The effect of quasiparticle-self-energy on Cd2Re2O7 … · Outline Tunneling junction spectroscopy and point-contact spectroscopy of superconductors Blonder-Tinkham-Klapwijk (BTK)

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


Co-Investigators

Yousef Rohanizadegan, Brock (MSc Thesis)

F. Razavi, M. Hajialamdari and M. Reedyk, Brock

R. Kremer, MPI & Brock


Tunneling junction spectroscopy


Tunneling junction spectroscopy

Problems: It is difficult to make good tunneling junctions with

superconductors which have complicated structure and a shortcoherence length.


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)


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


BTK theory


BTK theory

6: Andreev reflection


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


Experiments

Au-Nb point contact

(a) 10-Ω contact resistance

(b) 3-Ω contact resistance

Note: Experimental curves are broadened BTK curves


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!


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))


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)



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))



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


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



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)



∆ 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


KOs2O6 (Photoemission Spectroscopy)

Shimojima et al. PRL 99, 117003 (2007), using Dynes formula:

2∆

kBTc≥4.56

Tc=9.6 K


∆(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).


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. (?)


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)!


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 ∆.


Documents

The effect of quasiparticle-self-energy on Cd2Re2O7 … · Outline Tunneling junction spectroscopy and point-contact spectroscopy of superconductors Blonder-Tinkham-Klapwijk (BTK)