FAMU05

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Quantum Glassines in Coulomb Systems: From Field-Effect Transistors to High Tc Cuprates Collaborators: Darko Tanaskovic (FSU) Andrei Pastor (FSU) Sergey Pankov (Paris) Denis Dalidovich (FSU) Marcelo Rozenberg (Paris) Liliana Arachea (Trieste) Christos Panagopoulos (Cambridge) Funding NHMFL/FSU Alfred P. Sloan Foundation NSF grant DMR-9974311 Vladimir Dobrosavljevic Department of Physics and National High Magnetic Field Laboratory Florida State University

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Prologue: The sad story of the farmer and his silos Sometimes the ENTIRE SILOS simply explodes!!! (catastrophic “avalanches” - fluctuation on the scale of the system)

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Large fluctuations: “critical” states of matter Large fluctuations (critical opalescence) only near the critical point only critical super-critical sub-critical Why are the fractals so common???!!!

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Contents: “Dirty” conductors/insulators: electron glasses What is “known”: Coulomb gap, glassiness, no screening? Long-range Coulomb interactions: self-organized criticality at T=0 Quantum melting of electron glass: Anderson vs. Mott localization Glassiness as key to High Tc superconducitvity?

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Glassy behavior of disordered electrons?

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What is “known” about the Coulomb glass?

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Efros-Shklovskii theory: r(e) ≤ Cd(e-eF)d-1 (Bound !!) NOTE: in ALL dimensions!!! Coulomb Glass Model Experiment: tunneling spectra of Si:B (Mark Lee, Phys. Rev. Lett. 93, 256401 (2004)) T=0 Powerlaw behavior at low energy: critical state?

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Open questions: Why is the bound saturated? Why universal prefactor and exponent? Relation to possible glassy freezing ES assumed no screening. Why? Role of quantum fluctuations, MIT?

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EDMFT approach: controlled theory in large d A. A. Pastor and V. Dobrosavljevic, PRL 83, 4642 (1999) Physical content: environment (“cavity”) treated in a “Gaussian” approximation. (quasiparticles+plasmons)

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Approaching the Coulomb Glass: Pseudogap Phase Simulation (T. Vojta, 1995) At stronger disorder, the “plasma dip” disappears! Theory NO adjustable parameters!!!

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Exotic Features of the Electron Glass Phase

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What about the Efros-Shklovskii gap? EG Efros-Sklovskii theory: r(e) = Cd(e-eF)d-1 Gap EG ~ W-1/(d-1) Our analytical results give TG ~ W-1/(d-1) (at W large) This suggests that the universal Coulomb gap is a feature of the glassy phase. Consistent with vanishing ZFC compressibility at T=0 in the glass phase, thus no screening recent extension of our approach (Muller and Ioffe, 2004) explicitly show that lscr ~ 1/T. Thus zeff → MFT valid!!!

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Mobile electrons: quantum fluctuations MELT glass at T=0 Quantum Melting of the Electron Glass Glassy behavior deep in the insulator (Efros&Shklovskii, Pollak) Question: when does the glass melt? E-DMFT: “replica symmetry breaking” (Parisi-like scheme) Diverges at Anderson-like transition Vanishes at Mott transition

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Global Phase Diagram: DMFT picture of the Metal-Insulator Transition Dobrosavljevic, Tanaskovic, Pastor; PRL 90, 016402 (2003) W=U Wigner-Mott Solid (incompressible) Metal Wigner-Mott Glass (gapless) Metallic Glass Disorder Metallic glass phase: Hierarchical, correlated dynamics (scale invariant) Experiments by Popovic et al., PRL 2002 Kar et al., PRL 2003 “Replicon” modes: Non-Fermi liquid transport (a la Sachdev) Dalidovich and Dobrosavljevic, PRB (2002)

Glassy behavior as key to high-Tc superconductors?(C. Panagopoulos, V.Dobrosavljevic, cond-mat/0410111): 

Glassy behavior as key to high-Tc superconductors? (C. Panagopoulos, V.Dobrosavljevic, cond-mat/0410111)

Resistivity of a high Tcsuperconductor: 

Resistivity of a high Tcsuperconductor Puzzling “Marginal Fermi Liquid” behavior (Takagi, 92)

Glassy behavior and superconductivity?(C. Panagopoulos et al.): 

Glassy behavior and superconductivity? (C. Panagopoulos et al.) Standard spin-glass signatures at low doping muSR data within the superconducting phase glassiness persists!!! spin and charge correlation!

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The Abnormal Normal State of the High-Tc Superconductors Using 60 teslas ... ...to suppress the superconducting state ...(undress the electrons)… …to reveal the low-temperature normal-state phase diagram

Phase diagram: 

Phase diagram glassy insulator homogeneous metal inhomogeneous (glassy) metal SC glass STM imaging: evidence of an inhomogeneous state! (Takagi, PRL 2004). THEORY: Nano-scale phase separation Gorkov and Sokol 87, Kivelson, Dagotto et al Self-generated “stripe glass” Schmalian and Wolyness (EDMFT-2000) Charge tunneling gives logT Efetov, PRL 2003

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Conclusions: What have we learned from the EDMFT approach to the Coulomb glass? Coulomb repulsion + disorder = glassiness Absence of screening (at T=0) in the glassy phase Self-organized criticality, marginal stability → universal Coulomb gap Quantum fluctuations due to mobility of electrons Anderson localization: singular perturbation, stabilizes glass Intermediate metallic glass phase as seen in MOSFETs Possible key role in MOSFETs, high Tc superconductors,...