1. A Finite-Temperature Insulator?
Idan Tamir
Weizmann Institute of Science
Collaborators - M. Ovadia, D. Kalok, S. Mitra, B. Sacepe and D. Shahar
International Workshop
Localization, Interactions and Superconductivity
Chernogolovka, Russia, June 29 - July 3, 2015

2. Many Body Localization (MBL)
Interacting electrons
Disordered
Low-dimensional
Electrons are decoupled
from any external bath
Anderson-like localization of many-body wave functions in the Fock space
Anderson - quantum particle may become localized by a random potential.
Noninteracting systems of 1,2D - weak disorder localizes all states sig=0.
e-ph -> VRH
Only e-e???
P. W. Anderson, Phys. Rev. 109, 1492 (1958)
Gornyi, I. V., Mirlin, A. D. & Polyakov, D. G. Phys. Rev. Lett. 95, (2005)
Basko, D. M., Aleiner, I. L. & Altshuler, B. L. Annals of Phys. 321, 1126 (2006)
Oganesyan, V. & Huse, D. A. Phys. Rev. B 75, (2007)

3. Experimental Requirements for Observation of MBL
Interacting electrons
Disordered
Low-dimensional
Weak e-ph coupling
Experimental manifestations of this transition in real systems, where both electron-electron and electron-phonon interactions are present
Bi-stable I-V curve
Basko, D. M., Aleiner, I. L. & Altshuler, B. L. Phys. Rev. B 76, (2007).
Cold atoms: Schreiber, M., Hodgman, S. S., Bordia, P., Lüschen, H. P., Fischer, M. H., Vosk, R., Altman, E., Schneider, U., Bloch, I. eprint arXiv:

4. a:InO Hebard, A. F. & Paalanen, M. A. Phys. Rev. Lett. 65, 927 (1990)
Yazdani, A. & Kapitulnik, Phys. Rev. Lett. 74, 3037 (1995)

5. Observation of Bi-stable I-V curves in a:InO
T=10 mK
G. Sambandamurthy, L. W. Engel, A. Johansson, E. Peled, and D. Shahar Phys. Rev. Lett. 94, (2005)
Baturina, T. I., Mironov, A. Y., Vinokur, V. M., Baklanov, M. R. & Strunk, C. Phys. Rev. Lett. 99, (2007)

6. Bi-stable I-V curves Overheated Electrons Model
Simulated data
Electrons are weakly coupled to the phonons
M. Ovadia, B. Sacepe, and D. Shahar, Phys. Rev. Lett. 102, (2009)
B. L. Altshuler, V. E. Kravtsov, I. V. Lerner, and I. L. Aleiner, Phys. Rev. Lett. 102, (2009)

7. a:InO a Possible Finite Temperature Insulator
Disordered
Disordered
Low-dimensional
Interacting electrons
Weak e-ph coupling
Cooper pairs
Feigel’man, M. V., Ioffe, L. B. & M´ezard, M. Phys. Rev. B 82, (2010)
Low-dimensional
Interacting electrons
Weak e-ph coupling

8. Earlier Studies Measured Activation
𝑹 𝑻 = 𝑹 𝟎 ×𝒆𝒙𝒑 𝑻 𝑰 /𝑻
𝑹 𝑻 = 𝑹 𝟎 ×𝒆𝒙𝒑 𝑻 𝑰 /𝑻
Limited R range – standard 2 probe measurements
Activation conductivity
Sambandamurthy, G., Engel, L. W., Johansson, A. & Shahar, D. Phys. Rev. Lett. 92, (2004).

9. An Effort to Measure Higher R
Fix T and B
Wait 1 hour
Ramp V
Wait 10 seconds
Measure I
Extrapolate the scan to V=0
Determine R
𝑹=𝟕.𝟑𝟐× 𝟏𝟎 𝟏𝟎 
Won’t tell you:….
Smooth ramp – avoid capacitance overload of current amp.
Estimate leakage I: a null measurement was done several times.
These set of measurements indicated a (resistive) isolation of at
least a few 10^12 .
Pseudo-guarding (using distant wires and grounding the others) was also used
to reduce mutual capacitance to a minimum and draw resistive leakages away from the input of
the I amplifier. The result was that the largest leakage I is between the nonzero V offset of the I
amplifier input and the “pseudo-guard”, which cause a constant offset in I and should not influence
the I-V slope. Drifts in that I (caused by input V offset drift) are probably what limit the method’s
accuracy because they increase with the measurement time.
Keep P=IV below heating

10. The Results Activation Up to 10^6 – activation
Dashed line – activation
5-12 T – sub-activaton VRH (convex)
0.5-2 T – faster that activation (concave)

11. Variable Range Hopping Transport at High Magnetic Fields
VRH
Present data of two fields for convenience
Good fit down to 5 T (peak value)
Tes varies betweenType equation here K (~8.9 um) at 5 T to 14.8 K (~14 um) at 12 T.
𝑹 𝑻 = 𝑹 𝑬𝑺 ×𝒆𝒙𝒑 𝑻 𝑬𝑺 𝑻 𝟏/𝟐

12. Conductivity 𝜌 −1 Near Bc
Resistance Near Bc
Conductivity 𝜌 −1 Near Bc BC
𝝈 𝑻 = 𝝈 𝟎 ×𝒆𝒙𝒑 − 𝑻 𝟎 𝑻
𝝈 𝑻 = 𝝈 𝟎 ×𝒆𝒙𝒑 − 𝑻 𝟎 𝑻− 𝑻 ∗
In any real system sig=0 is not a realistic expectation. This is because when sig becomes very
small other, parallel, channels will carry the electronic current and contribute to sig. Each such
channel will lead to the measured being higher, and can account for the deviations we observe
at sig< 1:3 10^10 mho. These can be due to physical processes within the sample or, possibly,
due to leakage currents elsewhere in the measurement circuit. More recently, a theoretical paper
utilizing a mean field description to a system near the MBL transition suggested such deviations
should be expected.
Gopalakrishnan, S. & Nandkishore, R. Mean-field theory of nearly many-body localized metals.
Phys. Rev. B 90, (2014).

13. Fit Parameters BC
𝝈 𝑻 = 𝝈 𝟎 ×𝒆𝒙𝒑 − 𝑻 𝟎 𝑻− 𝑻 ∗

14. MBL?
Need to show that our electrons are ineffective in reaching equilibrium
Incorporate Cooper-pairing
Observed an abrupt drop in  by several orders of magnitude occurring at T <0.1 K
The data do not exclude the phenomenological finite-T insulator

15. Current Noise
Vtrap-1.5 Vesp-2.5

16. Activated conductivity
Simulated activated behavior in linear scale
T0=0.1
T (K)

17. Alternative to Finite-T Insulator
A quantitative analysis clearly renders this view inadequate for the following reason.
Fitting the B = 0:75 T data using an Arrhenius form leads to an activation T of 0.91 K. If a
mobility gap of such magnitude existed in our system we would expect a much sharper increase in
R at 0:91 > T > 0:05 K, as seen in the fit presented in the supplementary material. This drop is
clearly missing in our data rendering an activated interpretation highly unlikely unless the 0.91 K
gap only opens at T < 0:1 K. We are not aware of a theoretical work predicting such a possibility.
R_HA=470, A=3.85, E_c=0.054
A=ln(L/a), where L is the sample size and a is the size of a single JJ ->
a(L=200um)=4.25um >> fluctuation of the superconducting gap and coherence peaks of order 10 nm
𝑹 𝑻 = 𝑹 𝑯𝑨 ×𝒆𝒙𝒑 𝑨× 𝒆 𝑬 𝒄 /𝑻
T.I. Baturina, V.M. Vinokur, Annals of Physics 331 (2013)

18. R vs. B
Each curve ~ one and a half days Bc