Symmetry change of $d$-wave superconductivity in $\ensuremath{\kappa}$-type organic superconductors

Letter

Symmetry change of $d$ -wave superconductivity in $κ$ -type organic superconductors

S. Imajo, K. Kindo, and Y. Nakazawa

Phys. Rev. B 103, L060508 – Published 25 February 2021

Abstract

Magnetic-field-angle-resolved heat capacity of dimer-Mott organic superconductors $κ − {(BEDT − TTF)}_{2} X$ is reported (BEDT-TTF and $X$ represent bis(ethylenedithio)tetrathiafulvalene and a monovalent anion, respectively). Temperature and field dependence of heat capacity indicates that the superconductivity has line nodes on the Fermi surface, which is a typical feature of $d$ -wave superconductivity. In-plane field-angle dependence exhibits fourfold oscillations as well as twofold oscillations due to anisotropy of superconducting gap functions. From analyses of the fourfold term, the gap symmetry is determined as $d_{x^{2} - y^{2}} + s_{\pm}$ for $X = Cu [N {(CN)}_{2}] Br$ and $d_{x y}$ for $X = Ag {(CN)}_{2} H_{2} O$ . We suggest that the symmetry difference comes from the competition of $d_{x y}$ and $d_{x^{2} - y^{2}}$ antiferromagnetic fluctuations depending on lattice geometry.

Received 10 December 2020
Revised 9 February 2021
Accepted 16 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L060508

Physics Subject Headings (PhySH)

Superconducting order parameter Superconductivity

Organic superconductors

Specific heat measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Imajo ^1,2,*, K. Kindo², and Y. Nakazawa¹

¹Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
²The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan

^*imajo@issp.u-tokyo.ac.jp

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Vol. 103, Iss. 6 — 1 February 2021

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Figure 1
(a) Molecular arrangement of BEDT-TTF in the conducting plane of $κ − {(BEDT − TTF)}_{2} Cu [N {(CN)}_{2}] Br$ . (b) Fermi surface of $κ − {(BEDT − TTF)}_{2} X$ (red) in the first Brillouin zone (solid lines) and the extended Brillouin zone (dashed lines). As indicated, the axes $k_{x}$ and $k_{y}$ are defined according to the axes of the first Brillouin zone ( $k_{b}, k_{a}$ ) for $κ$ -Ag and $k_{a}$ and $k_{c}$ for $κ$ -Br, respectively. (c) The definition of magnetic field directions against the two-dimensional conducting plane of the sample. The polar angle $θ$ signifies the inclination from the plane, while the azimuthal angle $ϕ$ denotes the in-plane angle from the $a$ axis.
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Figure 2
(a) $C_{p} / T$ of $κ$ -Ag and $κ$ -Br as a function of squared temperature $T^{2}$ . For clarity, an offset is added to the data of $κ$ -Ag. The red squares denote the 0-T data, while the blue circles represent the data of the normal state in magnetic fields perpendicular to the conducting plane $H_{⊥}$ . The inset is an enlarged graph of (a) below $T^{2} = 4 K^{2}$ . The black solid lines are the linear fit to the data of the normal state. The open and solid symbols denote the data for $κ$ -Ag and $κ$ -Br, respectively. (b) Temperature dependence of the superconducting electronic heat capacity $C_{ele} / γ_{N} T$ . The dashed line indicates the electronic heat capacity of the normal state. The dotted lines indicate the quadratic temperature dependence of $C_{ele}$ . (c) Recovery of the low-temperature electronic heat capacity in fields. The top and bottom panels show the data for $κ$ -Ag and $κ$ -Br, respectively. The red circles (the left scale) represent the data in parallel fields, whereas the blue squares (the right scale) indicate those in perpendicular fields. The data of $κ$ -Br are taken from Ref. [25] (red circles), Ref. [10] (blue squares), and Ref. [26] (blue triangles). The black dashed curves signify the $\sqrt{H}$ dependence, and the colored thick curves are guides for the eye. (d) Polar-angle $θ$ dependence of heat capacity of $κ$ -Ag and $κ$ -Br. The solid and open symbols represent the obtained data and their mirrored reflection at $θ = 0^{\circ}$ confirm symmetric features. The solid and dashed curves are the fits to Eq. (1) with the displayed parameters $ε$ and $n$ .
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Figure 3
(a) Raw data of in-plane field-angle dependence of the heat capacity. The black curves are fits to the formula introduced in the text. (b) The fourfold oscillatory component derived from the data shown in (a) by subtracting the other components. The black curves for $κ$ -Ag (top panel) are fits to $C_{4} = C_{4}^{'} |\cos (2 ϕ)|$ , while those for $κ$ -Br (bottom panel) are fits to $C_{4} = C_{4}^{'} \cos (4 ϕ)$ . Since the $C_{4}$ term should not be expressed by such simple forms, the fittings are just approximations to describe the observed fourfold symmetry, leading to the difference of the fitting functions.
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Figure 4
(a) The amplitude of the fourfold oscillatory term in various fields as a function of reduced temperature $T / T_{c}$ . The positive (negative) value indicates that the maxima (minima) of the $C_{4}$ term are located at the directions of the crystal axes. (b) Schematic phase diagram of angle-resolved heat capacity for $d$ -wave superconductivity. In the red areas, the node positions are located at the directions of the minima of angle-resolved heat capacity. In the low-energy limit, namely, the low- $T$ and low- $H$ region, the node location corresponds to the minima of the $C_{4}$ term due to the predominant zero-energy Doppler effect [20, 21, 22]. The dotted curves indicate the region at which the sign of the $C_{4}$ term reverses and the amplitude of that becomes almost zero. (c) Determined positions of the gap nodes in the Fermi surface for $κ$ -Ag and $κ$ -Br. The green dots signify the position of the nodes.
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Physical Review B

covering condensed matter and materials physics

Symmetry change of $d$ -wave superconductivity in $κ$ -type organic superconductors

S. Imajo, K. Kindo, and Y. Nakazawa

Phys. Rev. B 103, L060508 – Published 25 February 2021

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Physical Review B

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Symmetry change of d-wave superconductivity in κ-type organic superconductors

S. Imajo, K. Kindo, and Y. Nakazawa

Phys. Rev. B 103, L060508 – Published 25 February 2021

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Symmetry change of $d$ -wave superconductivity in $κ$ -type organic superconductors