Dimensional Crossover of the Fulde–Ferrell–Larkin–Ovchinnikov State in Strongly Pauli-Limited Quasi-One-Dimensional Superconductors

Abstract

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in quasi-one-dimensional s-wave and d-wave superconductors with particular attention paid to the effect of the Fermi-surface anisotropy. The upper critical field H c2 (T ) is found to exhibit a qualitatively different behavior depending on the ratio of the hopping energies t b /t a and the direction of the FFLO modulation vector q, where t a and t b are the intra-and interchain hopping energies, respectively. In particular, when t b /t a < ∼ 0.1 and q a, we find a novel dimensional crossover of H c2 (T ) from one dimension to two dimensions, where a is the lattice vector of the most conductive chain. Just below the tricritical temperature T * , the upper critical field H c2 (T ) increases steeply as in one-dimensional systems, but when the temperature decreases, the rate of increase in H c2 (T ) diminishes and a shoulder appears. Near T = 0, H c2 (T ) shows a behavior typical of the FFLO state in two-dimensional systems, i.e., an upturn with a finite field at T = 0. When the angle between q and a is large, the upper critical field curve is convex upward at low temperatures, as in three-dimensional systems, but the magnitude is much larger than that of a three-dimensional isotropic system. For t b /t a > ∼ 0.15, the upper critical fields exhibit a two-dimensional behavior, except for a slight shoulder in the range of 0.2 > ∼ t b /t a > ∼ 0.15. The upper critical field is maximum for q a both for s-wave and d-wave pairings, while it is only slightly larger than the Pauli paramagnetic limit for q ⊥ a. The relevance of the present results to the organic superconductor (TMTSF) 2 ClO 4 is discussed.

Peculiarities of the orbital effect in the Fulde-Ferrell-Larkin-Ovchinnikov state in quasi-one-dimensional superconductors

“…As it was shown in Ref. [45], if the corrugation of the Fermi surface due to the interchain coupling is taken into account, the system looses its 1D character at T → 0 resulting in the finite value of the H c2 (T → 0). Figure 3 presents the normalized correction of T c = T c − T cP due to the orbital effect as a function of T cP /T c0 for different directions of the applied field.…”

Novel superconducting phenomena in quasi-one-dimensional Bechgaard salts

“…4. In particular, the onset curve for H a exhibits a peculiar "S" shape, a limited behavior at around 0.8 K and an increase again below 0.3 K. The behavior for H a resembles that observed in the pressure-induced superconductivity in (TMTSF) 2 PF 6 [147], and is recently theoretically treated within the FFLO scenario [133,135]. What is more, unusual modulation in in-plane field-angle φ dependence of T onset c is observed above 3.0 T. In particular, the maxima of the T onset c (φ) curve, which is located at φ = 0 • (H a) and φ = 90 • (H b ) at low fields, the latter is found to shift away from the crystalline b axis at high fields.…”

“…12(b). Indeed, it is theoretically shown that the FFLO state with q FFLO a generally acquires high T c in a Q1D system [135]. Observation of unusual phenomena resulting from the symmetry breaking with such a fixed q FFLO can be a hallmark of the Q1D FFLO state.…”

Simulating Artificial 1D Physics with Ultra‐Cold Fermionic Atoms: Three Exemplary Themes

“…However, in lower‐dimensional systems this detrimental effect is suppressed due to geometric constraints. [ 31,32,53 ] As a result, (quasi‐)1D systems are a good environment to search for the elusive FFLO state.…”