Two-fold symmetry of in-plane magnetoresistance anisotropy in the superconducting states of BiCh2-based LaO0.9F0.1BiSSe single crystal

Recently, two-fold symmetric in-plane anisotropy of the superconducting properties have been observed in a single crystal of BiCh2-based (Ch: S, Se) layered superconductor LaO0.5F0.5BiSSe having a tetragonal (four-fold-symmetric) in-plane structure; the phenomena are very similar to those observed in nematic superconductors. To explore the origin of the two-fold symmetric anisotropy in the BiCh2-based system, we have investigated the electron-doping dependence on the anisotropy by examining the in-plane anisotropy of the magnetoresistance in the superconducting states for a single crystal of LaO0.9F0.1BiSSe under high magnetic fields up to 15 T. We observed a two-fold symmetry of in-plane anisotropy of magnetoresistance for LaO0.9F0.1BiSSe. The results obtained for LaO0.9F0.1BiSSe are quite similar to those observed for LaO0.5F0.5BiSSe, which has a higher electron doping concentration than LaO0.9F0.1BiSSe. Our present finding suggests that the emergence of the in-plane symmetry breaking in the superconducting state is robust to the carrier concentration in the series of LaO1-xFxBiSSe.

show the in-plane anisotropy of magnetoresistance for LaO 0.9 F 0.1 BiSSe with a smaller electron doping concentration than LaO0.5F0.5BiSSe. As similar to the previous study, the magnetoresistance of the present sample also showed two-fold-symmetric behavior in the superconducting state, suggesting the universal behavior of nematic-superconductivity-like phenomena is in the LaO1-xFxBiSSe systems. This study shows that the BiCh2-based compound family will be a useful platform to study the physics and chemistry of nematic superconductivity in layered materials.

Experimental details
LaO0.9F0.1BiSSe single crystals were grown by a high-temperature flux method in an evacuated quartz tube. Polycrystalline LaO 0.9 F 0.1 BiSSe was prepared using the solid-statereaction method using powders of La 2 O 3 (99.9%), La 2 S 3 (99.9%), Bi 2 O 3 (99.999%), and BiF 3 (99.9%) and grains of Bi (99.999%) and Se (99.999%) [25]. A mixture of the starting materials was mixed with a nominal ratio of LaO0.9F0.1BiSSe, pressed into a pellet and annealed at 700 ºC for 20 h in an evacuated quartz tube. The polycrystalline LaO0.9F0.1BiSSe (0.62 g) were mixed with CsCl flux (2.2 g), and the mixture was sealed into an evacuated quartz tube. The tube was heated at 900 ºC for 12 h, slowly cooled to 645 ºC with a rate of 1.0 ºC /h, and furnace-cooled to room temperature. After furnace cooling, the quartz tube was opened under air atmosphere, and the product was filtered and washed with pure water. The chemical composition of the obtained crystal was investigated using energy-dispersive X-ray spectroscopy (EDX) spectroscopy. The average compositional ratio of the constituent elements (except for O and F) was estimated to be La : Bi : S : Se = 1 : 0.99 : 0.93 : 1.0, which was normalized by the La value. The analyzed atomic ratio is almost consistent with the nominal composition LaO0.9F0.1BiSSe. Considering the typical detection error in the EDX analysis, we regard the composition of the examined crystal as LaO0.9F0.1BiSSe.
The single crystals were ground with quartz powders to get homogeneous powders for the SXRD experiment [26]. The synchrotron powder X-ray diffraction (SXRD) was performed at the beamline BL02B2 SPring-8 at a wavelength of 0.495274 Å (proposal No. 2018B1246). The SXRD experiments were performed with a sample rotator system at room temperature; the diffraction data were collected using a high-resolution one-dimensional semiconductor detector (multiple MYTHEN system [27]) with a step size of 2 = 0.006º. The crystal structure parameters were refined using the Rietveld method with the RIETAN-EP software [28]. The schematic image of the crystal structure refined by the Rietveld refinement was depicted using the VESTA software [29].
The resistive anisotropy was investigated under magnetic fields up to 15 T using a superconducting magnet at the Institute for Materials Research (IMR) of Tohoku University To precisely investigate the anisotropy, a 3 He probe equipped with an accurate two-axes rotator system was used. The magnetic field perpendicular to the c-axis was applied. The electrodes were fabricated using Au wires and Ag pastes. we use the analysis result on the lattice constant for the confirmation that electron carrier has been doped in the crystal. As mentioned later, from the estimation of T c , we could assume that the carrier doping amount is close to the starting nominal value of x = 0.1. In the Rietveld refinement, we assumed that the in-plane Ch1 site [see Fig. 1(a)] was fully occupied by Se, and the Ch2 site was fully occupied by S, on the basis of the EDX analysis result and previous structural analysis [25]. The obtained reliable factor Rwp was Rwp = 11.5%. In fact, the 00l peaks and others related to c-axis direction are broadened and have a shoulder, which should be resulting in a slightly high

Results and discussion
Rwp. This may be due to the strain introduced during the sample preparation by grinding with quartz powders and the sticky nature of the crystals. However, the higher angle fitting with the tetragonal model (see the inset of Fig. 1) is quite nice. In addition, we did not obtain better Rwp with monoclinic model. Although the LaO1-xFxBiSSe phase undergoes a structural transition from tetragonal to monoclinic (P21/m), our recent study suggested that the transition is suppressed by 3% substitution of O by F [30]. Therefore, the crystal structure of the present crystal with nominal x = 0.1 can be regarded as tetragonal with four-fold symmetry in the conducting plane down to low temperature near Tc. These T c values are comparable to those observed for polycrystalline sanples with x = 0.1. Figure   3(a) shows the magnetic field dependence of resistance where the magnetic field perpendicular to the c-axis was applied. The superconducting states are suppressed with increasing magnetic field.  anisotropy measurement. To investigate the in-plane anisotropy in the superconducting states, the crystal was rotated using two rotation angles.  and  are defined as shown in Fig 4(b).  is defined as the formed angle from the c-axis to ab-plane and  is defined as the formed angle from the aaxis to the b-axis. The angle dependences of resistance were investigated for the superconducting states in between the onset and the zero-resistance states by tuning the temperature and magnetic field based on the obtained field-temperature phase diagram [ Fig. 3(b)]. Since the constant A related to the two-fold symmetry oscillation is clearly larger than B related to the four-fold symmetry, the appearance of the two-fold symmetry in the in-plane anisotropy of the upper critical field should be essential.
As introduced in the introduction, similar two-fold-symmetric in-plane anisotropy of magnetoresistance in the superconducting states has been observed for LaO0.5F0.5BiSSe. Since the present experiments revealed that LaO0.9F0.1BiSSe also exhibits the two-fold symmetry in the superconducting states, we conclude that the carrier concentration is not an essential parameter for the condition of the appearance of the phenomena in the LaO1-xFxBiSSe system. This fact surprised us because the Fermi surface topology is largely different between electron doping concentrations of x = 0.1 and x = 0.5 in the BiCh2-based compounds [32]. The phenomena similar to nematic superconductivity states in doped Bi2Se3 systems will motivate further experiments in LaO 1-x F x BiSSe and related systems. Although there are no theoretical studies predicting the emergence of nematic superconductivity in the BiCh 2 -based compounds, a theoretical study predicted the possible topological superconductivity in BiCh 2 -based systems [33]. Since the pairing mechanisms of the BiCh2-based superconductors have not been concluded [32], further theoretical and experimental investigations are needed, and the present result on the in-plane anisotropy of the superconducting states in LaO1-xFxBiSSe should be one of the key information for the goal.

Conclusion
We have investigated the transport properties of a single crystal of BiCh2-based superconductor LaO 0.9 F 0.1 BiSSe under high magnetic fields up to 15 T. From the c-axis electrical resistance (measured with a current along the c-axis), the upper critical field was determined. Also, the in-plane anisotropy of the electrical resistance was investigated using a 3 He probe equipped with a two-axes rotator system to investigate the in-plane anisotropy of magnetoresistance. From the in-plane anisotropy measurements, we observed two-fold symmetry of magnetoresistance in the superconducting states within the ab plane of LaO0.9F0.1BiSSe. Since the crystal possessed a tetragonal square plane with a tetragonal (four-fold) in-plane symmetry, the appearance of twofold symmetry indicates the rotational symmetry breaking in the superconducting states. The phenomena are very similar to those observed for LaO0.5F0.5BiSSe with a higher electron doping concentration. Therefore, we conclude that the carrier doping concentration, which affects the Fermi surface topology, is not an essential parameter for the emergence of the nematicsuperconductivity-like phenomena in LaO 1-x F x BiSSe. We hope that the results shown here are useful for further investigation on superconductivity pairing mechanisms of the BiCh 2 -based compounds and related studies on nematic superconductivity in layered systems.   The plotted data was fitted by the function of Asin(2 + )+Bsin(4 + ) + C.