Superconducting State of Small Nanoclusters

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Superconducting State of Small Nanoclusters Vlad
imir Kresin and Yurii Ovchinnikov
Lawrence Berkeley National Laboratory L.
Landau Institute for Theoretical Physics, Moscow,
Russia
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Superconducting state of small metallic
nanoparticles
N ? 102 - 103
(N is a number of delocalized electrons)
New family of high Tc superconductors
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Superconducting state of metallic nanoparticles
M. Tinkham et al. (Harvard U.) 1995-
N ? 104 105
Small metallic nanoparticles (clusters)
N ? 102 - 103
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Nanoclusters
Clusters small aggregates of atoms or molecules
An (e.g., Nan , Znn, Aln)
e.g., Al56 N 56 x 3 168
(each Al atom has 3 valence electrons)
Zn66 N 66 x 2 132
Metallic nanoclusters Discrete energy
spectrum Energy spacing depends on the particle
size
EF
?E
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Nanoparticles Discrete energy spectrum
The pairing is not essential if ?E gt
?
(Anderson, 1959) The pairing is important if
?E lt ? Usual superconductors
????? Estimation
Condition Ngt104 (?E????? Assumption the energy
levels are equidistant (?)
Shell
structure(1984)
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Shell Structure
Metallic clusters contain delocalized electrons
whose states form shells similar to those in
atoms or nuclei
Clusters
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Metallic clusters
Mass spectra of metallic clusters display magic
numbers
Magic numbers (Nm8,20,40,,168,,192,) correspon
d to filled electronic shells (similar to inert
atoms)
Cluster shapes Clusters with closed electronic
shells are spherical
There is a strong correlation
Number of electrons shape energy
spectrum
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Metallic nanoclusters
Metallic clusters contain delocalized
electrons whose states form shells similar to
those in atoms or nuclei Shell
structure W. Knight et
al. (1984) Shell structure
pairing W.Knight et
al. (1984)
J.Friedel (1991)
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Magic clusters
spherical shape (quantum
numbers n,L) degeneracy g 2(2L1)
e.g. Nm 168 L 7 g 30
(!)
Lowest unoccupied shell
Highest Occupied shell
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Incomplete shell
e.g., N 166 (Nm 168) shape
deformation sphere ellipsoid splitting

LUS
HOS
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Magic clusters
spherical shape (quantum
numbers n,L) degeneracy g 2(2L1)
e.g. Nm 168 L 7 g 30 (!)

Electrons at HOS (EF) can form the pairs

Superconducting state
Lowest unoccupied shell
Highest Occupied shell
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Pairing is similar to that in nuclei
A.Bohr , B.Mottelson, D.Pines(1958)
S.Beljaev (1959) A.Migdal (1959)
The pair is formed by two electrons
mj,1/2 -mj,-1/2
Metallic clusters - Coulomb forces -
electrons and ions - electronic and
vibrational energy levels
electron- vibrational interaction
-increase in size ? bulk metal
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high degeneracy
peak in density of states
(similar to van Hove) increase in
TC e.g., L 7 (N168 e.g.,
Al56 degeneracy G 2(2L 1) 30
(30 electrons at EF)
EF
HOS
? ? V?
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Arbitrary strength of the electron vibrational
coupling
(W. McMillan (1968))
Clusters
Bulk
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Critical temperature
T TC
C. Owen and D. Scalapino (1971) V. Kresin
(1987)
Matrix method
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LUS (lowest unoccupied shell)
?
HOS (highest occupied shell)
Parameters N, ??LH, gL, gH EF, ,
?b Examples N 168 ??LH 70meV, gL 30 gH
18 25meV ?b 0.5 EF105K
(L 7)
(L 4)
TC150K
Ga56 (N 168) TC160K Zn190(N380) TC105K
(Tcb 1.1K)
(Tcb 0.9K)
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Simple metallic clusters (Al, Ga, Zn, Cd)
Tc ? 150K
Change in the parameters ( , ?E, etc)
Room temperature
EF
?E
Conditions - small HOS-LUS energy spacing -
large degeneracy of H and L shells - small
splitting for slightly unoccupied shells e.g.,
N168, 340 N166
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Superconducting state of nanoclusters

(manifestation observables) Energy
spectrum experimentally measured excitation
spectrum (e.g. HOS LUS internal (?E)) is
temperature dependent
- clusters at various
temperatures
1)TltltTc 2)TgtTc

e.g., Cd83 (N166)
1)TltltTc
2)TgtTc

h?min. 34 meV h?min. 6
meV - photoemission spectroscopy odd-even
effect the spectrum strongly depends on the
number of electrons being odd or even
LUS
HOS
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Clusters with pair correlation are
promising building blocks for tunneling networks.
Macroscopic superconducting current at high
temperatures Depositing clusters on a surface
without strong disturbance of the shell structure
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(No Transcript)
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Bulk superconductivity (R0)Tunneling--gt
Josephson tunneling
(tunneling of the pairs)dissipationless
macroscopic current (R0)
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Superconducting state of nanoclusters
Proposed Experiments Energy
spectrum experimentally measured excitation
spectrum (e.g. HOS LUS internal (?E)) is
temperature dependent
- clusters at various
temperatures
1)TltltTc 2)TgtTc
-
photoemission spectroscopy odd-even effect the
spectrum strongly depends on the number of
electrons being odd or even
LUS
HOS
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• Experiments
• Selection ( mass spectroscopye.g.,
• 
  Ga56)
• - Cluster beams at different temperatures
• (TgtTc
  and TltTc)
• - Spectroscopy ( photoemission)
• Magnetic properties

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Summary
The presence of shell structure and the
accompanying high level of degeneracy in small
metallic nanoclusters leads to large increase in
the value of the critical temperature
e.g., Ga56 (N168) Tc ? 150K

• Main factors
• - large degeneracy of the highest occupied shell
  (HOS) small HOS- LUS space
• incomplete shell
• small shape deformation
• Manifestations of the pairing
• temperature dependence of the spectrum
• - odd-even effect
• - clusters with superconducting pair correlation
  are promising blocks for tunneling network.

LUS
HOS
Phys.Rev.B 74,024514 (2006)
Small nanoclusters form a new family of high Tc
superconductors