quantum phase tunneling in 1d superconductors l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Quantum Phase Tunneling in 1D Superconductors PowerPoint Presentation
Download Presentation
Quantum Phase Tunneling in 1D Superconductors

Loading in 2 Seconds...

play fullscreen
1 / 13

Quantum Phase Tunneling in 1D Superconductors - PowerPoint PPT Presentation


  • 135 Views
  • Uploaded on

Quantum Phase Tunneling in 1D Superconductors. K. Arutyunov , M. Zgirski, M. Savolainen, K.-P. Riikonen, V. Touboltsev. University of Jyväskylä, Department of Physics, Jyväskylä, 40014, FINLAND. SUMMARY 1. Introduction:

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Quantum Phase Tunneling in 1D Superconductors' - eddy


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
quantum phase tunneling in 1d superconductors
Quantum Phase Tunneling in 1D Superconductors

K. Arutyunov, M. Zgirski, M. Savolainen, K.-P. Riikonen, V. Touboltsev

University of Jyväskylä, Department of Physics, Jyväskylä, 40014, FINLAND

SUMMARY

1. Introduction:

1.1 What determines shape of a superconducting transition R(T)?

1.2 Fluctuations vs. system dimensionality.

2. Thermal PS activation in 1D channels.

3. Quantum PS activation in 1D channels.

what determines experimentally observed shape of a superconducting transition r t
What determines experimentally observed shape of a superconducting transition R(T)?

homogeneity of the sample

response time of the measuring system

thermodynamic fluctuations

quick response measurements, but inhomogeneous sample

realtively homogeneous sample, but very slowly response

inhomogeneous sample and unrealistically fast response

dTcexp = MAX (dTcsample, dTcmeasure, dTcfluct)

Hereafter we assume:

homogeneous sample, the measuring system is fast enough to follow accordingly the temperature sweeps, but ’integrates’ contributions of instant thermodynamics fluctuations

dTcmeasure, dTcsample < dTcfluct

fluctuations vs system dimensionality
Fluctuations vs system dimensionality

normal metal

superconductor

N

S

top

bottom

3D

no contribution of N inclusions: normal current is shunted by supercurrent 

abrupt bottom

S inclusions reduce the total system resistance 

rounded top

sFLUCT ~ (T-Tc) –(2-D/2)

(Aslamazov – Larkin)

2D

N inclusions block the supercurrent 

rounded bottom

(Langer – Ambegaokar)

1D

dimensionality of a superconductor

Dimensionality of a system is set by the relation of characteristic

physical scale to corresponding sample dimension L. For a superconductor this scale is set by the temperature - dependent superconducting coherence length x(T). Coherence length tends to infinity at critical temperature.

Dimensionality of a superconductor

thermal fluctuations
Thermal fluctuations

J.S. Langer, V . Ambegaokar, Phys. Rev. 164, 498 (1967), D.E. McCumber, B.I. Halperin, Phys. Rev. B 1, 1054 (1970)

x(T)

Infinitely long 1D wire of cross section s

√s << x(T)

Experiment:

J. E. Lukens, R.J. Warburton, W. W. Webb, Phys. Rev. Lett. 25, 1180 (1970)

R. S. Newbower, M.R. Beasley, M. Tinkham, Phys. Rev. B 5, 864, (1972)

If the wire is infinitely long, there is always a finite probability that some fragment(s) will instantly become normal

The minimum length on which superconductivity can be destroyed is the coherence length x(T).

The minimum energy corresponds to destruction of superconductivity in a volume ~ x(T) s:

DF = Bc2x(T) s, where Bc(T) is the critical field.

If the thermal energy kBT is the only source of destruction of superconductivity, then in the limit R(T) << RN the effective resistance is proportional to the corresponding probability:

R(T) ~ exp (- DF / kBT)

phase slip concept

DF

’s denote rates for both processes.

Phase slip concept

Let us consider macroscopically coherent superconducting state. It can be characterized by a wave function

Y = |Y| eij.

Dependence of the free energy F vs. superconducting phase j of a 1D current-carrying superconductor can be represented by a tilted ‘wash board’ potential with the barrier height DF.

The system can change its quantum state in two ways:

1. via thermally activated phase slips

2. via quantum tunneling.

Both processes in case of non-zero current lead to energy dissipation 

finite resitance

existing experiments on qps
Existing experiments on QPS

N. Giordano and E. R. Schuler, Phys. Rev. Lett. 63, 2417 (1989)

N. Giordano, Phys. Rev. B 41, 6350 (1990); Phys. Rev. B 43, 160 (1991); Physica B 203, 460 (1994)

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

C. N. Lau, N. Markovic, M. Bockrath, A. Bezyadin, and M. Tinkham, Phys. Rev. Lett. 87, 217003 (2001)

’Unique’ nanowires of classical superconductors

MoGe film on top of a carbon nanotube

more systematic study is required

!

samples fabrication shape control

Before sputtering

50 nm

Before sputtering

After sputtering

number of scans

After sputtering

wire height (nm)

Samples: fabrication & shape control

Objective: to enable R(T) measurements of the same nanowire with progressively reduced diameter

ion beam sputtering enables non-destructive reduction of a nanowire cross section

ion beam sputtering provides ’smoth’ surface treatment removing original roughness

r t transitions vs wire diameter
R(T) transitions vs. wire diameter

Effect of sputtering

Solid lines are fits using PS thermal activation model

Langer-Ambegaokar / McCumber-Halperin

The shape of the bottom part of the R(T) dependencies of not too narrow Al wires can be nicely described by the model of thermal activation of phase slips

Wires are sufficiently homogeneous!

current induced activation of phase slips
Current-induced activation of phase slips

I-V characteristics

Ic (T)

Sample:

L = 10 mm

√σ ~ 70 nm

At a given temperature T < Tc transition to a resistive state can be induced by a strong current *

single step transition

Ic ~ T3/2

single phase slip center activation

’true’ 1D limit

’short’ wire limit

* R. Tidecks ”Current-Induced Nonequilibrium Phenomena in Quasi-One-Dimensional Superconductors”, Springer, NY, 1990.

quantum phase tunneling in case of a short wire simplified model

t0

1 / GQPS

V

DVQPS

t

Quantum Phase Tunneling in case of a short wire (simplified model)

Full model (G-Z)

A. Zaikin, D. Golubev, A. van Otterlo, and G. T. Zimanyi, PRL 78, 1552 (1997)

A. Zaikin, D. Golubev, A. van Otterlo, and G. T. Zimanyi, Uspexi Fiz. Nauk 168, 244 (1998)

D. Golubev and A. Zaikin, Phys. Rev. B 64, 014504 (2001)

If the wire length L is not much larger than the temperature dependent superconducting coherence length x(T), then only a single phase slip can be activated at a time: simplified model

QPS are activated at a rate: GQPS = B exp (-SQPS),

where B ≈ (SQPS / t0) · (L / x), SQPS = A·(RQ / RN)·(L / x), A ~ 1, RQ = h / 4e2 = 6.47 kW,

RN – normal state resistance, t0 = h / D - duration of each QPS.

Each phase slip event creates instantly a voltage jump: DVQPS = I·RN·(x / L), where I is the measuring current.

Time-averaged voltage <V> = DVQPS· (t0 · GQPS).

Defining the effective resistance as R(T) ≡ Reff = <V> / I,

one gets:

Reff / RN = (x / L) · (t0 · GQPS)

experimental evidence of qps
Experimental evidence of QPS

After etching the wire becomes thinner

Top part (in logarithmic scale) of the R(T) transition can be nicely fitted by the Langer-Ambegaokar model of thermal phase slip activation

For the thinner wire a ’foot’ develops at the very bottom part, which cannot be fitted by L-A model at any reasonable parameters of the sample

Quantum phase slip mechanism?

conclusions
Conclusions
  • ion beam sputtering method has been developed to reduce the cross section of lift-off pre-fabricated Al nanowires
  • the method enables galvanomagnetic measurements of the same nanowire in between the sessions of sputtering
  • the shape of the bottom part of the R(T) dependencies of not too narrow Al wires can be nicely described by the model of thermal activation of phase slips
  • a ’foot’ develops at the low temperature part of the R(T) dependencies of the very thin Al wires, which can be assosiated with quantum phase slip phenomena