends on time, but some characteristics (e.g., undamped current) tend to a constant value. For a weak perturbation, the system behaves as an insulator. If the perturbation is not small (on the order of the gap in the spectrum), nonlinear effects lead to substantial differences: a certain part of the embedded current is preserved in the former case, while the initial current in the latter case acquires a certain addition.