Pair-density-wave superconductivity of faces, edges, and vertices in systems with imbalanced fermions

Abstract

We describe boundary effects in superconducting systems with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting instability, using Bogoliubov-de-Gennes and Ginzburg-Landau formalisms. Firstly, we show that in dimensions larger than one the standard Ginzburg-Landau (GL) functional formalism for FFLO superconductors is unbounded from below. This is demonstrated by finding solutions with zero Laplacian terms near boundaries. We generalize the GL formalism for these systems by retaining higher order terms. Next, we demonstrate that a cubic superconductor with imbalanced fermions, at a mean-field level has a sequence of the phase transitions. At low temperatures it forms Larkin-Ovchinnikov state in the bulk but has a different modulation pattern close to the boundaries. When temperature is increased the first phase transition occurs when the bulk of the material becomes normal while the surfaces remain superconducting. The second transition occurs at higher temperature where the system retains superconductivity on the edges. The third transition is associated with the loss of edge-superconductivity while retaining superconducting gap in the vertices. We obtain the same sequence of phase transition by numerically solving the Bogoliubov-de Gennes model.

The absence of superconductivity in the next-to-leading order Ginzburg-Landau functional for Bardeen-Cooper-Schrieffer superconductor

“…We note that our conclusions do not apply for spin imbalanced superconductors, where a higher-order generalizations of Ginzburg-Landau functional have energy minimizing solutions both for pair-density-wave states [24][25][26][27][28] and for homogeneous states [29].…”

Surface Pair-Density-Wave Superconducting and Superfluid States

“…In calculations of the two-dimensional system, the term 0.5|∇ψ| 4 was retained in the Ginzburg-Landau expansion, for details see Ref. [33].…”

Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited. Enhanced superconductivity at boundaries with and without magnetic field

“…Coulomb repulsion-induced boundary states were reported to form in certain cases in a threedimensional continuous model where the interaction was attractive for small and repulsive for higher energies [17]. Superconductivity enhancement in the form of pairdensity-wave (PDW) boundary states was found in spin imbalanced superconductors [20,21] as well.…”