M.V.Feigel’man L.D.Landau Institute

1. M.V.Feigel’manL.D.Landau Institute Proposals for CESM Project Meeting 12/07/2012 Moscow Team members: Pavel Ioselevich PhD student (3d year) Konstantin Tikhonov PhD student (defense in December) Alexander Shtyk PhD student (1st year)

2. Subject1.Interplay between strong disorder and interaction in large systems of quantum spins ½. Background: 1) Analytic theory “Superconductor-insulator transition and energy localization” Phys.Rev. B 82, 184534 (2010)(M.F.,L. Ioffe, M. Mezard) 2) Exact diagonalization General framework: eigen-states localization in interacting quantum systems (Nature Communications, in press)

3. Phase diagram Major feature: green and red line meet at zero energy Temperature Energy What else could one expect? Hopping insulator Superconductor (Long-range-order) Full localization: Insulator with Discrete levels g gc

4. Phase diagram-version 2 Here green and red line do not meet at zero energy Temperature Do gapless excitation exist WITHOUT Long-range order ? Energy Hopping insulator with Mott (or ES) law Full localization: Insulator with Discrete levels Superconductor Long-range order g gc2 gc1

5. Different definitions for the fully many-body localized state • 1.    No level repulsion (Poisson statistics of the full system spectrum) • 2.    Local excitations do not decaycompletely • 3.    Global time inversion symmetry is not broken (no dephasing, no irreversibility) • 4.   No energy transport (zero thermal conductivity) • 5. Invariance of the action w.r.t. local time transformations t → t + φ(t,r): d φ(t,r)/dt = ξ (t,r) – Luttinger’s gravitational potential

6. Possible collaborations within CESM 1) N. Prokofiev (Amherst) Reason for collaboration: to extend existing analytic theory by large-scale Quantum Monte Carlo studies 2) D. Kharzeev (Stony Brook) Reason for collaboration: to develop general field- theoretical approach to the problem of energy localization

7. Subject 2. Superconductivity induced on a surface of a material with Dirac spectrum 2.1 Superconductive-normal phase transitions in arrays of small islands deposited on graphene/graphite and topological insulators.Background: Proximity-induced superconductivity in graphene , M.V.Feigel'man, M.A.Skvortsov, and K.S.Tikhonov,JETP Lett. 88(11), 747-751 (2008) General idea: tunable superconductor-metal-insulator transitions. Proposed research: Extension of the earlier results for specific experimental realizations Possible collaborations within CESM: Yu. Latyshev (IRE RAS) Reason for collaboration: joint theoretical/experimental studies

8. 2.2 Superconductivity in layered graphene-like materials Topological insulator Bi2Se3 intercalated with Cu is known to possess superconductivity with Tc ~ 10K On the other hand, recently a possibility to compose stacks of different graphene-like atomically thin layers becomes available (MoS2, NbSe2, etc). Bulk NbSe2 is known to be superconducting. Stacks of NbSe2 and graphene present potentially interesting superconducting system to be studied. Proposed research: theory of superconducting state Possible collaboration within CESM: L. Levitov (MIT)

9. 2.3 Majorana surface states and their effects upon tunneling spectra and unusual Josepshon current-phase relationsBackground: arXiv:1205.4193Majorana state on the surface of a disordered 3D topologicalinsulator,P.A.Ioselevich, P.M.Ostrovsky, and M.V.Feigel'manProposed research: Josephson current for STM with superconducting tipPossible collaborations within CESM: ???

10. Subject 3. Electron-phonon energy transfer in low-dimensional electron structures at low temperatures. BackgroundCooling power P(T) due to electron-phonon inelastic processes at low temperatures is known to depend crucially on degree of disorder: in 3D metals it is ~ T5 in clean case ql >> 1 but drops down faster in the dirty limit ql << 1 where it is ~ T6. Recently it was found (A.Shtyk, M. Feigel’man and V. Kravtsov, paper in preparation) that in the case of incomplete Coulomb screening (e.g. in 2DEG in hetrostructures) P(T) can be strongly enhanced. Proposed research: to study e-ph cooling and ultrasound attetuation for electrons in graphene and for surface states of topological insulators (where strong spin-orbital coupling is also expected to lead to new effects). Possible collaborations within CESM: L. Levitov (MIT)

11. Subject 4. Theory of nonlocal edge conductivity in disordered HgTe quantum wells Background Edge states in 2D topological insulator HgTe is known to provide ballistic nonlocal conductance in micron-size sample (Buhmann, Molenkamp, et al). However, recent results by Z-D Kvon et al on much large samples of disordered HgTe quantum well (Phys. Rev. Lett. 108, 226804 (2012), Phys. Rev. B 84, 121302 (2011)) show non-local and weakly T-dependent conductivity in the range of 0.02-0.1 e2/h. Such low values of conductivity together with absence of insulating behavior in a single-channel conductor present a challenge for theory. Proposal for research Theoretical study of elastic and inelastic backscattering of electrons on the edge of time-reversal invariant 2D insulator. Collaboration within CESM: Z-D Kvon (ISP SB RAS)