ucf and 1 f noise in diffusive metals
Download
Skip this Video
Download Presentation
UCF and 1/f noise in Diffusive Metals

Loading in 2 Seconds...

play fullscreen
1 / 36

UCF and 1/f noise in Diffusive Metals - PowerPoint PPT Presentation


  • 398 Views
  • Uploaded on

UCF and 1/f noise in Diffusive Metals. Collaborators: B. Golding, W.H. Haemmerle (AT&T Bell Labs) P. McConville, J.S. Moon, D. Hoadley (MSU) . Boulder Summer School 2005 – Lecture #4 Norman Birge, Michigan State University. With thanks to A.D. Stone and S. Feng. Supported by NSF DMR.

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 'UCF and 1/f noise in Diffusive Metals' - benjamin


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
ucf and 1 f noise in diffusive metals

UCF and 1/f noise in Diffusive Metals

Collaborators:

B. Golding, W.H. Haemmerle (AT&T Bell Labs)

P. McConville, J.S. Moon, D. Hoadley (MSU)

Boulder Summer School 2005 – Lecture #4

Norman Birge, Michigan State University

With thanks to A.D. Stone and S. Feng

Supported by NSF DMR

outline
Outline
  • 1/f noise in metals - background
  • Low-temperature 1/f noise and UCF
  • Symmetries and Random Matrix Theory
  • 1/f noise vs. B in Bi, Li, and Ag
  • Comparison of Lf from WL and UCF
  • Appendix: Tunneling systems in disordered solids
1 f noise in metals
1/f noise in metals

V(t)

R

I

Power spectral density:

Experimental observations:

with

and

how to produce a 1 f spectrum
R

t

Many fluctuators, P(log(t))~const.

How to produce a 1/f spectrum

Single two-level fluctuator:

power spectrum

the dutta horn model
The Dutta-Horn model

D(E)

Broad distribution of thermally activated processes produces nearly 1/f spectrum:

E

~1 eV

E

E >> kT  distribution is nearly flat on scale of kT

mobile defects 1 f noise
Mobile defects  1/f noise

Additional evidence:

annealing reduces noise

symmetry properties of noise

correlates with low resistivity ratio

Limitations of Dutta-Horn model:

assumes T-independent coupling of defect motion to resistance

“local interference” model

1 f noise vs t in bi films birge golding haemmerle prl 62 195 1989 prb 42 2735 1990
1/f noise vs. T in Bi filmsBirge, Golding, Haemmerle, PRL 62, 195 (1989) & PRB 42, 2735 (1990).

t = 90 nm

Bi low carrier density  high resistivity

1/f noise grows as T decreases!

why does 1 f noise grow at low t
Why does 1/f noise grow at low T?
  • density of mobile defects decreases as T drops
  • coupling of defect motion to resistance must increase

not local interference

recall from previous lectures universal conductance fluctuations ucf in wires
Recall from previous lectures:Universal conductance fluctuations (UCF) in wires

G varies randomly with B or EF

G  e2/h for L

ucf magnetofingerprint depends on exact positions of scatterers1
UCF “magnetofingerprint” depends on exact positions of scatterers

L

Conductance change for phase-coherent sample with L < Lf (phase coherence length)

Altshuler & Spivak, JETP Lett. 42, 447 (1985)

Feng, Lee, & Stone, PRL 56, 1960 (1988)

ucf in macroscopic samples l l f
LfUCF in macroscopic samples (L>Lf):

N = number of “coherence boxes”

Lf

temperature dependence of ucf noise feng lee stone prl 56 1960 1986
Temperature dependence of “UCF noise”Feng, Lee & Stone, PRL56, 1960 (1986)

Lf

(quasi-2D case)

Lf

t

  • Conductance change in “coherence volume”

motion of single defect:

multiply by number of defects in box:

energy averaging: If

Total conductance fluctuation in box :

temperature dependence of ucf noise feng lee stone prl 56 1960 19861
L

t

w

Lf

Lf

Temperature dependence of “UCF noise”Feng, Lee & Stone, PRL56, 1960 (1986)

2. Conductance fluctuation in entire sample

temperature dependence of ucf noise feng lee stone prl 56 1960 19862
Temperature dependence of “UCF noise”Feng, Lee & Stone, PRL56, 1960 (1986)

3. Tunneling model of disordered solids:

Bi, t=11 nm

4. Dephasing length in quasi-2D:

Final answer:

symmetries and ucf random matrix theory
Symmetries and UCF: Random Matrix Theory

-- eigenvalues of random matrices do not obey Poisson statistics

-- eigenvalues exhibit level repulsion

Poisson: uncorrelated levels

Gaussian Orthogonal Ensemble

rmt and the ucf variance altshuler shklovskii soviet physics jetp 64 127 1986
RMT and the UCF varianceAltshuler & Shklovskii, Soviet Physics JETP 64, 127 (1986).

k = number of independent eigenvalue sequences; s = level degeneracy

noise vs b in bi birge golding haemmerle prl 62 195 1989 prb 42 2735 1990
Noise vs. B in BiBirge, Golding, Haemmerle, PRL 62, 195 (1989) & PRB 42, 2735 (1990).

Noise drops by a factor of 2 in applied field B > Bc=(h/e)/Lf2

Confirms connection to UCF:

Noise crossover function (Stone):

other fun games with ucf and 1 f noise li moon birge golding prb 53 r4193 1996 56 15124 1997
Other fun games with UCF and 1/f noise: LiMoon, Birge & Golding, PRB 53, R4193 (1996) & 56, 15124 (1997).

Li has low spin-orbit scattering  =1 at B=0

Break spin-degeneracy when gBB > kT

GOE  GUE

 = 1  2

s = 2  1

k = 1  2

 = 2

can we obtain quantitative estimate of l f from 1 f noise vs b
Can we obtain quantitative estimate of Lf from 1/f noise vs. B?

Bi exhibits superconducting fluctuations at low T;

try Ag

t = 14 nm

Noise vs. T in Ag

noise vs b in ag mcconville and birge prb 47 16667 1993 crossover function with help from d stone
Noise vs. B in AgMcConville and Birge, PRB 47, 16667 (1993).(crossover function with help from D. Stone)
slide23
Noise crossover function with spin & SOAltshuler & Spivak, JETP Lett. 42, 447(1985); Stone, PRB 39, 10736 (1989).

UCF correlation function, T=0

Response to small chance in impurity potential, T>0

Incorporate spin effects: spin-orbit scattering, Zeeman splitting

Noise crossover function:

comparison of l f from wl and ucf
Comparison of Lf from WL and UCF

McConville and Birge, PRB 47, 16667 (1993).

WL

noise

Hoadley, McConville and Birge, PRB 60, 5617 (1999).

why don t l f wl and l f ucf agree at low t in ag
Why don’t LfWL and LfUCF agree at low T in Ag?
  • Crossover to strong spin-orbit scattering
    • But AuPd data is even stronger!
  • Noise measurements are out of equilibrium?
    • Noise vs. B unchanged with drive current
a proposal to explain the discrepancy in ag trionfi lee and natelson prb 72 035407 2005
A proposal to explain the discrepancy in AgTrionfi, Lee, and Natelson, PRB 72, 035407 (2005).

saturated UCF

WL

unsaturated UCF

does the 1 f noise saturate ucf
Does the 1/f noise saturate UCF?

g(ln(t) = const. for tmin < t < tmax

UCF “magnetofingerprint”

It would take ~ 200 decades of 1/f noise at the level measured to saturate the UCF!

summary
Summary
  • 1/f noise in metals comes from defect motion
  • 1/f noise is enhanced at low T due to long-range quantum interference (UCF)
  • Noise vs. B reveals RMT crossovers (GOEGUE, Zeeman splitting, etc.)
  • Discrepancy in Lf determined from WL and UCF
    • Maybe due to crossover from unsaturated to saturated UCF
appendix tunneling systems in disordered insulating solids
Appendix: Tunneling systems in disordered (insulating) solids

I. Crystalline Solids

“Every atom knows its place”

vacancy

Point defects are not mobile at low temperature (1eV10,000K)

~1 eV

ii disordered solids
II. Disordered Solids

dislocation

More disorder  more low barriers

ii disordered solids1
II. Disordered Solids

dislocation

More disorder  more low barriers

dynamics in a double well potential
Dynamics in a double-well potential

High T: over the barrier

(thermal activation)

Low T: through the barrier

(tunneling)

Asymmetry energy:

Tunneling energy:

e d k b t @ w 0 v
e, D, kBT << @w0 < V

 two-level tunneling system (TLS)

Hamiltonian in left-right basis

Eigenvalues:

Eigenstates:

where

the standard tunneling model anderson halperin and varma phillips 1972
The standard “tunneling model”Anderson, Halperin and Varma; Phillips (1972)

Hypotheses: 1) P(,l)=P0c(T) ~ T

2) TLS scatter phonons k(T) ~ T2

Experimental Data:

Zeller and Pohl (1971)

ad