Transcript Slide 1

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:
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
Theory:
David Pekker
Tzu Chieh Wei
Nayana Shah
Paul 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
2D
Motivation (SIT)
Approaching 1D
R_sq_c~6.5kOhm
R_sq_c~6.5kOhm
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).
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].
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).
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, Nature 404, 971 (2000)
Sample Fabrication
4 nm
TEM image of a wire;
Nominal thickness = 3 nm (Mikas Rimeika)
Schematic picture of the pattern
Nanowire + Film Electrodes used in
transport measurements
R_square=200 μΩ cm/10 nm=200 Ω
Measurement Scheme
pi-Filter
Room Temp
Low Temp
Low -T Filter
Cernox
Thermometer
Sample
Circuit Diagram
Sample mounted on the 3He
insert.
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
Parameter:
Nominal thickness of
the deposited MoGe film
Rsquare  100 400
A. Bollinger, R. Dinsmore, A. Rogachev and
A. Bezryadin,
Phys. Rev. Lett. 101, 227003 (2008)
Little’s phase slip
∆(x)=│∆(x)│exp[iφ]
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) 
Simplified formula: Arrhenius-Little fit:
RAL ≈ RN exp[-ΔF(T)/kBT]
Possible Origin of Quantum Phase Slips
4
10
He3
3
He4
R (T)
10
2
10
4
10
QPS on
1
3
10
R (T)
10
0
1
2
3
T (K)
2
10
QPS off
origin of quantum phase slips
1
10
1
2
3
T (K)
4
5
4
5
p.1245
p.4887
Tunneling junction
Diffusive coherent wire acts as coherent scatterer
oxide
e
metal
e
metal
Barrier shape
Barrier shape
Insulating behavior is due to Coulomb blockade
21
30
25
19
18
R0=17.4 k
17
0
1
2
T (K)
3
4
G0 / (G0 - G(T))
R (k
20
20
G0=57.5 S
15
10
5
0
0.0


G0
kT
R
 9 B  27  0.019 K  0.067 
G0  G (T )
EC
R0


Golubev-Zaikin formula
0.5
1.0
T (K)
1.5
2.0
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:
Q ~ e
  0
RN<6.45kΩ
RN>6.45kΩ
Q  0
A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin,
Phys. Rev. Lett. 101, 227003 (2008)
RCSJ Model of a Josephson junction
RN
φ1
φ2
I
C
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).
EJ /EC
Insulator
Superconductor
1
RQ= h/4e2=6.45kΩ
RQ/RN
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
# 10,000
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
Widths decrease with increasing temperature.
Sahu, M. et al. (arXiv:0804.2251v2)
Switching rate out of the superconducting state
FD
Experimental data
Derived switching rates
K 1

dI 1  K
( K ) 
ln   P( j ) /  P(i) 
dt I  j 1
i 1

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).
MQT in high-TC Josephson junctions
T*
  (p / 2 )exp(U / kBTesc )


U  4 2 I 00 / 6 1  I / I 0 
 p  2eI 0 / C
3/2
p (I )  2 kBT *
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
phase-slips
Model of stochastic switching dynamics
• Competition between
 hI 
 
– heating caused by each phase slip event
 2e 
– 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).
Simulated temperature bumps
T = 1.9 K
I = 0.35 μA
TC =2.7 K
5
Sharp T bump due to a PS
(ns)
10
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)
Crossover temperature T*
 F (T , I ) 
QPS T 
QPS (T , I ) 
exp  

 kBTQPS 
2


Giordano formula the for QPS rate
TAPS T 
 F (T , I ) 
TAPS (T , I ) 
exp  

2
 kBTTAPS 
TAPS 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
• For Thermally Activated Phase slips (TAPS) (based on
LAMH),   TAPS exp   F (T , I ) 
2
TAPS


kBT


1/2
 F (T , I ) 
 1   L   1  F (T ) 

exp






k
T
 2   ξ(T )   τGL   kBT 

B

where,
6 I C (T ) 
I 
F (T , I ) 
1



2e
I
C 

5/4
• For Quantum Phase Slips (QPS),
 QPS
 F (T , I ) 

exp  

 kT
2
B QPS 

QPS
1/2
 F (T , I ) 
 1   L   1   F (T ) 

 exp  

 


k
T
 2   ξ(T )   τ GL   kBTQPS 
B 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
T* vs. IC(0)
T *  IC (0)
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
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).