Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 51 (2018)

Superconducting gap symmetry in organic superconductorλ-(BETS)2 GaCl4 studied by µSR with DFT
D. P. Sari,∗1,∗2 H. Aizawa,∗3 T. Koretsune,∗4 H. Seo,∗5 and I. Watanabe∗2The superconducting gap symmetry determination inλ-(BETS)2 GaCl4 has been intriguing, since the superconducting state of this organic superconductor may
be linked to that of the isostructural compound, λ(BETS)2 FeCl4 , showing a ﬁeld-induced superconductivity in the ﬁelds > 17 T.1) We have performed transverse ﬁeld µSR in ﬁelds of 150 Oe down to 0.3 K at
ISIS Muon Facility in the UK. The temperature dependence of superﬂuid density was best described by
the s+d-wave with a dominant s-wave component.2)
Motivated by the µSR result, we have performed theﬁrst-principles electronic structure calculations with thegeneralized-gradient approximation on the basis of thedensity functional theory (DFT). The VASP software
package adopting the plane-wave basis set with cutoﬀ
energies of 500 meV was used. The ground state chargedensities were computed using 4 × 4 × 4 k-point sampling and crystal structure information from Ref. 3)
was used. Furthermore, we constructed maximally localized Wannier orbitals on BETS dimers to make thetight-binding energy band (dimer model) reproduce theband structure of DFT based on the experimental crystal data. The calculation was done by using the HOKUSAI RIKEN supercomputer.
Figure 1 shows the DFT band energy of λ(BETS)2 GaCl4 . Since the system has four BETS
molecules or two BETS dimers, contributing to the electronic properties, in one unit cell, there exist two bands
close to the Fermi level. Those two bands were well reproduced by the dimer model with the parameter transfer integral, in the unit of meV, as follows: tc = 64, td1= 52, td2 = 13, td3 = 76, td4 = 64, te = −17. Accordingly, the Fermi surface was consisting of an open sheet
and a closed pocket as shown in the bottom right panelof Fig. 1.
The superconducting gap was then calculated by using the Random Phase Approximation (RPA) method
following the extended Hubbard model,H=∑⟨i,j⟩tij c†iσ cjσ +∑i∑
U ni↑ ni↓ +Vij niσ njσ ,(1)⟨i,j⟩,σ,σ ′where t is the transfer integral, and U and V are
intra- and inter-dimer interactions. We assumed a spinﬂuctuation-mediated superconductor in the spin singletchannel. U = 0.2 eV was introduced in the calculationin order to investigate the low-energy interaction on theBETS dimer.4) The result is shown in Fig. 2 showingthat the red colored area is the result from RPA. More∗1
∗2
∗3
∗4
∗5

Department of Regional Environment Systems, Shibaura Inst.
of Tech.
RIKEN Nishina Center
Institute of Physics, Kanagawa University
Department of Physics, Tohoku University
Condensed Matter Theory Laboratory, RIKEN

Fig. 1. DFT band structures of λ-(BETS)2 GaCl4 . The tight-binding
band structure using a dimer model with parameter inter-dimertransfer integral tc − te is shown as a broken line. The upper rightpanel shows a 2 × 2 molecular arrangement of the a-c conducting

plane. The grey ellipse represents a BETS dimer and c–e represents inter-dimer transfer integral. The bottom right panel is theFermi surface.

α=1

α=2Fig. 2. Superconducting gap function from the band indexes 1 and2, which are bands from the open sheet and closed pocket Fermi
surface, respectively. The red and blue colored areas denote theRPA result and fitting result, respectively.

over, the pairing symmetry from RPA was then ﬁtted
to a linear combination of deﬁned pairing symmetries in
the k-space, with the basis functions as follows:
isotropic s-wave: fs0 (kx , ky ) = 1
extended s-wave: fs1 (kx , ky ) = 2[cos(kx ) + cos(ky )]dx2 −y2 -wave:fdx2 −y2 (kx , ky ) = 2[cos(kx )−cos(ky )]. (2)The ﬁtting result is shown in the blue-colored area ofFig. 2. We found that there exists a ﬁnite dx2 −y2 -wave
component in conjunction with s-wave components fromthe contribution of two bands mentioned above. However, this mixture symmetry of s + dx2 −y2 indicates only
one order parameter since the superconducting gap looks
almost continuous along the Fermi surface, as shown in
Fig. 2. Thus, from the µSR and DFT calculation weassign a new type of superconducting gap symmetry inλ-(BETS)2 GaCl4 , s + d-wave.
References
1) S. Uji et al., Syn. Met. 133–134, 481–483 (2003).
2) D. P. Sari et al., to be submitted.
3) H. Tanaka et al., J. Am. Chem. Soc. 121, 760–768 (1999).
4) C. Hotta, H. Fukuyama, J. Phys. Soc. Jpn. 69, 2577
(2000).

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