Theory of Lifetime Effects in Point-Contacts: Application to Cd 2 Re 2 O 7

Transcription

1 Theory of Lifetime Effects in Point-Contacts: Application to Cd 2 Re 2 O 7 Božidar Mitrović Department of Physics Brock University St. Catharines, Ontario, Canada McMaster, May 24, 2013

2 Outline Tunneling junction spectroscopy and point-contact spectroscopy of superconductors Blonder-Tinkham-Klapwijk (BTK) theory of point-contacts Previous attempts to include the quasiparticle lifetime effects in the BTK theory BTK theory with self-energy effects Application to point-contact spectroscopy of Cd 2 Re 2 O 7

3 Credits Yousef Rohanizadegan, Brock F. Razavi, M. Hajialamdari and M. Reedyk, Brock R. Kremer, MPI & Brock M. Przedborski and K. Samokhin, Brock

4 Tunneling junction spectroscopy

5 Tunneling junction spectroscopy Problems: It is difficult to make good tunneling junctions with superconductors which have complicated structure and a short coherence length.

6 Point-contact spectroscopy

7 BTK theory The BTK theory is based on: 1. Bogoliubov equations d 2 2mdx 2 µ+v(x) 2 2 d 2 2mdx 2 +µ V(x) ( u(x,t) v(x, t) =0 in N, 0 in S ) = i t ( u(x,t) v(x, t) ) 2. Demers-Griffin model for the N-S interface: V(x) = Hδ(x)

8 BTK theory Stationary plane wave solutions ( u(x,t) v(x, t) ) = E = ( 2 k 2 2m µ)2 + 2 [ u 2 0 = 1 ] E = 1 v0 2 2 E ( u0 v 0 ) e kx Et/ Density of states N(E) = Re [ (u 2 0 v2 0 ) 1] E = Re E2 2

9 BTK theory

10 BTK theory 6: Andreev reflection

11 BTK theory Z = H v F metallic contact: Z=0 tunneling regime: Z 5 G NS = di NS dv = 2N(0)ev FA + de df(e ev) [1+A(E) R(E)] dv Fit parameters: and Z

12 Experiments Au-Nb point contact (a) 10-Ω contact resistance (b) 3-Ω contact resistance Note: Experimental curves are broadened BTK curves

13 Dynes formula and phenomenological extention of the BTK theory Dynes formula (PRL 41, 1509 (1978)): E iγ N D (E) = Re (E iγ)2 2 Eliashberg theory: E N(E) = Re E2 2 (E), (E) = 1(E)+ 2 (E) Mitrović & Rosema (J. Phys.: Condens. Matter 20, (2008)): quasiparticle lifetime Γ = Im (E = 0 ) When Γ, 2 N D (E) and N(E) give nearly identical results (except near E=0). Nevertheless N D (E) is wrong!

14 Dynes formula and phenomenological extention of the BTK theory Phenomenological extension of the BTK theory to include finite quasiparticle lifetime: ( ) ( ) u(x,t) u0 = e v(x, t) v kx (E iγ)t/ 0 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 (Plecenník et al., PRB 49, (1994); de Wilde et al., Physica B 218, 165 (1996))

15 BTK theory with self-energy in S McMillan, Phys. Rev. 175, 559 (1968): Eliashberg version of Bogoliubov Equations {[ 2 d 2 ( ) ( ) u(x,e) u(x,e) 2mdx 2 µ]τ 3 +Σ(x,E)} = E v(x, E) v(x, E) Σ(x,E) = (1 z(x,e))τ 0 +φ(x,e)τ 1, (x,e) = φ(x,e) z(x, E)

16 BTK theory with self-energy in S The resulting theory is identical to the BTK theory but with complex and energy dependent gap (E) G NS = di NS dv = 2N(0)ev FA A(E) = u 2 v 2 γ 2 + de df(e ev) [1+A(E) R(E)] dv R(E) = [ u 4 + v 4 2Re(u 2 v 2 )]z 2 (z 2 +1) γ 2 γ = u 2 +(u 2 v 2 )z 2 u = E 2 2 (E)/E v = E 2 2 (E)/E. (Y. Rohanizadegan, MSc. Thesis, Brock University (2013))

17 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

18 Application to Cd 2 Re 2 O 7 Razavi, Rohanizadegan, Hajialamdari, Reedyk, Mitrović and Kremer, submitted to PRL (May, 2013) 2.00 Normalized conductance Voltage (mv) Temperature 0.36(2) K 0.45(5) K 0.571(2) K 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 1.207(3) K

19 Application to Cd 2 Re 2 O 7 Fits: T=0.831 K: A with 2, B with Γ T=0.360 K: C with 2, D with Γ Normalized conductance Normalized Conductance Voltage (V) A C B D Voltage (V)

20 Application to Cd 2 Re 2 O 7 and 2 and Γ Energy Gap (mev) Temperature (K) 2 k B T c =5.0(1) Temperature (K) T c =1.02 K

21 KOs 2 O 6 (Photoemission Spectroscopy) Shimojima et al. PRL 99, (2007), using Dynes formula: 2 k B T c 4.56 T c =9.6 K

22 Model of a rattler Mitrović and Nicol (unpublished): α 2 F is a cutoff Lorentzian at Ω R =2.2 mev λ R =3 T c =6 K k B T c /ω ln = k B T c =5.73

23 Comparison with other experiments NMR: Vyaselev et al., PRL 89, (2002) Allen & Rainer, Nature 349, 396 (1991) A large NMR coherence peak Cd 2 Re 2 O 7 is a BCS superconductor with 2 =3.68 k B T c

24 Comparison with other experiments Specific heat: Hiroi & Hanawa, J. Phys. Chem. Solids 63, 1021 (2002): γexp γ band =2.63 λ=1.63 Razavi et al., submitted to PRL C e γt c =1.15 < the BCS value of 1.43 anisotropic/multiband supercond. (?) or Note: There is a kink at T =80 % T c! k B T c /ω ln > 0.24, i.e. extreme strong coupling (?)

25 Comparison with other experiments Far-IR: Hajialamdari et al., J. Phys.: Condens. Matter 24, (2012) New peaks appear in the superconducting state at T =0.5 K (< 0.8 K)!

26 Possible scenario There is a structural transition in Cd 2 Re 2 O 7 below T c (at 0.8 K) similar to the transition in KOs 2 O 6. The new low frequency phonon modes appear which couple strongly to the electrons leading to a large low temperature.