Superconductivity in FeSe Thin Films Driven by the Interplay between Nematic Fluctuations and Spin-Orbit Coupling

Abstract

The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both s-wave and d-wave symmetries are equally favored, and Tc is consequently suppressed. However, the presence of a sizable spin-orbit coupling or inversion symmetry-breaking at the film interface lifts this harmful degeneracy and selects the s-wave state, in agreement with recent experimental proposals. The resulting gap function displays a weak anisotropy, which agrees with experiments in monolayer FeSe and intercalated Li1−x(OH)xFeSe.In most iron-based superconductors (FeSC), superconductivity is found in close proximity to a magnetically ordered state, suggesting that magnetic fluctuations play an important role in binding the Cooper pairs [1][2][3][4]. Indeed, the fact that the Fermi surface of these materials is composed of small hole pockets and electron pockets separated by the magnetic ordering vector led to the proposal of a sign-changing s +− wave state, in which the gap function has different signs in the hole and in the electron pockets. However, the recent observation of superconductivity over 70 K in monolayer FeSe brought new challenges to the field [5][6][7][8][9][10][11][12][13][14]. In contrast to the standard FeSC, no long-range magnetic order is observed in thin films or even bulk FeSe [15], and the Fermi surface of monolayer FeSe consists of electron pockets only [6,7,11,16]. Since T c in monolayer FeSe is the highest among all FeSC, the elucidation of its origin is a fundamental step in the search for higher T c in these systems.One of the proposed scenarios to explain the dramatic ten-fold increase of T c in monolayer FeSe with respect to the 8 K value in bulk FeSe [17] was the strong coupling to an optical phonon mode of the SrTiO 3 (STO) substrate [16,18,19], which is manifested by replica bands observed in ARPES [16]. Although such a coupling can certainly enhance T c [20][21][22][23][24], recent experiments indicate that the STO substrate may not be essential to achieve the high-T c state. In particular, T c up to 40 K was observed in electrostatically-gated films of FeSe with different thickness grown both on STO and MgO substrates [25]. Similar values of T c were reported in FeSe coated with potassium [26,27] and in the bulk sample Li 1−x (OH) x FeSe [28,29], which consists of intercalated FeSe layers. In common to all these systems is the fact that their Fermi surface consists of electron pockets only, suggesting that doping by negative charge carriers plays a fundamental role in stabilizing the high-T c state.Importantly, recent experiments in K-coated bulk FeSe [26] revealed that, besides shifting the chemical potential, electron-doping also su...

Structure of the pairing gap from orbital nematic fluctuations

“…Interestingly a similar feature of such quasidegeneracy of sand d-wave solutions was obtained also in the spin fluctuation mechanism [5,31]. In addition, the exact degeneracy between s-and d-wave symmetry was found when nematic fluctuations are assumed independent from momentum and frequency [37]. The third, fourth, and fifth largest eigenvalues in Fig.…”

Role of the orbital degree of freedom in iron-based superconductors

“…As one theoretical study shows, the coupling of the d xy orbital to the nematic order parameter is necessary for predicting the correct gap symmetry in FeSe. 50 On the other hand, the energy scale of the band reconstruction shows a strong momentum dependence, indicating that the anisotropy is unlikely to be dominated by the on-site occupation difference between the d xz and d yz orbitals. Instead, other mechanisms must be considered to correctly describe the momentum-dependence orbital anisotropy.…”

Constraints on the total coupling strengthto bosons in the iron based superconductors

“…Since the less correlated iron phosphides also achieve relatively small ’s, it is reasonable to infer that moderate correlations are somehow favorable for superconductivity. In addition to driving large ‐scale band renormalizations, the electronic interactions are also believed to drive pairing in the FeSCs through the formation of antiferromagnetic spin fluctuations or possibly other electronic mechanisms .…”

“…Other fundamental and still unresolved questions concern the role of retardation (frequency) and the particular momentum dependence of the interactions responsible for pairing (dominated for instance by specific nesting vectors or small momentum transfers . A full accounting of all of these effects in detail is practically impossible for the multi ‐band Fermi surfaces present in the FeSC; nevertheless, the effective mass of the quasiparticles near the Fermi level of a Fermi ‐liquid ‐like system can provide some insight into the overall strength of the many ‐body effects and the relevant interactions.…”