Multiband description of the upper critical field of bulk FeSe

Open Access

Multiband description of the upper critical field of bulk FeSe

M. Bristow, A. Gower, J. C. A. Prentice, M. D. Watson, Z. Zajicek, S. J. Blundell, A. A. Haghighirad, A. McCollam, and A. I. Coldea

Phys. Rev. B 108, 184507 – Published 6 November 2023

Abstract

The upper critical field of multiband superconductors can be an essential quantity to unravel the nature of superconducting pairing and its interplay with the electronic structure. Here we experimentally map out the complete upper critical field phase diagram of FeSe for different magnetic field orientations at temperatures down to $0.3 K$ using both resistivity and torque measurements. The temperature dependence of the upper critical field reflects that of a multiband superconductor and requires a two-band description in the clean limit with band coupling parameters favoring interband over intraband interactions. Despite the relatively small Maki parameter in FeSe of $α \sim 1.6$ , the multiband description of the upper critical field is consistent with the stabilization of a Fulde-Ferrell-Larkin-Ovchinnikov state below $T / T_{c} \sim 0.3$ . We find that the anomalous behavior of the upper critical field is linked to a departure from the single-band picture, and FeSe provides a clear example of where multiband effects and the strong anisotropy of the superconducting gap need to be taken into account.

Received 11 June 2023
Accepted 29 September 2023

DOI:https://doi.org/10.1103/PhysRevB.108.184507

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Multiband superconductivity Superconductivity

Unconventional superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Bristow¹, A. Gower ^1,*, J. C. A. Prentice², M. D. Watson^1,†, Z. Zajicek ¹, S. J. Blundell¹, A. A. Haghighirad ^1,3, A. McCollam^4,‡, and A. I. Coldea ^1,§

¹Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
²Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
³Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
⁴High Field Magnet Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands

^*Present address: Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
^†Present address: Diamond Light Source, Division of Science, Didcot OX11 0DE, United Kingdom.
^‡Present address: School of Physics, University College Cork, Ireland.
^§Corresponding author: amalia.coldea@physics.ox.ac.uk

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 108, Iss. 18 — 1 November 2023

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) and (b) Resistivity versus applied magnetic field for FeSe (S1) at different constant temperatures for $H | | c$ and $H | | (a b)$ , respectively. (c) and (d) Torque versus magnetic field at constant temperatures for $H | | c$ (T2) and $H | | (a b)$ (T1), respectively. The torque has arbitrary units. (e) Resistivity against applied magnetic field for FeSe (S2) at $\sim 0.35$ K at different angles in magnetic field. (f) Calculated Fermi surface of FeSe with experimental lattice parameters, shifted to match quantum oscillations data (as detailed in Fig. S3 in the SM) [6, 20, 21]. The colors in (f) reflect the variation of the Fermi velocity from 200 meV Å for an in-plane electron pocket to 23 meV Å for its related out-of-plane value. The corresponding anisotropy is $Γ = λ_{c} / λ_{a b} \sim$ 4.5.
Reuse & Permissions
Figure 2
(a) Upper critical fields of FeSe for $H | | c$ and $H | | (a b)$ obtained from transport (solid symbols) and torque measurements (open symbols) scaled against reduced temperature $T / T_{c}$ , where the superconducting transition temperature $T_{c}$ is 9.08 and 8.5 K, respectively. The blue and red lines are WHH fits for $H | | c$ and $H | | (a b)$ , respectively, using different $α$ values. (b) The temperature dependence of coherence lengths (left axis, blue and red) and anisotropy of the upper critical field (right axis, black). The $H_{c 2} (T \to 0)$ values were used to find the zero-temperature coherence lengths. The horizontal dashed line represents the 3D-2D crossover length of $\sim c / \sqrt{2}$ , where $c$ is the $c$ -axis lattice constant. Solid lines are a guide to the eye using the two-band model (described later). (c) Angular dependence of the superconducting upper critical field, $μ_{0} H_{c 2} (θ)$ at $0.35 K$ for different single crystals of FeSe (raw data are shown in Fig. S2 in the SM). The dotted black line is a fit to the 3D Ginzburg-Landau (GL) model, and the dashed black line represents a fit to the 2D Tinkham model [25], both for upper critical fields from resistivity data. The solid black and red lines are two-band fits to upper critical fields from resistivity and torque, respectively.
Reuse & Permissions
Figure 3
Upper critical fields of FeSe for (a) $H | | c$ (squares) and (b) and (c) $H | | (a b)$ (triangles). In (a) the dotted blue line corresponds to $s^{+ +}$ intraband pairing ( $λ_{11} = 0.81, λ_{22} = 0.29$ , and $λ_{12} = λ_{21} = 0.1$ ), the dashed red line corresponds to $s^{\pm}$ pure interband pairing ( $λ_{11} = λ_{22} = 0, λ_{12} = λ_{21} = 0.5$ ), and the solid black line corresponds to interband $s^{\pm}$ pairing with a dominant band ( $λ_{11} = 0.81, λ_{22} = 0$ , and $λ_{12} = λ_{21} = 0.5$ ). Here the $s^{\pm}$ interband model is best, with $α = 0$ and $η \sim 0.01$ . (b) Two-band models of the upper critical field when $H | | (a b)$ for the case where no FFLO state is present. The solid blue curve represents the $s^{+ +}$ case, the solid red curve represents the pure $s^{\pm}$ case, and the solid black curve represents the $s^{\pm}$ case with a dominant band [same band coupling parameters as in (a)]. (c) Two-band models when $H | | (a b)$ with the inclusion of an FFLO modulation. The curves represent the same cases as in (b), and the dashed lines of the same color are the FFLO modulation $Q / Q (0)$ (right axis) for each case. Again, the $s^{\pm}$ case with a dominant band offers the best description using $α = 1.6$ and $η \sim 0.02$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics