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September, 18, Rome , Italy
Tunnel-Fluctuoscopy: Fluctuation Induced Low-Bias Anomaly
Andrey Varlamov SPIN-CNR, Italy
in collaboration with
Andreas Glatz, Valerii Vinokur (ANL), USA
Giaver formula for tunnel current
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Zero bias anomaly in disordered metal (Altshuler, Aronov, 1979)
Fluctuation Renormalization of the density of states (E. Abrahams, M. Redi and E. Woo, 1970,
C. Di Castro, C. Castellani, R. Raimondi, A.Varlamov, 1990)
Manifestation of the SF DOS in tunneling conductivity (A.Varlamov, V. Dorin, 1983)
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Sum rule:
Δ Δ*
T>Tc T<Tc
Fluctuation pseudogap in tunneling conductivity
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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B. Sacepe, C. Chapelier, T. I. Baturina, V. M. Vinokur, M. R. Baklanov, M. Sanquer, 2010
Khachaturov, Chernyak, Belogolovsky, 1986
Fluctuation pseudogap in tunneling conductivity : Experimental confirmations
Diagrammatic approach (Varlamov, Dorin, 1983, Richardson, 1997)
The equivalence with Giaver formula
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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iων è eV+iδ
Tunnel fluctuoscopy
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Tunnel current:
We only need first order in transparency and fluctuations:
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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We use the following dimensionless parameters
à Two different contributions which need to be analytically continued
with °E=exp(°e)≈1.78…
Regular part
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Anomalous part
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Complete result
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Full fluctuation contribution to the tunneling current:
with
Anomalous contribution at small voltages
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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conductance near Tc0
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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The central peak disappears near t=1.36
near Hc2(0)
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Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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Tunneling conductance at h=0, near Tc0
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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The non-linear behavior of the second term of the tunnel current is responsible for the fine structure (local maximum) at the center of the gap.
Temperature and voltage dependence of the tunneling conductance due to superconducting fluctuations. The overall behavior of both terms of the tunnel current results in a pronounce pseudo-gap structure of the conductance near the superconducting region.
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Tunneling conductance at t=0.05 above hc2(0)=0.69
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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3
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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conductance near hc2(t)
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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tunneling conductance plotted for t=s*x and h=s*hc2(x) for x2[0;1] and s=1.1 (2 different views)
ß view from “Tc0” to “Hc2(0)”
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Pseudogap structure in experiments
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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B. Sacepe et. al., Nature Comm.. 140, 1 (2010).
Tunneling conductance STM measurements on 3.6nm (a) 5nm (b) thick TiN films (»¼10nm). Tc=1.27K (a) or 0.98K (b)
ZBA in intrinsic Josephson Junctions
(V. Krasnov et al.) unpublished, 2013
Fluctuoscopy of Disordered Two-‐Dimensional Superconductors
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dI/
dV
(Ha
b=
16T
) /
dI/dV
(Hc=
16T
)dI/
dV
(Ha
b=
16T
) /
dI/dV
(Hc=
16T
)
dI/
dV
(Ha
b=
16T
) /
dI/dV
(Hc=
16T
)
Fig.3. The ratio of dI/dV in parallel fieldto that in the perpendicular field of 16 T.It shows clearly the superconductingparts of the spectra, which are suppressed by the c-axis field but less so by the field in the ab-plane. (a) a full-scale view at different T close to Tc.
(a)
(b)
(c)
peak
(c) Zoom-in into the zero-biasarea. The zero-bias peak is seen up to 95K, few degrees, corresponding to T/Tc~1.06
(b) Zoom-in into the peakarea. The residual of the superconducting peak is seenabove Tc~90K up to ~115K, corresponding to T/Tc~1.28.
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