Phonons, electron-phonon coupling and superconductivity in Mo Sb ...

Phonons, electron-phonon
coupling and superconductivity in
Mo 3
Sb 7
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
Sb 7
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
Sb 7
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
Sb 7
.
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.

to find an answer, we calculate the T c
using two formulas:
●
●
What is a mechanism of superconductivity in Mo 3
Sb 7
?
electron-phonon or electron-paramagnon interaction
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

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
Sb 7
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
Sb 7
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
Sb 7
●
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
Sb 7
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
Sb 7
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.