SIT and MQT in 1D

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

Alexey Bezryadin

Department of PhysicsUniversity of Illinois at Urbana-Champaign

Acknowledgments

Experiment: Andrey Rogachev – former postdoc; now at Utah Univ.Myung-Ho Bae – postdoc.Tony Bollinger – PhD 2005; now staff researcher at BNLDave Hopkins – PhD 2006; now at LAM researchRobert Dinsmore –PhD 2009; now at IntelMitrabhanu Sahu –PhD 2009; now at IntelMatt Brenner –grad student

Theory: David Pekker Tzu Chieh Wei Nayana ShahPaul Goldbart

Outline

- 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)

1. D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989).2. P. Xiong, A.V. Herzog, and R.C. Dynes, Phys. Rev. Lett. 78, 927 (1997).

2D

R_sq_c~6.5kOhm

Approaching 1D

R_sq_c~6.5kOhm

Motivation (MQT)

1. Leggett, A. J. J. Phys. Colloq. (Paris), 39, C6-1264 (1978). 2. Caldeira, A.O. & Legget, A.J. Phys. Rev. Lett. 46, 211 (1981).3. 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).

- 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].

Sample FabricationMethod of Molecular Templating

A. Bezryadin, C.N. Lau, and M. Tinkham, Nature 404, 971 (2000)

Si/ SiO2/SiN substrate with undercut

~ 0.5 mm Si wafer500 nm SiO2

60 nm SiNWidth of the trenches ~ 50 - 500 nm

HF dip for ~10 seconds

R_square=200 μΩ cm/10 nm=200 Ω

Schematic picture of the patternNanowire + Film Electrodes used in transport measurements

4 nm

TEM image of a wire; Nominal thickness = 3 nm (Mikas Rimeika)

Sample Fabrication

R_square=200 μΩ cm/10 nm=200 Ω

Low -T Filter

Room Temp

Low Temp

Sample

pi-Filter

CernoxThermometer

Measurement Scheme

Sample mounted on the 3Heinsert.

Circuit Diagram

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

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

Dichotomy in nanowires evidence for SIT

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

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

400100squareR

Parameter: Nominal thickness ofthe deposited MoGe film

Little’s phase slip

William A. Little, “Decay of persistent currents in small superconductors”, Phys. Rev., 156, 396 (1967).

∆(x)=│∆(x)│exp[iφ]

Langer, Ambegaokar, McCumber, Halperin theory (LAMH)

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

The barrier, derived using GL theory

Simplified formula: Arrhenius-Little fit: RAL ≈ RN exp[-ΔF(T)/kBT]

Possible Origin of Quantum Phase Slips

101

102

103

104

543210

R (

T)

T (K)

He3 He4

origin of quantum phase slips

101

102

103

104

54321

R (

T)

T (K)

QPS off

QPS on

e e

metal metal

oxide

Tunneling junctionDiffusive coherent wire acts as coherent scatterer

Barrier shape

p.4887

p.1245

Barrier shape

Insulating behavior is due to Coulomb blockade

0

0 0

9 27 0.019 0.067( )

B K

C

G k T R

G G T E R

30

25

20

15

10

5

02.01.51.00.50.0

G0

/ (G

0 -

G(T

))T (K)

G0=57.5 S

21

20

19

18

17

x103

43210T (K)

R (

k

R0=17.4 k

Golubev-Zaikin formula

Dichotomy in nanowires:High-bias measurements.

Fits: Golubev-Zaikin theoryPRL 86, 4887 (2001).

Superconductor-insulator transition phase diagram

A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin, Phys. Rev. Lett. 101, 227003 (2008)

Possible origin of the SIT:Anderson-Heisenberg uncertainty principle:

eQ ~0

0Q

RN<6.45kΩ

RN>6.45kΩ

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

C

RN

φ1 φ2 I

Schmid-Bulgadaev diagram

RQ/RN

EJ /EC

1

SuperconductorInsulator

RQ= h/4e2=6.45kΩ

A. Schmid, Phys. Rev. Lett., 51, 1506 (1983)S. A. Bulgadaev, “Phase diagram of a dissipative quantum system.” JETP Lett. 39, 315 (1984).

Theoretical approach to our data

LAMH applies if:

Switching current in thin wires: search for QPS

V-I curves

High Bias-Current Measurements

Switching and re-trapping currents vs. temperatures

MoGe Nanowire

Switching Current Distributions

ΔT=0.1 K# 10,000Bin 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. BezryadinAccepted in Nature Physics (2009).

Switching current distributionsof a single 1-μm Nb junction.

“Macroscopic Quantum Tunneling in 1 micron Nb junctions” By Richard Voss and Richard Webb, Phys. Rev. Lett. 47, 265 (1981)

Voss and Webb observe QPS (MQT) in 1981

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

Widths decrease with increasing temperature.

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

Switching rate out of the superconducting state

1

1 1

1( ) ln ( ) / ( )

K K

j i

dIK P j P i

dt I

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. B 9, 4760 (1974).

FD

Experimental data Derived switching rates

p B esc( / 2 )exp( / )U k T

3/2

0 0 04 2 / 6 1 /U I I I

02 /p eI C

*( ) 2p BI k T

T*

MQT in high-TC Josephson junctions

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

Tails due to multiple phase-slips

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

Model of stochastic switching dynamics

• Competition between

– heating caused by each phase slip event – cooling

• 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. B 68,134515 (2003). 2. Shah, N., Pekker D. & Goldbart P. M.. Phys. Rev. Lett. 101, 207001 (2008).

2

hI

e

Simulated temperature bumps

5 10(ns)

T = 1.9 K I = 0.35 μA TC =2.7 K

Sharp T bump due to a PS Gradual cooling after a 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

TAPS only

TAPS and QPS

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

( , )( , ) exp

2 B

TAPSTAPS

TAPS

F T IT I

k T

T

( , )( , ) exp

2 B

QPSQPS

QPS

F T IT I

k T

T

Giordano formula the for QPS rate TAPS rate

Crossover temperature T*

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

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

where,

• For Quantum Phase Slips (QPS),

TAPSTAPS

B

1/2

GL B B

( , )exp

2

1 1 ( ) ( , )exp

2 ξ( ) τ

F T I

k T

L F T F T I

T k T k T

5/4

C

C

6 ( )( , ) 1

2

I T IF T I

e I

QPSQPS

B QPS

1/2

GL B QPS B QPS

( , )exp

2

1 1 ( ) ( , )exp

2 ξ( ) τ

F T I

k T

L F T F T I

T k T k T

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

T* vs. IC(0)

* (0)CT I

Preliminary results: shunting the wires

Fit without dissipation

Fit with Caldeira-Leggett

M. Brenner and A. Bezryadin, to be publishedExact fits: Bardeen microscopic theory

Conclusions

- 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).