2035-7 Conference on Superconductor-Insulator Transitions 18-23 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
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.
Collaborators Madhavi Chand S P Chockalingam John Jesudasan Anand Kamlapure, Mintu Mondal, Archana Mishra, Vivas Bagwe Vikram Tripathi Johan Vanacken, Gufei Zhang Leuven
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, 214503 (2008) Evolution of superconducting properties with disorder Tunneling measurements S. P. Chockalingam, Madhavi Chand et al., Phys. Rev. B 79, 094509 (2009).
Introduction Δ: Binding energy of Cooper Pair Ψ=Ψ 0 e iθ 1.2 Δ (mev) 0.8 0.4 Can phase fluctuations destroy superconductivity at a lower temperature? 0 1 2 3 4 5 6 7 8 T(K) T c
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, 027001 (2007).
Superconductor-Insulator Transitions Quench-condensed Bi films Sambandamurthy et al., Phys Rev B 64, 104506 (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, 157006 (2008).
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?
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
Stability Phase diagram of NbN Stoichiometric NbN Tc (K) 16 15 14 13 12 11 10 9 Nb 2 N Nb 1-x N 40 80 120 160 200 240 280 Sputtering Power (W) Increasing Nb/N 2 ratio in the plasma
Growth Protocols of dc sputtered of NbN films Substrate Temperature: 600 0 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-2.56 37 38 39 40 41 42 43 44 45 2θ (degrees) 40 45 2θ (degrees) MgO 250W Intensity (arb. units) l-8.77 l-2.56 0 50 100 150 200 250 300 350 Φ (degrees)
ρ(μω m) 5 4 3 2 1 2-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 0 6 8 10 12 14 16 18 20 T (K) ρ n (μω μω-m) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 10 11 12 13 14 15 16 17 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
Hall Effect (20K) H(T) 0 2 4 6 8 10 12 xy (μωm) ρ x -4.0x10-4 -8.0x10-4 -1.2x10-3 -1.6x10-3 l 7.47 8.38 6.78 4.51 3.33 2.14 1.54 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
(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 ( 4.413 10 ) 3 = 2.33 10 29 el / m 3
Stoichiometric NbN Tc (K) 16 15 14 13 12 11 10 9 Nb 2 N Nb 1-x N 40 80 120 160 200 240 280 Sputtering Power (W) n exp =2.39X10 29 el/m 3 n theo =2.33X10 29 el/m 3 18 15 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) 12 9 6 8.0 16.0 24.0 n (X10 28 electrons m -3 )
Carrier density and T c σ n (Ω -1 m -1 ) T c (K) 18 15 12 9 1.6x10 6 1.2x10 6 8.0x10 5 4.0x10 5 6 8.0 16.0 24.0 n (X10 28 electrons m -3 ) 0 8 16 24 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
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-200 1.80*10 10 2.09*10 6 3.96 14.80 4.72 2.38*10 28 7.15 1.50 1-NbN-150 1.68*10 10 1.95*10 6 2.91 17.82 4.30 2.23*10 28 4.90 1.40 1-NbN-100 1.40*10 10 1.62*10 6 3.28 17.58 4.33 1.86*10 28 4.60 1.16 1-NbN-80 1.37*10 10 1.59*10 6 3.34 16.65 4.45 1.82*10 28 4.58 1.14 1-NbN-40 1.33*10 10 1.54*10 6 3.04 15.12 4.67 1.77*10 28 4.05 1.11 2-NbN-25 1.31*10 10 1.52*10 6 2.28 14.79 4.72 1.74*10 28 2.98 1.09 2-NbN-30 1.24*10 10 1.44*10 6 2.07 13.08 5.02 1.65*10 28 2.56 1.03 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
McMillan theory for strong coupling superconductor T c = Θ 1.45 exp 1.04(1 * λ μ + λ) ( ) 1+ 0.62λ 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 + 1.04( 1+ KN ( 0) ) ( 0) μ ( 1 0.62KN ( 0) )
3.0 Fit to McMillan theory ln ( T Θ ) = ln c * 1.45 KN + 1.04( 1+ KN ( 0) ) ( 0) μ ( 1 0.62KN ( 0) ) 2.8 ln(t c ) 2.6 2.4 2.2 ln(θ D /1.49)=4.54 Θ=14020Κ λ=1.02 2.28 2.0 1.8 K=<g 2 >/(M<ω 2 >) =9.06*10-29 ev m3 1.4x10 28 2.1x10 28 2.8x10 28 N(0) (states ev -1 m -3 )
Electron Phonon coupling λ=1.02 2.28 T c ~16.11K Obtained from McMillan Rowell inversion of tunneling data Τ c ~14K λ 1.45 Kihlstrom et al. (1985)
Studies on disorder
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 1.36-8.77
Evolution of T c and ρ n with l T c (K) 16 14 12 10 8 (a) c (K) T 1 2 3 4 5 6 7 8 9 18 15 12 9 6 8.0 16.0 24.0 l n (X10 28 electrons m -3 ) ρ n (μω m) 12 10 8 6 4 2 (b) l~1.38-8.77 σ n (Ω -1 m -1 ) 1.6x10 6 1.2x10 6 8.0x10 5 4.0x10 5 80x10 8.0x10 28 16x10 1.6x10 29 24x10 2.4x10 29 n (electrons m -3 ) 0 1 2 3 4 5 6 7 8 9 T c decreases and ρ n increases with increase in disorder l
Why does the carrier density change with disorder? n (X10 28 electrons m -3 ) 25 20 15 10 5 0 0 1 2 3 4 5 6 7 8 9 l n varies with disorder by a factor of 10 Not accounted for by chemical effects alone Localization effects?
Evolution of Normal State with disorder (μω m) ρ 8 7 6 5 4 3 2 1 l 1.54 2.14 3.33 4.51 6.78 7.47 8.38 0 0 50 100 150 200 250 300 T (K) Does not follow Mott Variable range Hopping: T ρ ~ exp T Anderson Insulator or unusual metal? 0 1/ 4
Hall measurement ρ xy X10-10 (Ω m) 0 2 4 6 8 10 12 0-0.50-1.00-1.50-2.00-2.50-3.00 20K 40K 70K 105K 145K 180K 232K 285K B (T) l = 8.38 ρ xy x10-10 (Ω m) B (T) 0 0 2 4 6 8 10 12-1 -2-3 -4-5 -6 285K 250K 200K 150K 100K 75K 50K 30K 17K l = 4.51 ρ xy X10-10 (Ω m) -2-4 -6-8 -10-12 -14-16 0 2 4 6 8 10 12 0 12K 25K 50K 75K 100K 150K 195K 240K 285K B (T) l~1.54
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.
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
f(e) Anderson Localization E c ~E F Fermi Glass R H x10-10 (V m 3 /A Wb) E c ~E F 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 σ σ xx xy l 8.38 E c ( N( E )) 2 F ( N ( E ) ) 3 0 0 50 100 150 200 250 300 T (K) F Both temperature independent ρ (μω m) 0.8 0.6 0.4 0.2 0 50 100 150 200 250 300 T (K)
Electron phonon scattering? 1 τ ( T ) = τ 1 impurity + 1 τ phonon ( T) 0.750 0.8 0.6 0.745 ρ(μω m m) 0.4 l=8.38 ρ(μω m m) 0.740 Δρ phonon =02 μω m 0.2 0 50 100 150 200 250 300 T (K) 0.735 150 200 250 300 T (K) 02 0.7 = 3 3% The effect of phonons is overshadowed by impurity scattering
Temperature dependence of the Hall resistance R H x10-10 (V m 3 /A Wb) 12 l 10 8 6 4 1.54 3.33 4.51 6.78 7.47 2 0 50 100 150 200 250 300 R H T (K) = V t H IB ρ(μω m) 8 6 4 2 l = 1.54 12 10 8 6 4 0 2 0 50 100 150 200 250 300 T (K) R H x10-11 (V m 3 /A Wb)
R H x10-10 (V m 3 /A Wb) 1.2 1.0 0.8 0.6 0.4 l = 2.14 l =1.54 2 3 4 5 6 7 8 ρ(μω m) R H x10-11 (V m 3 /A Wb) 8 7 6 5 l = 4.51 l = 3.33 1.5 2.0 2.5 3.0 ρ(μω m) R H x10-11 (V m 3 /A Wb) 3.6 3.4 3.2 3.0 2.8 2.6 l = 6.78 l = 7.47 0.7 0.8 0.9 1.0 ρ(μω m) ( ) ( ) R T = Aρ T H ( ) = + ( ) R T R Aρ T H H0 R H0 ~1.0-2.0 10-11 V m 3 /A Wb
2x10-2 2x10-2 l~3.33 Δρ (μωm) ρ(μω m) 1x10-2 5x10-3 0-5x10-3 2.68 2.64 2.60 ρ =2.66μΩ m 0 14K 15K 15.75K 16.5K 17.25K 18K 18.75K 20K 0 2 4 6 8 10 12 H(T) 0T 12T 2.56 5 10 15 20 25 T(K) l 3.33 γ=4.35
Phenomenological Phase Diagram T (K) 21 18 15 12 T9 6 Anderson Insulator T c Superconductor Fermi Glass Regime 3 0 1 2 3 4 5 6 7 8 9 l (at 17K) No intrinsic meaning
Tunneling measurement I NbN/Oxide layer I-V characteristics of the (300X300 μm 2 ) tunnel junction 1.0 0.8 2.17K V di/dv (Ω -1 ) 0.6 0.4 0.2-6 -4-2 0 2 4 6 V (mv) Ag Counter electrode Tunnel junctions with resistance varying between 1-10Ω: Good for tunneling spectroscopy in the Superconducting state.
Fitting the tunneling spectra di/dv (Ω -1 ) 1.0 0.8 0.6 0.4 0.2 2.17K -6-4 -2 0 2 4 6 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).
Resistance measurement NbN/Oxide layer Resistance measurement of the NbN layer I V 100 80 R (Ω) 60 40 Ag Counter electrode 20 0 10 12 14 16 18 20 T(K)
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 ) 1.0 0.8 0.6 0.4 0.2 (a) 2.17K 3.5K 4.5K 7.0K 10.35K 12.35K 14.0K 14.6K -15-10 -5 0 5 10 15 V (mv) di/dv (Ω 1 ) 0.30 0.25 0.20 0.15 0.10 005 5 (b) 2.23K 2.91K 4.30K 5.05K 6.70K 7.35K 8.00K 9.00K 0-15 -10-5 0 5 10 15 V (mv) di/dv (Ω 1 ) 0.20 0.15 0.10 5 (c) 2.17K 3.35K 4.3K 4.9K 5.5K 6.4K 7.0K 7.4K 0-15 -10-5 0 5 10 15 V (mv) Low bias: Relevant region for superconductivity
T c ~15.6K l~6.5 di/dv (Ω 1 ) 1.5 1.2 0.9 0.6 0.3 2.5K 4K 5.5K 8.5K 10 K 11.5K 12.9K 14.4K 15K -6-4 -2 0 2 4 6 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) 2.8 2.4 2.0 1.6 1.2 0.8 0.4 Δ 0 2 4 6 8 10 12 14 16 T(K) Γ 1.0 0.8 0.6 0.4 0.2 R(T)/R(20K)
T c ~14.9K l~6 di/dv (Ω -1 ) 1.0 0.8 0.6 0.4 0.2 2.17K 3.50K 4.50K 7.0K 10.35K 12.35K 14.0K 14.6K -6-4 -2 0 2 4 6 V( (mv) Δ, Γ (mev) 2.5 Δ 2.0 1.5 1.0 0.5 Γ 2 4 6 8 10 12 14 16 T(K) 16 1.6 1.2 0.8 0.4 ρ (μω m)
T c ~7.7K l~1.4 0.18 di/dv (Ω -1 ) 0.12 6 2.17K 3.35K 4.30K 4.90K 5.50K 6.40K 7.00K 7.40K 0-4 -3-2 -1 0 1 2 3 4 V (mv) TT c Δ 0 Δ Γ Δ, Γ (mev) Δ reduces to 60% of its low temperature value at T c. 16 1.6 1.2 0.8 0.4 Δ 0 2 3 4 5 6 7 8 9 T(K) Γ 6 4 2 ρ (μω m)
Temperature dependence of Δ and Γ di/dv Δ, Γ (mev) 1.0 0.8 0.6 0.4 0.2 2.5 2.0 1.5 1.0 0.5 Least disorder T c =14.9K 2Δ/k B T c =4.36 l~6-6 -4-2 0 2 4 6 Δ V (mev) Γ 2 4 6 8 10 12 14 16 18 T(K) 1.0 0.8 0.6 0.4 0.2 R/R(10K) di/dv (Ω 1 ) Δ, Γ (mev) Intermediate disorder T c =9.5K 2Δ/k B T c =3.91 l~2.3 0.30 0.25 0.20 0.15 0.10 005 5 0 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2-4 -2 0 2 4 Δ V (mv) 2 3 4 5 6 7 8 9 10 11 T(K) Γ 1.1 0.9 0.7 0.4 0.2 R/R(10K) di/dv Δ, Γ (mev) 0.21 0.18 0.15 0.12 9 6 3 Large disorder T c =7.7K 2Δ/k B T c =4.43 l=1.4 0-4 -3-2 -1 0 1 2 3 4 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 V (mev) Δ Γ 2 3 4 5 6 7 8 9 T(K) B 1.0 0.8 0.6 0.4 0.2 R/R(10K) Pseudogap state above T c?
2Δ/k B T c Measure of electron-phonon coupling strength within mean field theories of superconductivity. 3.0 2.8 N(0) is expected to decrease for films ln(t c ) 2.6 2.4 2.2 2.0 1.8 1.4x10 28 2.1x10 28 2.8x10 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
4.4 Δ 0 /k B T c 2Δ 4.2 4.0 3.8 Δ 0 (mev V) 2.7 24 2.4 2.1 1.8 1.5 1 2 3 4 5 6 l 8 10 12 14 16 T c (K) T Temp at which pairs form T c Zero resistance state T * Pseudogap state Insulator/ Metal Disorder
Γ (mev) Δ, 1.6 1.2 0.8 04 0.4 Pseudogap state? Δ(T)0 a T c Γ Δ 6 4 2 0 2 3 4 5 6 7 8 9 T(K) T (K) (μω m) ρ 21 18 15 12 9 6 3 0 Anderson Insulator T c NbN Superconductor Fermi Glass 1 2 3 4 5 6 7 8 9 l (at 17K) Γ (mev) Δ, 3.0 2.5 2.0 1.5 1.0 0.5 Δ(T) vanishes at T c Δ 0 3 6 9 12 15 T(K) Γ 1.5 1.2 0.9 0.6 0.3 (μω m) ρ Δ, Γ (mev) 1.6 1.2 0.8 0.4 Δ Γ 2 4 6 8 10 T(K) 5 4 3 2 1 0 ρ (μω m) Δ, Γ (mev) 2.4 2.0 1.6 1.2 0.8 0.4 Δ Γ 0.5 2 4 6 8 10 12 14 16 T(K) 2.5 2.0 1.5 1.0 ρ (μω ) Δ, Γ (mev) 2.5 2.0 1.5 1.0 0.5 Δ Γ 2 4 6 8 10 12 14 16 T(K) 1.6 1.2 0.8 0.4 ρ (μω m)
NbN Pseudogap state? Δ(T)0 a T c T (K) 21 Fermi 18 Anderson Insulator Glass 15 12 T c 9 6 Superconductor 3 0 1 2 3 4 5 6 7 8 9 l (at 17K) Δ(T) vanishes at T c Δ, Γ (mev) 1.6 1.2 Δ 0.8 0.4 Γ 1.0 0.8 0.6 0.4 0.2 2 3 4 5 6 7 8 9 T(K) R/R(10K) Δ, Γ (mev) 2.5 Δ 2.0 1.5 1.0 1.0 0.8 0.6 0.4 0.5 Γ 0.2 2 4 6 8 1012141618 T(K) R/R(10K)
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