Two-Band Superconductors: Hidden Criticality Deep in the Superconducting State

Abstract

We show that two-band superconductors harbor hidden criticality deep in the superconducting state, stemming from the critical temperature of the weaker band taken as an independent system. For sufficiently small interband coupling γ the coherence length of the weaker band exhibits a remarkable deviation from the conventional monotonic increase with temperature, namely, a pronounced peak close to the hidden critical point. The magnitude of the peak scales as ∝γ-μ, with the Landau critical exponent μ=1/3, the same as found for the mean-field critical behavior with respect to the source field in ferromagnets and ferroelectrics. Here reported hidden criticality of multiband superconductors can be experimentally observed by, e.g., imaging of the variations of the vortex core in a broader temperature range. Similar effects are expected for the superconducting multilayers.

Finite temperature effective field theory and two-band superfluidity in Fermi gases

“…This peaked behavior of the coherence length and related quantities was also considered in Ref. [50], where it was referred to as "hidden criticality". The peaked behavior near T c,2 is most clearly revealed in the γ susceptibility of the order parameters, ∂Ψ j /∂γ.…”

“…In the limit |g j | → ∞ (corresponding to K → ∞), the divergence of the action S B is exactly compensated by (52) using (50), so that the part of the effective action depending on the pair fields Ψ j is regularized. On the contrary, the density-field action S χ unrestrictedly increases when K → ∞.…”

Experimentally observable signatures of odd-frequency pairing in multiband superconductors

“…the exchange of whole Cooper pairs between bands. [21][22][23][24][25][26] However, conceptually much simpler is single-quasiparticle scattering, or tunneling, between the superconducting bands. The origin of interband quasiparticle scattering can be impurity scattering, but a common intrinsic source is superconductivity associated with specific orbitals, which subsequently hybridize to form the low-energy bands around the Fermi surface.…”

Beyond the standard model of Ginzburg–Landau theory: multiband superconductors

“…We expect that in general the sum will converge for all T T 2c , but converge very slowly or diverge for T T 2c . Komendova et al 17 argue that there is a possibility of hidden criticality near T 2c which becomes critical in the limit that the coupling goes to zero. This feature is likely to be associated with the anomalous behavior of the GL gaps near this point, and is expected to prevent the series from converging below this point.…”