Abstract
We describe boundary effects in superconducting systems with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting instability, using Bogoliubov-de-Gennes and Ginzburg-Landau (GL) formalisms. First, we show that in dimensions larger than one the standard 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 cuboid sample of a 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 faces 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.
Highlights
Fulde and Ferrell [1] and Larkin and Ovchinnikov [2] (FFLO) considered a superconducting state where a Cooper pair forms out of two electrons with different magnitude of momenta
Later it was shown that in other physical systems the fermionic imbalance occurs without any applied magnetic field
In the recent work [20], using microscopically derived Ginzburg-Landau (GL) model, it was shown that systems that support FFLO superconductivity in the bulk do not undergo a direct superconductor-normal metal phase transition
Summary
Fulde and Ferrell [1] and Larkin and Ovchinnikov [2] (FFLO) considered a superconducting state where a Cooper pair forms out of two electrons with different magnitude of momenta. In the recent work [20], using microscopically derived Ginzburg-Landau (GL) model, it was shown that systems that support FFLO superconductivity in the bulk do not undergo a direct superconductor-normal metal phase transition. By increasing the temperature and fermionic population imbalance in a square system, at the mean-field level, the system will undergo the following sequence of the phase transitions: superconducting bulk → superconducting edges → superconducting corners → normal state. We demonstrate an alternative, simpler Ginzburg-Landau expansion in the presence of boundaries, which exhibits the boundary pair-density-wave state but does not capture the same sequence of phase transitions. In the Appendix we confirm the existence of the boundary pair-density wave by solving a more general BdG including Hartree terms
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