A Finite-Temperature Insulator? Idan Tamir Weizmann Institute of Science Collaborators - M. Ovadia, D. Kalok, S. Mitra, B. Sacepe and D. Shahar http://arxiv.org/abs/1406.7510 International Workshop Localization, Interactions and Superconductivity Chernogolovka, Russia, June 29 - July 3, 2015

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, 206603 (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, 155111 (2007)

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, 052203 (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:1501.05661

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

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, 017003 (2005) Baturina, T. I., Mironov, A. Y., Vinokur, V. M., Baklanov, M. R. & Strunk, C. Phys. Rev. Lett. 99, 257003 (2007)

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, 176802 (2009) B. L. Altshuler, V. E. Kravtsov, I. V. Lerner, and I. L. Aleiner, Phys. Rev. Lett. 102, 176803 (2009)

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, 184534 (2010) Low-dimensional Interacting electrons Weak e-ph coupling

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, 107005 (2004).

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

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)

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. 23.6 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

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, 224203 (2014).

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

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

Current Noise Vtrap-1.5 Vesp-2.5

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

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)

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