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The effect of quasiparticle-self-energy on
Cd2Re2O7 superconductor
Bozidar Mitrovic
Department of PhysicsBrock University
St. Catharines, Ontario, Canada
Ottawa, June 15, 2016
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Outline
Tunneling junction spectroscopy and point-contact spectroscopyof superconductors
Blonder-Tinkham-Klapwijk (BTK) theory of point-contacts
Previous attempts to include the quasiparticle lifetime effects inthe BTK theory
BTK theory with self-energy effects
Application to point-contact spectroscopy of Cd2Re2O7
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Co-Investigators
Yousef Rohanizadegan, Brock (MSc Thesis)
F. Razavi, M. Hajialamdari and M. Reedyk, Brock
R. Kremer, MPI & Brock
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Tunneling junction spectroscopy
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Tunneling junction spectroscopy
Problems: It is difficult to make good tunneling junctions with
superconductors which have complicated structure and a shortcoherence length.
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Point-contact spectroscopy
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory
The BTK theory is based on:
1. Bogoliubov equations
− ~2
2m
d2
dx2− µ+ V (x) ∆
∆~2
2m
d2
dx2+ µ− V (x)
(
uv
)
= i~∂
∂t
(
uv
)
∆=0 in N, ∆ 6=0 in S
2. Demers-Griffin model for the N-S interface: V (x) = Hδ(x)
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory
Stationary plane wave solutions
(
u(x, t)v(x, t)
)
=
(
u0
v0
)
e~kx−Et/~
E =
√
(~2k2
2m− µ)2 +∆2
u20 =
1
2
[
1 +
√E2 −∆2
E
]
= 1− v20
Density of states N(E) = Re[
(u20 − v20)
−1]
= ReE√
E2 −∆2
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory
6: Andreev reflection
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory
Z =H
~vF
metallic contact: Z=0
tunneling regime: Z ≥5
GNS =dINS
dV= 2N(0)evFA
∫ +∞
−∞
dEdf(E − eV )
dV[1 +A(E)−R(E)]
Fit parameters: ∆ and Z
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Experiments
Au-Nb point contact
(a) 10-Ω contact resistance
(b) 3-Ω contact resistance
Note: Experimental curves are broadened BTK curves
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Dynes formula and phenomenological extention of the
BTK theory
Dynes formula (PRL 41, 1509 (1978)):
ND(E) = ReE − iΓ
√
(E − iΓ)2 −∆2
Eliashberg theory:
N(E) = ReE
√
E2 −∆2(E), ∆(E) = ∆1(E) + i∆2(E)
Mitrovic & Rosema (J. Phys.: Condens. Matter 20, 015215 (2008)):
quasiparticle lifetime Γ = − Im∆(E = ∆0)
When Γ,∆2 ≪ ∆ ND(E) and N(E) give nearly identical results
(except near E=0). Nevertheless ND(E) is wrong!
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Dynes formula and phenomenological extention of the
BTK theory
Phenomenological extension of the BTK theory to include finitequasiparticle lifetime:
(
u(x, t)v(x, t)
)
=
(
u0
v0
)
e~kx−(E−iΓ)t/~
The resulting theory is identical to the BTK theory but with the density
of states given by the Dynes formula.
Fit parameters: ∆, Z and Γ
(Plecennık et al., PRB 49, 10016 (1994); de Wilde et al., Physica B
218, 165 (1996))
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory with self-energy in S
McMillan, Phys. Rev. 175, 559 (1968): Eliashberg version ofBogoliubov Equations
[− ~2
2m
d2
dx2− µ]τ3 +Σ(x,E)
(
u(x,E)v(x,E)
)
= E
(
u(x,E)v(x,E)
)
Σ(x,E) = (1− z(x,E))τ0 + φ(x,E)τ1 , ∆(x,E) =φ(x,E)
z(x,E)
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory with self-energy in S
The resulting theory is identical to the BTK theory but with complex
and energy dependent gap ∆(E)
GNS =dINS
dV= 2N(0)evFA
∫ +∞
−∞
dEdf(E − eV )
dV[1 +A(E)−R(E)]
A(E) =|u|2|v|2|γ|2
R(E) =[|u|4 + |v|4 − 2Re(u2v2)]z2(z2 + 1)
|γ|2γ = u2 + (u2 − v2)z2
u =1√2
√
1 +√
E2 −∆2(E)/E
v =1√2
√
1−√
E2 −∆2(E)/E .
(Y. Rohanizadegan, MSc. Thesis, Brock University (2013))
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
BTK theory with self-energy in S
For the energies close to the gap edge ∆ the fit parameters are:
∆, Z and ∆2–the imaginary part of gap at the gap edge
Note: The temperature enters via ∆ and ∆2
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Application to Cd2Re2O7
Razavi, Rohanizadegan, Hajialamdari, Reedyk, Kremer, and Mitrovic,
Canadian Journal of Physics, 2015, 93(12), pp. 1646-1650 –
Canadian Journal of Physics Best Paper Award, 2015.
-0.001 0.000 0.001
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Nor
mal
ized
Con
duct
ance
Voltage (mV)
0.580(1) K 0.646(2) K 0.744(1) K 0.831(4) K 0.874(4) K
0.945(6) K 0.976(1) K 1.015(2) K Temperature
0.360(2) K 0.420(5) K 0.571(2) K
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Application to Cd2Re2O7
Fits:
T=0.831 K: A–with ∆2, B–with Γ
T=0.360 K: C–with ∆2, D–with Γ
0.96
1.00
1.04
1.08
A
Nor
mal
ized
con
duct
ance
B
D
-0.001 0.000 0.0010.7
0.8
0.9
1.0
1.1
1.2
C
Nor
mal
ized
Con
duct
ance
Voltage (V)
-0.001 0.000 0.001
Voltage (V)
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Application to Cd2Re2O7
∆ and ∆2 ∆ and Γ
0.2 0.4 0.6 0.8 1.00.00
0.05
0.10
0.15
0.20
0.25
0.2 0.4 0.6 0.8 1.0
E
nerg
y G
ap (m
eV)
Temperature (K)
Temperature (K)
2∆
kBTc=5.0(1) Tc=1.02 K
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
KOs2O6 (Photoemission Spectroscopy)
Shimojima et al. PRL 99, 117003 (2007), using Dynes formula:
2∆
kBTc≥4.56
Tc=9.6 K
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
∆(T ) of Cd2Re2O7 for different crystallographic planes
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.00
0.05
0.10
0.15
0.20
0.25
0.30
(001) plane (110) plane (111) plane (100) plane
Del
ta (m
eV)
Temperature (K)
The solid line is the BCS prediction with measured Tc and ∆(0).
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Comparison with other experiments
Specific heat:
Hiroi & Hanawa, J. Phys. Chem. Solids 63, 1021 (2002):
γexp
γband=2.63 ⇒ λ=1.63
Razavi et al., CJP 93, 1646 (2015)
Note:There is a kink at T =80 % Tc!
∆Ce
γTc=1.15 < the BCS value of 1.43
⇓
anisotropic/multiband supercond. (?)
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Comparison with other experiments
Far-IR:
Hajialamdari et al., J. Phys.: Condens. Matter 24, 505701 (2012)
New peaks appear in the superconducting state at T =0.5 K (< 0.8
K)!
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy
Possible scenario
There is a structural transition in Cd2Re2O7 below Tc (at 0.8 K)similar to the transition in KOs2O6. The new low frequency phonon
modes appear which couple strongly to the electrons leading to a
large low temperature ∆.
B. Mitrovic The Lifetime Effects in Point-Contact Spectroscopy