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SIT and MQT in 1D (Superconductor-insulator transition and macroscopic quantum tunneling in quasi-one-dimensional superconducting wires) Alexey Bezryadin Department of Physics University of Illinois at Urbana-Champaign. Acknowledgments. Experiment:

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SIT and MQT in 1D

(Superconductor-insulator transition and macroscopic quantum tunneling in quasi-one-dimensional superconducting wires)

Alexey Bezryadin

Department of Physics

University of Illinois at Urbana-Champaign




Andrey Rogachev – former postdoc; now at Utah Univ.

Myung-Ho Bae – postdoc.

Tony Bollinger – PhD 2005; now staff researcher at BNL

Dave Hopkins – PhD 2006; now at LAM research

Robert Dinsmore –PhD 2009; now at Intel

Mitrabhanu Sahu –PhD 2009; now at Intel

Matt Brenner –grad student


David Pekker

Tzu Chieh Wei

Nayana Shah

Paul Goldbart



  • Motivation
  • Fabrication of superconducting nanowires and our measurement setup
  • Source of dissipation: Little’s phase slip
  • Evidence for SIT
  • Evidence for MQT of phase slips (i.e. observation of QPS)

- Conclusions


Motivation (SIT)


Approaching 1D



  • D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett.62, 2180 (1989).
  • P. Xiong, A.V. Herzog, and R.C. Dynes, Phys. Rev. Lett.78, 927 (1997).
motivation mqt
Motivation (MQT)

- Leggett initiates the field of macroscopic quantum physics. Macroscopic quantum phenomena can occur and can be theoretically described (Leggett ‘78). (A superposition of macroscopically distinct states is the required signature of truly macroscopic quantum behavior) [1,2,3].

- Macroscopic quantum tunneling (MQT) was clearly observed and understood in Josephson junctions (Clarke group ‘87) but not on nanowires. [4].

- MQT is proposed as a mechanism for a new qubit design (Mooij-Harmans ‘05) [5].

- Quantum phase slip in superconducting wires may have interesting device applications, e.g. in fundamental current standards (Mooij-Nazarov‘06) [6].

  • Leggett, A. J. J. Phys. Colloq.(Paris), 39, C6-1264 (1978).
  • Caldeira, A.O. & Legget, A.J. Phys. Rev. Lett.46, 211 (1981).
  • Great book on MQT: S. Takagi. Macroscopic quantum tunneling.
  • Cambridge University Press, 2002.
  • 4. Martinis, J. M., Devoret, M. H. & Clarke, J. Phys. Rev. B 35, 4682 (1987).
  • 5. Mooij, J. E. & Harmans, C. J. P. M. New J. Phys.7, 219 (2005).
  • 6. Mooij, J. E. & Nazarov Y. V. Nature Physics 2, 169 (2006).
sample fabrication
Sample Fabrication

Method of Molecular Templating

Si/ SiO2/SiN substrate with undercut

~ 0.5 mm Si wafer

500 nm SiO2

60 nm SiN

Width of the trenches ~ 50 - 500 nm

HF dip for ~10 seconds

R_square=200 μΩ cm/10 nm=200 Ω

A. Bezryadin, C.N. Lau, and M. Tinkham, Nature404, 971 (2000)


4 nm

Sample Fabrication

Schematic picture of the pattern

Nanowire + Film Electrodes used in transport measurements

TEM image of a wire;

Nominal thickness = 3 nm (Mikas Rimeika)

R_square=200 μΩ cm/10 nm=200 Ω


Measurement Scheme

Sample mounted on the 3He


Circuit Diagram


Tony Bollinger's sample-mounting procedure in winter in Urbana

  • Procedure (~75% Success)
    • - Put on gloves
    • - Put grounded socket for mounting in vise with grounded indium dot tool connected
    • - Spray high-backed black chair all over and about 1 m square meter of ground with anti-static spray
      • - DO NOT use green chair
      • - Not sure about short-backed black chairs
    • - Sit down
    • - Spray bottom of feet with anti-static spray
    • - Plant feet on the ground. Do not move your feet again for any reason until mounting is finished.
    • - Mount sample
    • - Keep sample in grounded socket until last possible moment
    • - Test samples in dipstick at ~1 nA

Dichotomy in nanowires

 evidence for SIT


Nominal thickness of

the deposited MoGe film

A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin,

Phys. Rev. Lett. 101, 227003 (2008)


Little’s phase slip


William A. Little,

“Decay of persistent currents in small superconductors”,

Phys. Rev., 156, 396 (1967).


Langer, Ambegaokar, McCumber, Halperin theory (LAMH)

The barrier, derived using GL theory 

The attempt frequency, using the TDGL theory (due to McCumber and Halperin) 

RAL ≈RNexp[-ΔF(T)/kBT]

Simplified formula: Arrhenius-Little fit:


origin of quantum phase slips



Possible Origin of Quantum Phase Slips


Tunneling junction








Diffusive coherent wire acts as coherent scatterer

Barrier shape

Barrier shape


R0=17.4 kW

Insulating behavior is due to Coulomb blockade

Golubev-Zaikin formula


Dichotomy in nanowires:

High-bias measurements.

Fits: Golubev-Zaikin theory

PRL 86, 4887 (2001).


Superconductor-insulator transition phase diagram

Possible origin of the SIT:

Anderson-Heisenberg uncertainty principle:



A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin,

Phys. Rev. Lett.101, 227003 (2008)







RCSJ Model of a Josephson junction

Stewart-McCumber RCSJ model

(ћ C/2e) d2φ/dt2 + (ћ/2eRN ) dφ/dt+ (2e EJ/ ћ) sinφ = I (from Kirchhoff law)

Particle in a periodic potential with damping : classical Newton equation

md2x/dt2 + ηdx/dt– dU(x)/dx = Fext


Schmid-Bulgadaev diagram

A. Schmid, Phys. Rev. Lett., 51, 1506 (1983)

S. A. Bulgadaev, “Phase diagram of a dissipative quantum system.” JETP Lett. 39, 315 (1984).






RQ= h/4e2=6.45kΩ

switching current in thin wires search for qps
Switching current in thin wires: search for QPS

V-I curves

High Bias-Current Measurements

switching current distributions
Switching Current Distributions

ΔT=0.1 K

# 10,000

Bin size = 3 nA

! The widths of distributions

increases with decreasing

temperature !

M. Sahu, M. Bae, A. Rogachev, D. Pekker, T. Wei, N. Shah, P. M. Goldbart, A. Bezryadin

Accepted in Nature Physics (2009).


Voss and Webb observe QPS (MQT) in 1981

“Macroscopic Quantum Tunneling in 1 micron Nb junctions”

By Richard Voss and Richard Webb, Phys. Rev. Lett.47, 265 (1981)

Switching current distributions

of a single 1-μm Nb junction.


Voss and Webb: width of the switching current distribution vs. T

R. Voss and R. Webb

PRL 47, 265 (1981)

temperature dependence of the widths of the distributions
Temperature dependence of the widths of the distributions

Widths decrease with increasing temperature.

Sahu, M. et al. (arXiv:0804.2251v2)

switching rate out of the superconducting state
Switching rate out of the superconducting state


Derived switching rates

Experimental data

Here, K=1 the channel in the distribution with the largest value of the current .

ΔI, is the bin width in the distribution histograms.

T.A. Fulton and L.N. Dunkleberger, Phys. Rev. B9, 4760 (1974).


MQT in high-TC Josephson junctions


M.-H. Bae and A. Bezryadin, to be published

A single phase slip causes switching due to overheating(one-to-one correspondence of phase slips and switching events)

Tails due to multiple


model of stochastic switching dynamics
Model of stochastic switching dynamics

Competition between

heating caused by each phase slip event


At higher temperatures a larger number of phase slips are required to cause at switching.

At low enough temperatures a single phase slip is enough to cause switching. Thus there is one-to-one correspondence between switching events and phase slips!

1. M. Tinkham, J.U. Free, C.N. Lau, N. Markovic, Phys. Rev. B68,134515 (2003).

2. Shah, N., Pekker D. & Goldbart P. M.. Phys. Rev. Lett.101, 207001 (2008).

simulated temperature bumps
Simulated temperature bumps

T = 1.9 K

I = 0.35 μA

TC =2.7 K




Gradual cooling after a a PS

Sharp T bump due to a PS

CV(T) and KS(T) decreases as the temperature is decreased.

->Easier to heat the wire due to lower CV and increased ISW

switching rates at different temperatures
Switching rates at different temperatures

TAPS only


and QPS

Sahu, M. et al. (arXiv:0804.2251v2)


Crossover temperature T*

TAPS rate

Giordano formula the for QPS rate

1. Giordano,N. Phys. Rev. Lett.61, 2137 (1988).

2. M. Tinkham, J.U. Free, C.N. Lau, N. Markovic, Phys. Rev. B 68,134515 (2003)

and the references therein.

phase slip rates
Phase slip rates
  • For Thermally Activated Phase slips (TAPS) (based on LAMH),


  • For Quantum Phase Slips (QPS),

Switching rate at 0.3K compared to TAPS and QPS

T=0.3 K

QPS rate

TAPS rate

Sahu, M. et al. (arXiv:0804.2251v2)


TQPS and T* for different nanowires

T* increases with increasing critical current

Sahu, M. et al. (arXiv:0804.2251v2), To appear in Nature Physics

preliminary results shunting the wires
Preliminary results: shunting the wires

Fit with Caldeira-Leggett

Fit without dissipation

Exact fits: Bardeen microscopic theory

M. Brenner and A. Bezryadin, to be published


- SIT is found in thin MoGe wires

- The superconducting regime obeys the Arrhenius thermal activation of phase slips

- The insulating regime is due to weak Coulomb blockade

- MQT is observed at high bias currents, close to the depairing current

- At sufficiently low temperatures, every single QPS causes switching in the wire. (This is due to the fact that phase slips can only occur very near the depairing current at low T. Thus the Tc is strongly suppressed by the bias current. Thus the Joule heat released by one phase slip needs to heat the wire just slightly to push it above the critical temperature).