Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs

Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs

D. S. Inosov d.inosov@fkf.mpg.de Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany    J. S. White Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland    D. V. Evtushinsky Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    I. V. Morozov Moscow State University, Moscow 119991, Russia Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    A. Cameron School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK    U. Stockert Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    V. B. Zabolotnyy Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    T. K. Kim Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    A. A. Kordyuk Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany Institute for Metal Physics of the National Academy of Sciences of Ukraine, 03142 Kyiv, Ukraine    S. V. Borisenko Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    E. M. Forgan School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK    R. Klingeler Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    J. T. Park Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany    S. Wurmehl Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    A. N. Vasiliev Moscow State University, Moscow 119991, Russia    G. Behr Leibnitz Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany    C. D. Dewhurst Institut Laue-Langevin, 6 Rue Jules Horowitz, F-38042 Grenoble, France    V. Hinkov Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
Abstract

We report superconducting (SC) properties of stoichiometric LiFeAs ( K) studied by small-angle neutron scattering (SANS) and angle-resolved photoemission (ARPES). Although the vortex lattice exhibits no long-range order, well-defined SANS rocking curves indicate better ordering than in chemically doped 122-compounds. The London penetration depth  nm, determined from the magnetic field dependence of the form factor, is compared to that calculated from the ARPES band structure with no adjustable parameters. The temperature dependence of is best described by a single isotropic SC gap  meV, which agrees with the ARPES value of  meV and corresponds to the ratio , approaching the weak-coupling limit predicted by the BCS theory. This classifies LiFeAs as a weakly coupled single-gap superconductor, similar to conventional metals.

iron pnictide superconductors, small-angle neutron scattering, LiFeAs, penetration depth, coherence length, vortex phases
pacs:
74.70.Xa 61.05.fg 74.25.-q 74.25.Uv

In many of the recently discovered Fe-based superconductors (SC) KamiharaWatanabe08 (); RotterTegel08 (), a transition to the SC state is induced by chemical doping of a parent compound that at ambient conditions does not exhibit SC in its stoichiometric composition even at the lowest temperatures. Among the few known exceptions, the present record holder for the SC transition temperature, , is the stoichiometric LiFeAs ( K) WangLiu08 (); PitcherParker08 (); TappTang08 (). Others are low- superconductors NaFeAs ( K) ParkerPitcher09 (), FeSe ( K) ImaiAhilan09 (), LaFePO ( K) KamiharaHiramatsu06 (); FletcherSerafin09 (), and KFeAs ( K) SasmalLv08 (). The electronic structure of LiFeAs is quasi two-dimensional (2D) BandStructure () and supports superconductivity in the absence of any notable Fermi surface (FS) nesting or static magnetism BorisenkoZabolotnyy09 (). However, the presence of normal-state antiferromagnetic fluctuations has been suggested by As NMR measurements JeglicPotocnik10 (). Together with the weakness of the electron-phonon coupling predicted by the density functional theory JishiAlyahyaei10 (), this suggests that the SC pairing in this structurally simple compound possibly has the same magnetic origin as in higher- iron pnictides MazinSingh08 (); KurokiOnari08 (); InosovPark10 (). On the other hand, arguments advocating the phonon mechanism have also been raised recently KordyukZabolotnyy10 (). Therefore, to pinpoint the SC mechanism with certainty, details of the SC pairing symmetry and the coupling strength are required.

In a number of recent studies EskildsenVinnikov09 (); YinZech09 (); MagneticPinning (); InosovShapoval10 (), it was shown that doped iron arsenide superconductors are characterized by strong pinning of magnetic flux lines that precludes the formation of an ordered Abrikosov lattice. The role of the pinning centers can be played by magnetic/structural domains in the underdoped samples MagneticPinning (), by the dopant atoms themselves, such as Co or Ni, at higher doping levels InosovShapoval10 (), or by the electronic inhomogeneities that result from phase separation in some hole-doped 122-systems ParkInosov09 (). This served as our motivation to study the magnetic field penetration in a single crystal of stoichiometric LiFeAs, which possesses a non-magnetic ground state with tetragonal crystal symmetry, thus excluding all of the above-mentioned strong pinning mechanisms from consideration. In the following, we will compare these results with ARPES measurements of the electronic structure to establish the microscopic origin of the measured quantities.

(a, b) SANS diffraction patterns measured at
(a) Magnetic field dependence of the VL form factor at
ARPES spectra of LiFeAs measured on the double-walled electron-like M-barrel in the SC (a) and normal (b) states. (c) The integrated energy distribution curves (IEDCs) of the same spectra. (d) The low-temperature IEDC after normalization, fitted to the Dynes function.
Fig. 4 (color online).: ARPES spectra of LiFeAs measured on the double-walled electron-like M-barrel in the SC (a) and normal (b) states. (c) The integrated energy distribution curves (IEDCs) of the same spectra. (d) The low-temperature IEDC after normalization, fitted to the Dynes function.

Next, we turn to the temperature evolution of the form factor. As follows from Eq. (2), for , . The scattered intensity therefore scales . In Fig. Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs (b), the measured integrated intensity is plotted as a function of temperature, and the vertical axis is scaled to the value of that resulted from the low-temperature fit of the form factor. By fixing and to the values found previously, we can now fit the two SC gaps and the coefficients , using as the fitting function. It turns out that independently of the parameter initialization, the fit converges to a single value of the gap  meV. This value of the energy gap corresponds to the ratio , approaching the weak-coupling limit of 3.53 predicted by the BCS theory of conventional superconductivity BCS57 (). For comparison, corresponding to a -wave gap is also shown in the same figure, producing a poor fit. This essentially excludes the possibility of two-gap SC or gap nodes in LiFeAs.

Now we compare these results with those of ARPES, to establish their relationship to the microscopic electronic properties, such as band dispersion and the SC gap. An analysis of the leading edge shift along the FS contours implies an isotropic gap for every FS sheet BorisenkoZabolotnyy09 (). To quantify the low-temperature gap value , we employed the Dynes function fitting procedure DynesNarayanamurti78 () to the ARPES spectra measured on the double-walled electron-like M-barrel [Fig. Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs (a, b)]. The energy distribution curves integrated in a wide momentum window along the FS radius (IEDCs), measured in the SC state below 1 K and in the normal state at 23 K, are shown in Fig. Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs (c). In order to reveal the true shape of the spectrum in the SC state, the low-temperature IEDC was normalized by the Fermi-function-corrected normal state spectrum, as shown in Fig. Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs (d). The good quality of the Dynes-function fit confirms the robustness of such normalization. The resulting low-temperature value of  meV is in perfect agreement with that extracted above from the temperature dependence of .

The knowledge of the band dispersion together with the SC gap allows the calculation of macroscopic properties in the SC state with no adjustable parameters. The superfluid density at is proportional to the integral of Fermi velocity along the FS perimeter ChandrasekharEinzel93 (); EvtushinskyInosov09 (); KhasanovEvtushinsky09 (), and in the clean limit,

(6)

where , , , are physical constants, and is the -axis lattice parameter. Although the FS of LiFeAs consists of several electron- and hole-like sheets BorisenkoZabolotnyy09 (), for the evaluation of the integral (6) the renormalized Fermi velocity, extracted from ARPES data, can be well approximated by its average value of  eV Å. For the experimental LiFeAs band structure, this formula yields  nm, which is only slightly lower than our directly measured value. Similarly, at , the BCS coherence length is proportional to the ratio of Fermi velocity to gap magnitude, BCS57 (), which equals  nm in our case. This corresponds to the upper critical field  T, in agreement with direct measurements SongGhim10 ().

In summary, we have evaluated several important SC parameters of LiFeAs from two complementary experiments. We have demonstrated that its order parameter is isotropic and in contrast to the higher- ferropnictides EvtushinskyInosov09 () is characterized by a single SC gap  meV. This value is close to the BCS limit of , which indicates that LiFeAs is a weakly coupled single-gap superconductor, similar to conventional metals.

We thank B. Büchner and B. Keimer for their helpful suggestions and support, and acknowledge discussions with L. Boeri and S. A. Kuzmichev. Sample growth was supported by the DFG project BE 1749/12. SANS experiments were done with financial assistance from the EPSRC UK and MaNEP. I. V. M. acknowledges support from the Ministry of Science and Education of Russian Federation under the State contract P-279. ARPES spectra were measured with the “-ARPES” end station, using synchrotron radiation from the BESSY II storage ring in Berlin.

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Fig. 3.: (a) Magnetic field dependence of the VL form factor at  K, fitted to Eq. (2). (b) Temperature dependence of at  T. The vertical axis is scaled to the value of that resulted from the form-factor fit in panel (a). For comparison, for the -wave gap is shown by the dashed line.
Fig. 3.: (a) Magnetic field dependence of the VL form factor at  K, fitted to Eq. (2). (b) Temperature dependence of at  T. The vertical axis is scaled to the value of that resulted from the form-factor fit in panel (a). For comparison, for the -wave gap is shown by the dashed line.
Fig. 2 (color online).: (a, b) SANS diffraction patterns measured at and 0.5 T, respectively. The 0.25 T data are summed up over the rocking curve from to , whereas the 0.5 T data are shown for the zero rocking angle. Both datasets are smoothed with a 3-pixel FWHM Gaussian filter. (c) Angle-averaged diffracted intensity as a function of momentum transfer , measured at different magnetic fields between 0.25 T and 1.5 T. For clarity, the zero line of each curve is offset from the one below it. Vertical arrows show the expected peak positions for a perfect triangular lattice . Solid lines are Gaussian fits. (d) Averaged intensities on the left () and right () sides of the ring as functions of the rocking angle, measured at  T.
Fig. 2 (color online).: (a, b) SANS diffraction patterns measured at and 0.5 T, respectively. The 0.25 T data are summed up over the rocking curve from to , whereas the 0.5 T data are shown for the zero rocking angle. Both datasets are smoothed with a 3-pixel FWHM Gaussian filter. (c) Angle-averaged diffracted intensity as a function of momentum transfer , measured at different magnetic fields between 0.25 T and 1.5 T. For clarity, the zero line of each curve is offset from the one below it. Vertical arrows show the expected peak positions for a perfect triangular lattice . Solid lines are Gaussian fits. (d) Averaged intensities on the left () and right () sides of the ring as functions of the rocking angle, measured at  T.
Fig. 1 (color online).: (a) Magnetic susceptibility of LiFeAs, measured upon warming after cooling in magnetic field (FC) and in zero field (ZFC). (b) Photo of the sample prepared for SANS measurements inside the single-crystalline silicon box (see text).
Fig. 1 (color online).: (a) Magnetic susceptibility of LiFeAs, measured upon warming after cooling in magnetic field (FC) and in zero field (ZFC). (b) Photo of the sample prepared for SANS measurements inside the single-crystalline silicon box (see text).
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