Surface Pair-Density-Wave Superconducting and Superfluid States

Abstract

Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pairdensity-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.

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

“…state. The solutions are very similar to those obtain from the Ginzburg-Landau approach in [20], shown on the same figure.…”

“…Note however that, at a microscopic level, the mechanism of formation of surface states is substantially more complex than the simple energy argument given in [20]. As pointed out in [20], at the level of Ginzburg-Landau theory, the state has oscillatory energy density and boundaries are accompanied with beneficial energy segments. However the ability of the system to start with such a segment depends on microscopic boundary conditions applied at a single-electron level.…”

“…We see the appearance of regimes in the phase diagram, in which superconductivity does not exists in the bulk, but exists only on the boundaries. More specifically, we see two different surface states; (1) the surface-pair-density-wave state discussed in [20], and the surface superconducting state which can appear in conventional superconductors [27]. The crosses mark the points for which the pairing field is shown in Figure 4.…”

“…Since this term is of higher order in amplitude than the lowest order beneficial gradient term, there will exist inhomogeneous superconducting states for any α, as long as the gradient coefficients are negative. This term was used to find two-dimensional solutions in [20]. Here we derive from the microscopic theory the following estimate for the coefficient κ in Eq.…”

“…(i) We demonstrate this effect in microscopic models for imbalanced fermions without relying on a Ginzburg-Landau expansion. (ii) For a Ginzburg-Landau approarch, we explain that, as alluded in [20], in dimensions larger than one, it is necessary to retain more terms in the Ginzburg-Landau expansion than what is done in the standard calculations [21] to describe systems with boundaries. (iii) We show that a three dimensional cubic superconductor with imbalanced fermions, undergoes a sequence of phase transitions where superconductivity survives at sub-domains of sequentially lower dimensions.…”