Phonons, electron-phonon coupling and superconductivity in Mo 3 from ab-initio calculations Małgorzata Sternik Department of Materials Research by Computers, Institute of Nuclear Physics, Polish Academy of Science, Kraków
Superconductivity happens when the charge carriers overcome their mutual repulsion and bind together into Cooper pairs. In conventional, low-temperature superconductors, phonons - quantized vibrations of the crystal lattice - are responsible for this pairing. Hg (1911)... MgB 2 (2001)... CeCu 2 Si 2 (1973) UBe 13 - (1983) UPt 3 (1984) PuCoGa 5 ( P.Piekarz et al., PRB 72,014521 (2005)) an unconventional mechanism with antiferromagnetic fluctuations Pairing between fermions can be either induced by phonons, magnons or mediated by some other boson field. Experimental arguments that the superconducting properties are not induced by phonons the quadratic temperature dependence of electrical resistivity Fermi energy considerably lower than ħω D
Mo 3 cubic bcc-structure (space group Im3m) a = 9.58 A Z=20 atoms in the primitive unit cell Mo (12e) with x=0.3432 Sb1 (12d) Sb2 (16f) with x=0.1624 A paramagnetic intermetallic compound Mo 3 is a type II superconductor with the critical temperature Tc 2.2 K. (Z.Bukowski, Wrocław 2002) The temperature characteristics of the specific heat, the superconducting gap, and the magnetic critical field suggest that the conventional electron phonon interaction might be responsible for the superconductivity. In 2007, Candolfi et al. argued that spin fluctuations (SFs) are present in Mo 3. This interpretation is supported by two unusual features: the quadratic temperature dependence of both electrical resistivity and magnetic susceptibility, (above Tc) the high value of the susceptibility at room temperature.
What is a mechanism of superconductivity in Mo 3? electron-phonon or electron-paramagnon interaction to find an answer, we calculate the T c using two formulas: the McMillan formula (electron-phonon coupling - EPC) the formula including the interaction of electron with paramagnons The electron-phonon coupling EPC constant - λ ph The electronic structure the electronic part of the EPC constant McMillan-Hopfield parameters η i The phonon dispersion relations the phonon part of the EPC constant <ω i2 >
Calculations of phonons Structure VASP package (G.Kresse) Density Functional Theory approach Pseudopotential: in the core region - the full-potential projector augmented wave (PAW) method, valence electrons for Mo atoms (4p 6 5s 1 4d 5 ) and Sb atoms (5s 2 5p 3 ) represented by plane wave expansions. The structure optimization was finished when residual forces were less than 10-5 ev/å. The Hellmann-Feynman forces arise when atoms are displaced from their equilirium positions. Dynamical properties Phonon software (K.Parlinski) From the Hellmann-Feynman forces the dynamical matrix is calculated. The diagonalization of the dynamical matrix provides the phonon frequencies and polarization vectors. The number of necessary displacements is determined by the symmetry of structure and by the number of nonequivalent atoms. The value of displacement is chosen to generate the H-F forces larger than computational noise. The obtained dispersion relations are accurate when a supercell sizes are large enough to assure that the force constants fall sufficiently with distance.
Phonons in Mo 3 calculated measured a(a) 9.64 9.58 Mo (0.3421,0,0) (0.3432,0,0) Sb1 (0.25,0,0.5) (0.25,0,0.5) Sb2 (0.1608,0.1608,0.1608) (0.1624,0.1624,0.1624) M Mo = 95.940 M Sb = 121.750 three characteristic maxima of the phonon DOS 2.8, 4.4 and 6.3 THz
Electronic structure Korringa-Kohn-Rostoker (KKR) multiple scattering method Bartłomiej Wiendlocha Janusz Toboła Stanisław Kaprzyk AGH University of Science and Technology, Kraków
the McMillan-Hopfield η i parameters EPC constant λ ph = 0.54 It qualifies Mo 3 as a medium coupling superconductor.
The influence of SFs on the superconducting critical temperature T c experimental T c = 2.2 K for Mo 3 a McMillan-type formula λ eff = λ ph = 0.54 the formula including the interaction of electron with paramagnons estimated λ sf = 0.03 The observed magnitude of the superconducting critical temperature can be explained taking into account the SF effects, but the λ sf parameter has to be relatively small.
Conclusions Superconductivity in Mo 3 is analyzed using the combined electronic structure and phonon calculations. The electron-phonon coupling constant λ ph = 0.54. This value explains very well the experimental value of T c = 2.2 K. The possible influence of spin fluctuations on the superconductivity in Mo 3 is found to be weak. B.Wiendlocha, J.Toboła, M.Sternik, S.Kaprzyk, K.Parlinski and A.M.Oleś, Phys. Rev. B 78, 060507 (2008)
Aknowledgment Krzysztof Parlinski Andrzej Oleś Paweł Jochym Jan Łażewski Przemek Piekarz Department of Materials Research by Computers, Institute of Nuclear Physics, Kraków Bartłomiej Wiendlocha Janusz Toboła Stanisław Kaprzyk AGH University of Science and Technology, Kraków
2.9 THz 4.6 THz 6.7 THz experimental phonon density of states measured by neutron scattering in ILL (not published) This result confirm our prediction 2.8, 4.4 and 6.3 THz.