Conference on Superconductor-Insulator Transitions May 2009

Transcription

1 Conference on Superconductor-Insulator Transitions May 2009 Tunneling studies in a disordered s-wave superconductor close to the Fermi glass regime P. Raychaudhuri Tata Institute of Fundamental Research Mumbai India

2 Tunneling studies on a 3-dimensional disordered s-wave superconductor close to the Fermi Glass regime Pratap Raychaudhuri Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai.

3 Collaborators Madhavi Chand S P Chockalingam John Jesudasan Anand Kamlapure, Mintu Mondal, Archana Mishra, Vivas Bagwe Vikram Tripathi Johan Vanacken, Gufei Zhang Leuven

4 Plan of the talk Introduction What is good about NbN (films)? Tuning the disorder with deposition conditions Transport and Hall measurements S. P. Chockalingam, Madhavi Chand et al., Phys. Rev. B 77, (2008) Evolution of superconducting properties with disorder Tunneling measurements S. P. Chockalingam, Madhavi Chand et al., Phys. Rev. B 79, (2009).

5 Introduction Δ: Binding energy of Cooper Pair Ψ=Ψ 0 e iθ 1.2 Δ (mev) Can phase fluctuations destroy superconductivity at a lower temperature? T(K) T c

6 Beyond Anderson Theorem 2-dimension T=0 H = J < i, j> = ρ cos ( θ θ ) Continuous system H s d 3 i r θ j 2 Increasing disorder Amit Ghosal, Mohit Randeria and Nandini Trivedi, Phys. Rev. Lett. 81, 3940 (1998) also M. V. Feigelman et al., Phys. Rev. Lett. 98, (2007).

7 Superconductor-Insulator Transitions Quench-condensed Bi films Sambandamurthy et al., Phys Rev B 64, (2001) Y. Liu et al., Phys Rev B 47, 5931 (1993) R P Barber et al, Phys. Rev. B 49, 3409 (1994) B. Sacepe et al., Phys. Rev. Lett. 101, (2008).

8 Can Superconductivity get destroyed by (thermal) phase fluctuations in a 3D disordered film? Ideal Sample: A disordered superconductor with no intentional source of granularity 3D single crystal / epitaxial thin film with vacancy. At which level of disorder does this effect manifest itself?

9 ξ 5nm T c ~16K λ 200nm NbN Thickness of our films > 50nm Grows as epitaxial thin film on (100) MgO substrate using reactive magnetron sputtering: MgO NbN NaCl structure

10 Stability Phase diagram of NbN Stoichiometric NbN Tc (K) Nb 2 N Nb 1-x N Sputtering Power (W) Increasing Nb/N 2 ratio in the plasma

11 Growth Protocols of dc sputtered of NbN films Substrate Temperature: C, Total Ambient pressure (Ar+N 2 ): 5mTorr Log Intensity (arb units) 1-NbN-250W 1-NbN-150W 1-NbN-200W 1-NbN-40W (200) NbN (100) (a) 40W Log Intensity (arb. units) l-8.77 l θ (degrees) θ (degrees) MgO 250W Intensity (arb. units) l-8.77 l Φ (degrees)

12 ρ(μω m) NbN-30 2-NbN-25 NbN films on MgO (100) Correlation between ρ n and T c 1-NbN-40W 1-NbN-80W 1-NbN-100W 1-NbN-150W 1-NbN-200W T (K) ρ n (μω μω-m) Tc (K) Inverse correlation between normal state resistivity and T c Dirty films have lower T c : Anderson Theorem??? m ρ 2 = n or τ? ne τ

13 Hall Effect (20K) H(T) xy (μωm) ρ x -4.0x x x x10-3 l T c ~16.4K n~2.39x10 29 T c ~8.13K n~4.77x10 28 Carrier density varies by a factor of 5 from 4.77*10 28 electrons/m 3 to 2.39*10 29 electrons/m 3

14 (Electronic) Carrier density Nb 4d band Matheiss, PRB 5, 315 (1969) Nb atoms contribute to the carriers 5 electrons per Nb atom Face Centered Cubic structure has 4 Nb atoms per unit cell20 electrons/unit cell Lattice parameter of the unit cell: a=4.413å 20 Electronic Carrier density= 10 ( ) 3 = el / m 3

15 Stoichiometric NbN Tc (K) Nb 2 N Nb 1-x N Sputtering Power (W) n exp =2.39X10 29 el/m 3 n theo =2.33X10 29 el/m The carrier density changes by 1 order of magnitude: 2.11x10 28 el/m 3 to 2.39x10 29 el/m 3 T c (K) n (X10 28 electrons m -3 )

16 Carrier density and T c σ n (Ω -1 m -1 ) T c (K) x x x x n (X10 28 electrons m -3 ) n (X10 28 electrons m -3 ) T c is likely to be primarily governed by carrier density rather than disorder scattering. σ n n σ n = 2 ne τ m No significant change in carrier mobility. Theoretical value of n for the stoichiometric compound: n~2.34*10 29 electrons/m 3

17 Sample Name Parameters extracted from free electron theory k f (m -1 ) v f (m/s) l (Å) B c2 (0) (T) GL (0) (nm) N(0) (states/m 3 -ev) 1-NbN * * * NbN * * * NbN * * * NbN * * * NbN * * * NbN * * * NbN * * * a N(0)=0.511 states/nbn-ev APW calculations: 0.54 states/nbn-ev Matheiss (1969) Specific heat: 0.50 states/nbn-ev Geballe (1966) Ioffe-Regel disorder parameter: k F l = λ π de Broglie l l 2 Measure of mean free path as a function of de-broglie wavelength at Fermi level

18 McMillan theory for strong coupling superconductor T c = Θ 1.45 exp 1.04(1 * λ μ + λ) ( ) λ λ = 2 g N 0 = 2 M ω ( ) KN ( 0) λelectron phonon interaction constant μ electron-electron repulsive interaction μ =0.13 K depends primarily on lattice properties ln ( T ) Θ = ln c * 1.45 KN ( 1+ KN ( 0) ) ( 0) μ ( KN ( 0) )

19 3.0 Fit to McMillan theory ln ( T Θ ) = ln c * 1.45 KN ( 1+ KN ( 0) ) ( 0) μ ( KN ( 0) ) 2.8 ln(t c ) ln(θ D /1.49)=4.54 Θ=14020Κ λ= K=<g 2 >/(M<ω 2 >) =9.06*10-29 ev m3 1.4x x x10 28 N(0) (states ev -1 m -3 )

20 Electron Phonon coupling λ= T c ~16.11K Obtained from McMillan Rowell inversion of tunneling data Τ c ~14K λ 1.45 Kihlstrom et al. (1985)

21 Studies on disorder

22 Measure of disorder: l The Ioffe-Regel parameter is calculated from the ρ n and R H, using free electron approximation n = = 1 R e H ( ) 3π 2 n 1/ 3 ρ = m = 2 ne τ k ne F n 2 l Ioffe-Regel (at 17K) parameter varies from

23 Evolution of T c and ρ n with l T c (K) (a) c (K) T l n (X10 28 electrons m -3 ) ρ n (μω m) (b) l~ σ n (Ω -1 m -1 ) 1.6x x x x x10 8.0x x10 1.6x x10 2.4x10 29 n (electrons m -3 ) T c decreases and ρ n increases with increase in disorder l

24 Why does the carrier density change with disorder? n (X10 28 electrons m -3 ) l n varies with disorder by a factor of 10 Not accounted for by chemical effects alone Localization effects?

25 Evolution of Normal State with disorder (μω m) ρ l T (K) Does not follow Mott Variable range Hopping: T ρ ~ exp T Anderson Insulator or unusual metal? 0 1/ 4

26 Hall measurement ρ xy X10-10 (Ω m) K 40K 70K 105K 145K 180K 232K 285K B (T) l = 8.38 ρ xy x10-10 (Ω m) B (T) K 250K 200K 150K 100K 75K 50K 30K 17K l = 4.51 ρ xy X10-10 (Ω m) K 25K 50K 75K 100K 150K 195K 240K 285K B (T) l~1.54

27 f(e) Anderson Localization E c E c <E F Small Disorder: Metal E c E c ~E F E c >E F Moderate Disorder: Fermi Glass Large Disorder: Insulator E F E c For an Anderson insulator electrical transport takes place through carriers excited over the mobility edge.

28 Resistivity for an Anderson insulator f(e) L Friedman, J Non-Cryst Solids 6, 329 (1971) σ xx E c -E F >>k B T σ xx E F E c >E F Insulator E c E c E F N( Ec ) exp ( ) 3 Ec EF σ xy N( Ec ) exp kt B kt B ( ) 2 E c -E F >k B T 1 ( N( E )) 2 F f( E) de T E c 1 σ xy RH ( T) = ρ T 2 H ( σ ) xx σ xy 1 ( N( E )) 3 F f( E) de T ( ) E c

29 f(e) Anderson Localization E c ~E F Fermi Glass R H x10-10 (V m 3 /A Wb) E c ~E F σ σ xx xy l 8.38 E c ( N( E )) 2 F ( N ( E ) ) T (K) F Both temperature independent ρ (μω m) T (K)

30 Electron phonon scattering? 1 τ ( T ) = τ 1 impurity + 1 τ phonon ( T) ρ(μω m m) 0.4 l=8.38 ρ(μω m m) Δρ phonon =02 μω m T (K) T (K) = 3 3% The effect of phonons is overshadowed by impurity scattering

31 Temperature dependence of the Hall resistance R H x10-10 (V m 3 /A Wb) 12 l R H T (K) = V t H IB ρ(μω m) l = T (K) R H x10-11 (V m 3 /A Wb)

32 R H x10-10 (V m 3 /A Wb) l = 2.14 l = ρ(μω m) R H x10-11 (V m 3 /A Wb) l = 4.51 l = ρ(μω m) R H x10-11 (V m 3 /A Wb) l = 6.78 l = ρ(μω m) ( ) ( ) R T = Aρ T H ( ) = + ( ) R T R Aρ T H H0 R H0 ~ V m 3 /A Wb

33 2x10-2 2x10-2 l~3.33 Δρ (μωm) ρ(μω m) 1x10-2 5x x ρ =2.66μΩ m 0 14K 15K 15.75K 16.5K 17.25K 18K 18.75K 20K H(T) 0T 12T T(K) l 3.33 γ=4.35

34 Phenomenological Phase Diagram T (K) T9 6 Anderson Insulator T c Superconductor Fermi Glass Regime l (at 17K) No intrinsic meaning

35 Tunneling measurement I NbN/Oxide layer I-V characteristics of the (300X300 μm 2 ) tunnel junction K V di/dv (Ω -1 ) V (mv) Ag Counter electrode Tunnel junctions with resistance varying between 1-10Ω: Good for tunneling spectroscopy in the Superconducting state.

36 Fitting the tunneling spectra di/dv (Ω -1 ) K V (mv) N s ( E) E Γ i = Re 2 1/2 2 ( E Γ i ) Δ Δ di d G ( V ) N ( ) ( ){ ( ) ( )} = = s E Nn E ev f E f E ev de dv V dv R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys. Rev. Lett. 41, 1509 (1978).

37 Resistance measurement NbN/Oxide layer Resistance measurement of the NbN layer I V R (Ω) Ag Counter electrode T(K)

38 Tunneling spectra T c ~14.9K l~6 T c ~9.5K l~2.3 T c ~7.7K l~1.4 di/dv (Ω -1 ) (a) 2.17K 3.5K 4.5K 7.0K 10.35K 12.35K 14.0K 14.6K V (mv) di/dv (Ω 1 ) (b) 2.23K 2.91K 4.30K 5.05K 6.70K 7.35K 8.00K 9.00K V (mv) di/dv (Ω 1 ) (c) 2.17K 3.35K 4.3K 4.9K 5.5K 6.4K 7.0K 7.4K V (mv) Low bias: Relevant region for superconductivity

39 T c ~15.6K l~6.5 di/dv (Ω 1 ) K 4K 5.5K 8.5K 10 K 11.5K 12.9K 14.4K 15K V (mv) Small increase in Γ due to ph induced recombination of el and hole like quasiparticles: R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys. Rev. Lett. 41, 1509 (1978). Δ (mev) Δ T(K) Γ R(T)/R(20K)

40 T c ~14.9K l~6 di/dv (Ω -1 ) K 3.50K 4.50K 7.0K 10.35K 12.35K 14.0K 14.6K V( (mv) Δ, Γ (mev) 2.5 Δ Γ T(K) ρ (μω m)

41 T c ~7.7K l~ di/dv (Ω -1 ) K 3.35K 4.30K 4.90K 5.50K 6.40K 7.00K 7.40K V (mv) TT c Δ 0 Δ Γ Δ, Γ (mev) Δ reduces to 60% of its low temperature value at T c Δ T(K) Γ ρ (μω m)

42 Temperature dependence of Δ and Γ di/dv Δ, Γ (mev) Least disorder T c =14.9K 2Δ/k B T c =4.36 l~ Δ V (mev) Γ T(K) R/R(10K) di/dv (Ω 1 ) Δ, Γ (mev) Intermediate disorder T c =9.5K 2Δ/k B T c =3.91 l~ Δ V (mv) T(K) Γ R/R(10K) di/dv Δ, Γ (mev) Large disorder T c =7.7K 2Δ/k B T c =4.43 l= V (mev) Δ Γ T(K) B R/R(10K) Pseudogap state above T c?

43 2Δ/k B T c Measure of electron-phonon coupling strength within mean field theories of superconductivity N(0) is expected to decrease for films ln(t c ) x x x10 28 N(0) (states ev -1 m -3 ) with lower T c Electron-phonon coupling strength λ Ν(0)V is expected to reduce. Measure of electronphonon coupling strength: 2Δ/k B T c

44 4.4 Δ 0 /k B T c 2Δ Δ 0 (mev V) l T c (K) T Temp at which pairs form T c Zero resistance state T * Pseudogap state Insulator/ Metal Disorder

45 Γ (mev) Δ, Pseudogap state? Δ(T)0 a T c Γ Δ T(K) T (K) (μω m) ρ Anderson Insulator T c NbN Superconductor Fermi Glass l (at 17K) Γ (mev) Δ, Δ(T) vanishes at T c Δ T(K) Γ (μω m) ρ Δ, Γ (mev) Δ Γ T(K) ρ (μω m) Δ, Γ (mev) Δ Γ T(K) ρ (μω ) Δ, Γ (mev) Δ Γ T(K) ρ (μω m)

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47 NbN Pseudogap state? Δ(T)0 a T c T (K) 21 Fermi 18 Anderson Insulator Glass T c 9 6 Superconductor l (at 17K) Δ(T) vanishes at T c Δ, Γ (mev) Δ Γ T(K) R/R(10K) Δ, Γ (mev) 2.5 Δ Γ T(K) R/R(10K)

48 Connection with BEC All visible matter consists of Fermions T Pair Formation Temperature Thermal Bosonic Particles T c Superfluid Attractive Interaction BCS BEC Preformed Pairs Disorder