Possible collaboration within CESM

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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M.V.Feigel’man

L.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 (1
st

year)


Subject

1
.

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)

Phase diagram

Superconductor

(Long
-
range
-
order)

Hopping insulator



g

Temperature

Energy

Full localization:

Insulator with

Discrete levels

g
c

Major feature:
green

and
red

line


meet at zero energy

What else could


one expect?

Phase diagram
-
version 2

Superconductor

Long
-
range order

Hopping insulator

with Mott (or ES) law



g

Temperature

Energy

Full localization:

Insulator with

Discrete levels

g
c2

Here

green

and
red

line
do not

meet at zero energy

g
c1

Do gapless excitation exist
WITHOUT

Long
-
range order ?

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 decay

completely


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

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


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



2.2 Superconductivity in layered graphene
-
like materials



Topological insulator Bi
2
Se
3

intercalated with Cu is known to
possess superconductivity with T
c

~ 10K



On the other hand, recently a possibility to compose stacks of
different graphene
-
like atomically thin layers becomes available
(MoS
2
, NbSe
2
, etc). Bulk NbSe
2
is known to be superconducting.
Stacks of NbSe
2
and graphene present potentially interesting
superconducting system to be studied.



Proposed research
: theory of superconducting state


Possible collaboration within CESM
: L. Levitov (MIT)


2.3 Majorana surface states and their effects upon
tunneling spectra and unusual

Josepshon current
-
phase relations



Background:
arXiv:1205.4193



Majorana state on the surface of a disordered 3D topological

insulator
,P.A.Ioselevich, P.M.Ostrovsky, and M.V.Feigel'man


Proposed research:

Josephson current


for STM with superconducting tip


Possible collaborations within CESM:

?
??


Subject 3
. Electron
-
phonon energy transfer in
low
-
dimensional electron structures at low
temperatures.

Background

Cooling 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 ~ T
5

in clean case ql >> 1 but
drops down faster in the dirty limit ql << 1 where it is ~ T
6
.
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)


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 e
2
/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)