Quantum criticality in inter-band superconductors

TL;DR

This paper investigates quantum phase transitions to exotic superconducting states in multi-band fermionic systems, identifying a second-order transition to a pair density wave state driven by Fermi surface mismatch.

Contribution

It provides a detailed analysis of the quantum critical point in inter-band superconductors, characterizing its dynamic critical exponent and phase diagram.

Findings

Identifies a second-order quantum phase transition to a PDW superconducting state.

Determines the dynamic critical exponent as z=2 near the quantum critical point.

Fully characterizes the quantum critical point for dimensions d ≥ 2.

Abstract

In fermionic systems with different types of quasi-particles, attractive interactions can give rise to exotic superconducting states, as pair density wave (PDW) superconductivity and breached pairing. In the last years the search for these new types of ground states in cold atom and in metallic systems has been intense. In the case of metals the different quasi-particles may be the up and down spin bands in an external magnetic field or bands arising from distinct atomic orbitals that coexist at a common Fermi surface. These systems present a complex phase diagram as a function of the difference between the Fermi wave-vectors of the different bands. This can be controlled by external means, varying the density in the two-component cold atom system or, in a metal, by applying an external magnetic field or pressure. Here we study the zero temperature instability of the normal system as the Fermi wave-vectors mismatch of the quasi-particles (bands) is reduced and find a second order quantum phase transition to a PDW superconducting state. From the nature of the quantum critical fluctuations close to the superconducting quantum critical point (SQCP), we obtain its dynamic critical exponent. It turns out to be $z=2$ and this allows to fully characterize the SQCP for dimensions $d \ge 2$.