Low superfluid density and possible multi-gap superconductivity in BiS{}_{2}-based layered superconductor Bi{}_{4}O{}_{4}S{}_{3}

Low superfluid density and possible multi-gap superconductivity in BiS-based layered superconductor BiOS

P. K. Biswas pabitra.biswas@psi.ch Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    A. Amato Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    C. Baines Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    R. Khasanov Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    H. Luetkens Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    Hechang Lei Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    C. Petrovic Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA    E. Morenzoni elvezio.morenzoni@psi.ch Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

The magnetic penetration depth as a function of temperature in BiOS was studied by muon-spin-spectroscopy measurements. The superfluid density of BiOS is found to be very low. The dependence of on temperature possibly suggests the existence of two -wave type energy gaps with the zero-temperature values of 0.93(3) and 0.09(4) meV. The upturn in the temperature dependence of the upper critical field close to further supports multi-gap superconductivity in BiOS. The presence of two superconducting energy gaps is consistent with theoretical and other experimental studies. However, a single-gap -wave model fit with a gap of 0.88(2) meV can not be ruled out completely. The value of at  K is estimated to be nm, one of the largest of all known layered superconductors, reflecting a very low superfluid density.

74.25.F-, 74.25.Ha, 76.75.+i
thanks: Present address: Frontier Research Center, Tokyo Institute of Technology, 4259 Nagatsuta, Midori, Yokohama 226-8503, Japan.

Recent years have witnessed a growing interest in superconductivity within layered crystal structure compounds. The recent discovery of superconductivity in the BiS-based compound BiOS Mizuguchi1 (); Singh () with a transition temperature () of  K has further fostered the research interest in layered superconductors. Exotic superconductivity with higher and/or with unconventional pairing mechanism has often been found in materials with a layered crystal structure. In this context, the most familiar examples are the high- cuprates and the Fe-based superconductors, where the corresponding CuO or FeAn (An = P, As, Se, Te) layer plays an important role in determining the superconducting properties Bednorz (); Kamihara (); Hsu (). Similarly, the BiS layer is believed to be the basic building block for inducing superconductivity in BiOS and it is expected that the doping mechanism resembles that of cuprates and Fe-based superconductors. This argument is supported by the discovery of other BiS-based superconductors ReOFBiS (Re = La, Ce, Pr, and Nd) with values of 10.6, 3.0, 5.5, and 5.6 K, respectively Mizuguchi2 (); Xing (); Jha (); Demura ().

Up to now, only very few theoretical and experimental studies have been performed on BiOS. The parent phase (BiOS) is a band insulator which becomes superconducting after electron doping Mizuguchi1 (). A first principles band structure calculation indicates that the superconductivity in BiOS originates from two Bi 6 orbitals, as they intersect the Fermi surface Usui (). A RPA analysis of a two-orbital model for the BiS-based superconductors suggests that the spin fluctuations promote competing and superconducting states with similar pairing strengths Martins (). Transport measurements under pressure reveal that of BiOS decreases monotonically without distinct change of the normal state metallic behavior Kotegawa (). The exact nature of the superconducting state is still debated. Hall, Seebeck coefficients, and magnetoresistance measurements suggest exotic multi-band features in BiOS Tan (). Recent measurements of the temperature dependence of the magnetic penetration depth using the tunnel diode oscillator technique Shruti () indicate a conventional s-wave type superconductivity in BiOS. However, the tunnel diode data were collected only down to 1.6 K and hence remain elusive in determining the true symmetry of the superconducting order parameter in BiOS. Other experiments reported very strong coupling superconductivity with and with a large region of superconducting fluctuations above surviving at large magnetic fields Li () or impurity driven superconductivity Sathish () In this respect it is important to characterize the superconducting and magnetic properties of BiOS at a microscopic level and to obtain a detailed knowledge of the superconducting order parameter over the full temperature range.

In this Rapid Communication, we report on the results of muon-spin rotation and relaxation (SR) studies of the magnetic penetration depth as a function of temperature and on the symmetry of the superconducting gap in the BiOS superconductor. Our results show that the superfluid density in BiOS is very low. The observed is found to be well described by a two-gap -wave model, as seen in many layered Fe-based superconductors. A single s-wave gap model is also able to give a satisfactory fit of the data, albeit with lower statistical significance. For the two-gap model, the gap values at absolute zero are ,  meV, respectively. The corresponding gap to ratios are and . These values are close to those obtained for various Fe-based superconductors (see Ref. Biswas3, and references therein). We obtain the penetration depth,  nm.

Polycrystalline samples of BiOS were prepared by a solid state reaction method Mizuguchi1 (). Sample characterization measurements were performed at the Brookhaven National Laboratory, USA. Transport measurements at different applied fields were performed at the Paul Scherrer Institute (PSI), Villigen, Switzerland. Zero-field (ZF) and transverse-field (TF) SR experiments were carried out on the DOLLY and LTF SR instruments, located respectively at the E1 and M3 beamlines at PSI. The sample in the form of a pressed pellet was mounted on a copper fork-shaped sample holder in the DOLLY and on a silver plate in the LTF instrument. The sample was cooled from above to base temperature at during ZF-SR measurements and in a field of 300 Oe in TF-SR measurements. The typical counting statistics were million muon decays per data point. The ZF- and TF-SR data were analyzed using the free software package MUSRFIT Suter ().

Figure 1: (Color online) (a) Temperature dependence of the ac resistivity of BiOS. Inset shows the temperature variation of the resistivity in a set of magnetic fields of 0, 0.05, 0.1, 0.2, 0.4, 1, 2, 4, 6, 8, 10, 15, 20, 30, and 40 kOe. (b) Temperature dependence of the upper critical field of BiOS. The solid line is a fit to the data using an expression for charged boson. The dotted line is an empirical interpolation, which better reproduces the temperature region close to .

The ac resistivity of BiOS was measured as a function of temperature using a standard four-probe method in a Physical Property Measurement System (PPMS). Figure 1 (a) shows the temperature dependence of the resistivity . A metallic like behavior is observed between 5 K to 220 K with a relatively high residual resistivity value of 2 m.cm. The transition to the superconducting state is relatively sharp with a  (onset) of 4.8(1) K and  (zero) of 4.6(1) K. The inset shows the temperature variation of the resistivity in a set of magnetic fields from 0 to 40 kOe. exhibits positive magnetoresistance (MR) in the normal state (just above ). At 6 K, the value of MR increases by for an applied magnetic field of 40 kOe. The temperature dependence of the upper critical field shown in Fig. 1 (b), was determined from the resistive transitions, defined by a drop of the normal state resistivity values, determined just above . The curve shows a positive curvature close to and is linear thereafter. A similar behavior has also been observed in polycrystalline borocarbides Shulga (), MgB Shigeta (); Takano (), NbRe Karki (), and ReBiswas () and is considered as a signature of multi-gap superconductivity. A conventional Werthamer-Helfand-Hohenberg model can not describe of BiOS. However, to estimate at absolute zero, a fit to the data was made using the expression for charged bosons Micnas (),


The fit yields  kOe, which implies a Ginzburg coherence length  nm. To get a better estimation of close to , an empirical interpolation (shown as a dotted line in Fig. 1 (b)) was later used in Eq. 4 for calculating the temperature dependence of the penetration depth of BiOS.

Figure 2: (Color online) ZF-SR time spectra collected at 2 K and 6 K for BiOS. The solid lines are the fits to the data using the Eq. 2, described in the text.

ZF-SR measurements were performed to look for any unusual temperature-dependent relaxation processes, which may be associated with the onset of superconductivity. Figure 2 shows the ZF-SR time spectra of BiOS, collected below (at 2 K) and above (at 6 K) . Practically, no difference between the two data sets is observable. The ZF data can be described using a Kubo-Toyabe relaxation function Kubo () multiplied by an exponential decay function,


where is the initial asymmetry, and and are muon spin relaxation rates. In the fit, was kept as a common parameter for both set of data. The fits yield,  s,  s, and  s. The value of extracted from the fits reflects the presence of random local fields arising from the nuclear moments within BiOS. The nearly equal values of are consistent with the presence of diluted and randomly oriented electronic moments probably arising from impurities. The ZF-SR data completely rule out the presence of any magnetic anomaly in the superconducting state of BiOS as for instance the appearance of spontaneous magnetic fields associated with a time-reversal-symmetry breaking pairing state.

Figure 3: (Color online) TF-SR time spectra of BiOS collected at 19 mK and 5 K in a transverse field of 300 Oe. The solid lines are the fits to the data using the Eq. 3, described in the text.

Figure 3 shows the TF-SR time spectra collected at 19 mK and 5 K in a transverse field of 300 Oe. At 5 K, the sample is in the normal state and the local field probed by the muons is the applied field slightly broadened by the nuclear moments contribution, which is responsible for the weak relaxation of the precession signal. By contrast, the data collected at 19 mK shows a more pronounced damping due to the inhomogeneous field distribution generated by the formation of a vortex lattice in BiOS. The TF-SR time spectra were analyzed using Gaussian damped spin precession signal along with an exponential relaxation to take into account the corresponding component observed in the ZF spectra.


where and (0) are the initial asymmetries of the sample and background signals,  kHz/G is the muon gyromagnetic ratio Sonier (), and are the internal and background magnetic fields, is the initial phase of the muon precession signal, and and are the Gaussian and exponential muon spin relaxation rates, respectively. Since the ZF data indicate that the exponential relaxation rate is temperature independent, we use as a global common parameter in the TF-SR data fitting and obtain a value of 0.038(3) s. The background signal mainly comes from the silver sample holder where the relaxation rate is negligible.

Figure 4: (Color online) The temperature dependence of of BiOS for an applied field of 300 Oe. The dotted line parallel to the temperature axis shows the temperature independent value of , the nuclear magnetic dipolar contribution to .

Figure 4 shows the temperature dependence of for an applied field of 300 Oe. The Gaussian muon spin relaxation rate is proportional to the second moment of the internal field distribution sensed by the muons and can be expressed as , where is the contribution due to the inhomogeneous field distribution in the vortex state and  s is the nuclear magnetic dipolar contribution which is assumed to be temperature independent.

For a superconductor with hexagonal vortex lattice, is related to the penetration depth, by the Brandt equation Brandt2 (), which is based on a Ginzburg-Landau treatment of the vortex state,


Here is a reduced magnetic field and is the first moment of the field distribution, which in our case is very close to the applied field. Equation 4 was used to calculate , which is proportional to the superfluid density. Figure 5 shows the temperature dependence of for BiOS. The fits to the data were then made with a single- and a two-gap -wave model using the following functional form Carrington (); Padamsee ():


where is the value of the penetration depth at  K, is the value of the -th ( or 2) superconducting gap at  K and is the weighting factor of the first gap.

Each component of Eq. 5 can be expressed within the local London approximation (Tinkham (); Prozorov () as


where is the Fermi function, and . The temperature dependence of the gap is approximated by the expression  Carrington ().

Figure 5: (Color online) Temperature dependence of for BiOS. The curves are fits to the data using a (a) single- and (b) a two-gap -wave model.

The curves shown in Fig. 5 (a) and (b) are the fits to the data using the two models. Table 1 summarizes the corresponding fitted parameters. The two s-wave gap model gives a lower value than a single gap model thus suggesting that BiOS is a multiple gap superconductor and making a connection between BiS-based layered superconductors and the layered Fe-based superconductors Khasanov (); Biswas2 (); Biswas3 (); Paglione (). Other prominent examples of superconductivity are represented by MgB, NbSe, and LuFeSi Choi (); Yokoya (); Nakajima (); Biswas4 (). However, a single -wave gap can not be ruled out completely as claimed in ref. Shruti, .

From our data, we obtain nm. Remarkable is that the value of lambda at  K is one of the highest among all known bulk superconductors. This reflects a very low superfluid carrier density of cm. It should be noted that the value of is independent on details of analysis such as the correction for the field dependence of and it is not strongly dependent on the assumption of a vortex lattice of hexagonal symmetry. The assumption of a regular vortex structure is generally valid in the FC case if parameters such as the external field are chosen in a reasonable range and if the system is not extremely anisotropic. Having hexagonal or rectangular symmetry makes almost no difference in the value of the penetration depth and its temperature dependence. For instance, for a square arrangement the pre-factor of Eq. 4 would change only by 2 %. The effect of vortex disorder is more difficult to quantify exactly. Disorder would give an additional contribution to so that the estimated value for is actually an upper limit. Since the contribution of disorder adds quadratically to that of the intrinsic inhomogeneity of the vortex state we do not expect a big change of the value of . Even in systems, such as (FeCo)As where disorder may be important, measurements on the same system in the vortex state by TF-SR Williams () (sensitive to disorder) and in the Meissner state by low energy SR Ofer () (insensitive to this effect) gave very close results for and its temperature dependence.

Model Gap value Gap ratio
s-wave 0.88(2) 2.25(5) 1.7
s+s-wave 0.93(3), 0.09(4) 2.38(7), 0.22(9) 1.3
Table 1: Fitted parameters of the fits to the data of BiOS using different models.

In summary, resistivity and SR measurements have been performed on superconducting BiOS. Temperature dependence of the upper critical fields and also the absolute value,  kOe were determined from the resistivity measurements. The data shows a positive curvature close to , which is a sign of multi-gap superconductivity in BiOS. ZF-SR data show no sign of magnetic anomaly in the superconducting ground state of BiOS. The temperature dependence of is compatible with a two-gap -wave model with the zero-temperature gap values, ,  meV and penetration depth,  nm. The presence of two superconducting gaps in BiOS is predicted by theoretical works such as first principles band structure calculations suggesting two band crossing the Fermi surface and the RPA analysis of a two-orbital model for the BiS-based superconductors Usui (); Martins (). Hall, Seebeck coefficients and magnetoresistance measurements also further support our experimental finding Li (); Tan (). It is worth mentioning that even though our data are more compatible with a two-gap model, a single-gap model can not be ruled out completely. Our results show that BiOS is a bulk superconductor with a fully developed node-less superconducting energy gap and extremely low superfluid density compared to other layered superconductors.

The SR experiments were performed at the Swiss Muon Source (SS), Paul Scherrer Institute (PSI, Switzerland). Work at Brookhaven is supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the DOE Office for Basic Energy Science (H.L. and C.P.). P.K.B. would like to acknowledge M. Medarde and R. Sibille for their assistance in the transport measurements.


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