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XIX Ural International Winter School on the Physics of Semiconductors
February 20- 25, 2012 Ekaterinburg, Russia
Electron-hole Bose liquid is a novel
phase in strongly correlated 3d
systems
A.S. Moskvin
Department of Theoretical Physics,
Institute of Natural Sciences UFU
Concept of electron-hole Bose liquid in
strongly correlated 3d systems is based
on many earlier model approaches
suggested for strongly correlated
systems:
 Shafroth composite bosons
 Disproportionation scenario
(chemical route)
 Negative-U model
 Bipolarons
Some references
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P.W. Anderson, Phys. Rev. Lett. 34, 953 (1975)
S. P. Ionov, G. V. Ionova, V. S. Lubimov, and E. F. Makarov, Phys.Status
Solidi B 71, 11 (1975).
I.O. Kulik, A.G. Pedan, JETP, 1980, Vol. 52, No. 4, p. 742
J.E. Hirsch and D.J. Scalapino, PRB, 32, 5639 (1985)
C.M. Varma, PRL, 61, 2713 (1988)
John A Wilson, J. Phys.: Condens. Matter 12 (2000) R517–R547
T.H. Geballe and B.Y. Moyzhes, Physica C 341-348, 1821-1824 (2000);Low
Temperature Physics 27, 777 (2001)
K.V. Mitsen and O.M. Ivanenko, Phys. Usp. 47, 493 (2004)
K.D. Tsendin, B.P. Popov, and D.V. Denisov, Supercond. Sci. Technol. 19,
313 (2006)
S. Larsson, Int. J. Quantum Chem., 90, 1457 (2002); Physica C, 460-462,
1063 (2007)
Hiroshi Katayama-Yoshida, Koichi Kusakabe, Hidetoshi Kizaki, and Akitaka
Nakanishi, arXiv:0807.3770v1).
Outline
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Disproportionation and local bosons
Electron-hole (EH) dimers
EH Bose liquid: singlet local bosons
EH Bose liquid: triplet local bosons
EH Bose liquid in cuprates
EH Bose liquid in manganites
Key words: + mixed valence, electron-hole excitations,
charge transfer excitons, exciton self-trapping,
cuprates, manganites, pnictides, high-Tc
superconductivity, colossal magnetoresistance,…
Disproportionation as a way to
electron-hole Bose liquid
Disproportionation in 3d oxides
• At present, a charge transfer (CT)
instability with regard to disproportionation
is believed to be a rather typical property
for a number of perovskite 3d transitionmetal oxides such as CaFeO3, SrFeO3,
LaCuO3, RNiO3, moreover, in solid state
chemistry one consider tens of
disproportionated systems
Simple algebra for
disproportionation
• One-particle charge transfer and formation
of EH-dimer (charge transfer exciton)
3d  3d  3d
n
n
n 1
 3d
n 1
• Two-particle charge transfer in EH-dimer
3d
n 1
 3d
n 1
 3d
n 1
 3d
n 1
Composite local boson in EH-dimer
n
n
n+1
n-1
3d +3d →3d +3d
n+1
3d
n-1
n-1
+ 3d ↔ 3d + 3d
2
2
3d
3d
n-1
3d
3d
3d
n+1
3d
n 1
n-1
n-1
3d
3d
n-1
n 1
 3d
n 1
 com positelocal boson
 3d 
2
However,…
• To introduce a local composite boson we
need:
• 1. No configurational mixing for the both
n 1
n 1
and 3d
configurations,
3d
and a simple genealogy
(3d
n 1
(3d
n 1
)  (3d
n 1
)(3d ), or
)  (3d
n 1
)(3d )
2
2
Then…
3d
n 1
1
3d
n 1
2
H 3d
n 1
1
3d
n 1
2
 3d H 3d
2
1
2
2
t
B
12
is a two-particle, or boson transfer
integral:
e 2
| t12 |
t 
 J 12
U
B
12
To provide the boson mobility we
need (eg2)1A1g or (eg2)1A2g
composite boson structure
• To minimize the reduction effects of orbital
overlap and draw the strongest -bond into
boson transfer we need the eg2-type
configuration for composite boson.
• To minimize reduction effects of local electronlattice coupling we need S-type bosons with the
A1g or A2g symmetry.
• To minimize the reduction effects of spin
degrees of freedom we need spin singlet 1A1g or
1A
2g boson.
There are only several
specific 3dn configurations
that meet these
requirements. For highsymmetry crystal fields
these are shown in Figure.
Yet, all these point to spin
triplet local bosons!
However, for low-symmetry
crystal fields there are
configurations that permit
formation of spin singlet
composite local bosons, e.g.
Cu2+(3d9) in strong tetragonal
crystal field
Singlet local bosons in tetragonal
Cu2+ cuprates
• Cu2+(3d9) in strong tetragonal crystal field
corresponds to b1g(dx2-y2)-hole. Than the
Cu1+(3d10) electron center can be
considered as hole center Cu3+(3d8), or
b1g2:1A1g (Zhang-Rice singlet) with
localized two-electron composite spin
singlet boson b1g2:1A1g
Spin and orbital
singlet local bosons
(quantum charges)
Minimal model of the
EHBL:quantum charges
• The minimal model of the EHBL is
described by a Hamiltonian of local, or
hardcore bosons on a lattice
H hc    t mn P B Bn  B Bm P

m

n
mn
 Vmn N m N n    N n
mn
n
Equivalent s=1/2 pseudospin
Hamiltonian
• Anisotropic Heisenberg model in
external field
xy
sm sn  sn sm    J mnz smz snz    snz ;
H hc   J mn
mn
mn
n
1
1 

J  2tmn ; J  Vmn ; s 
B; s  
B ;
2
2
1
1 x
z



s    B B; s  
s  i s y .
2
2
xy
mn
z
mn

Typical T-n phase diagram of
2D local boson system
• n – is the deviation
from half-filling
• G. Schmid et al., Phys.
Rev. Lett. 88,167208
(2002).
Spin triplet but orbital
singlet local bosons
Effective Hamiltonian for triplet
s=1 local bosons on a spin-S
lattice
H EHBL   tij B B jm   Vij ni n j    ni

im
ij,m

i
 
 
 
  J s  s    J s  S 
  J ijhh

ij
 


S i  S j   J ijhb si  S j
ij
ij
bb
ij
ij
i
hb
ii
j
i
i
i
• A.S. Moskvin, Phys. Rev. B 79, 115102
(2009)
• These Hamiltonians imply the preformed
EH Bose liquid. However, in the most
part of 3d systems under study the
ground state is related with the bare 3dn
ions. Formation of the EHBL needs in
some transformations of the system, in
particular, the nonisovalent substitution,
photoexcitation, or mechanic pressure.
In any case the EHBL evolves from EHdimers.
Formation of the EHBL starts
with EH-dimers…
Let address EH-dimers in several
“hottest” 3d systems.
S- and P-type EH-dimers in
cuprates
Ψu =
5-
[CuO4] +[CuO4]
2
(Ψ eh - Ψ he )
7-
7-
[CuO4] +[CuO4]
2 tB
Ψg =
2e
1
1
2
5-
(Ψ eh + Ψ he )
ˆ Ψ he
t B  Ψ eh H
2e
Ψ g d|| Ψ u = 2eRAB
tB~1000 K !
(theoretical estimations
and different optical data,
see A.S. Moskvin, Phys.
Rev. B 84, 075116 (2011))
S- and P-type EH-dimers can be
termed as bonding and
antibonding ones, respectively
Energy of EH-dimer, or d-d CT
exciton = d-d CT gap
Two types of CT gap:
Franck-Condon and
non-Franck-Condon CT gaps
What is the energy of
EH-dimer in cuprates?
EH-dimers in parent cuprates
•
Simple illustration of the electron-lattice polarization effects for the CT
excitons: a) CT stable system; b) CT unstable system. Filling points to a
continuum of unbounded electrons and holes. Right panel shows the
experimentally deduced energy scheme for the CT states in La2CuO4
CT transitions in parent cuprates.
Optical manifestation of EH dimers
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Reconstruction of the whole NFC-FC CT band in Sr2CuO2Cl2. The scale of the respective
absorption coefficients differs by three orders of magnitude. Such an unconventional NFC-FC
structure of the optical spectra is a typical one for all parent cuprates. Vertical arrow points to a
hardly visible peak at ≈ 0.2 eV.
…………………………………………………………………………………………………………………
J.D. Perkins, R.J. Birgeneau, J.M. Graybeal et al., Phys. Rev. B58, 9390 (1998).
S.L. Cooper, D. Reznik, and A. Kotz et al., Phys. Rev. B 47, 8233 (1993).
Photoinduced absorption spectrum
of La2CuO4
• J. M. Ginder et al., Phys. Rev. B 37, 75067509 (1988)
• Y. H. Kim et al., Phys. Rev. Lett. 67, 2227 (1991).
CT gap in parent cuprates
• Energy gap over which the electron
and hole charge carriers are optically
activated in parent cuprate La2CuO4
(FC CT gap) to be
∆CT(opt)  2.0 eV !!!.
• (numerous optical measurements)
CT gap in parent cuprates
• Energy gap over which the electron and
hole charge carriers are thermally activated
in parent cuprate La2CuO4 (non-FC CT
gap) to be ∆CT(free EH)=0.89 eV !!!.
• Y. Ando, Y. Kurita, S. Komiya, S. Ono, and K.
Segawa, Phys. Rev. Lett. 92, 197001 (2004)
CT gap in parent cuprates
• Energy gap over which the electron-hole
dimers are thermally activated in parent
cuprate La2CuO4 (non-FC CT gap) to
be
∆CT(EH-dimer) 0.5 eV !!!.
• A.S. Moskvin, Phys. Rev. B 84, 075116 (2011)
EH-dimer in nickellates (Ni2+)
EH-dimer in manganites (Mn3+)
EH-dimer=CT exciton=quantum of
disproportionation
3
3
4
Mn  Mn 
 Mn  Mn
eg
2
One-electron transport with anti-JT transition
4
2
2
2
Mn  Mn  Mn  Mn
eg
Two-electron transport with dynamical
breathing mode
4
Spin structure of the S- and P-type
EH-dimers in LaMnO3
A. S. Moskvin, Phys. Rev. B 79, 115102 (2009).
EH-dimers in LaMn7O12
•
R. Cabassi, F. Bolzoni, E. Gilioli, F. Bissoli, A. Prodi, and A. Gauzzi, Phys.
Rev. B 81, 214412 (2010)
55Mn
NMR spectrum for EH dimers:
local field
1  S ( S  1)  5
S ( S  1)  5 
Hn  
A2 
A4  S
2  2S ( S  1)
2S ( S  1)

S  1, 2,3, 4
55Mn
•
55Mn
NMR spectrum for EH dimers
NMR frequencies for bare Mn4+,3+,2+ ions in
LaMnO3 (Tomka,Allodi,Shimizu) and theoretical
predictions for the EH-dimer in different spin states.
Shown by filling is a 55Mn NMR signal for slightly
nonstoichiometric LaMnO3 (Kapusta).
Formation of the EHBL phase in a
model La1-xSrxCuO4 cuprate
Toy S=1 charge pseudospin
model for mixed valence cuprate
• (Cu2+) M=0; (Cu1+) M=-1; (Cu3+) M=+1
• Effective pseudospin Hamiltonian
H    n S nz2  hn S nz   Vmn S mz S nz 
n
 D S
  t S
mn
(2)

S

S
S

D
m n 
m n
mn Tm  Tn   Tm  Tn  
mn
2
m
mn
mn

(1)
mn
S n2  S m2  S n2 
T  S z S  S S z 
Model parameters
• We made use of reasonable bare parameters as follows:∆=0.4,
h=0, t=0.1, Vnn=0.35 eV. These agree with experimental findings
for La2CuO4: ∆CT = 2∆ ≈ 0.8-0.9 eV; ∆EH = 2∆−Vnn ≈0.4-0.5 eV;
t ≈ Jnn ≈ 0.12 eV.
• The model impurity potential was produced by negative charges
q = e randomly located at the positions of La3+ ions and forming
an ”impurity zone” with radius 4a and parameters ∆ = ∆∗=-0.5,
h∗=0.35, t=0.1, Vnn∗=0.25 eV which are considered to be
constant all over the ”impurity zone”. It means that throught the
lattice covered by impurity potential the EHBL phase forms a
stable ground state with the electron-hole recombination energy
(or the energy of the inverse disproportionation reaction which
defines an energy scale of a robustness of the EHBL phase) as
large as ∆CT∗ ≈ (−2∆∗ +Vnn∗) =1.25 eV.
Quantum Monte-Carlo
simulation…
Phase pattern of the model CuO2 plane
x=0
x=0.03
x=0.06
Phase pattern of the model CuO2 plane
x=0.09
x=0.12
x=0.15
Phase pattern of the model CuO2 plane
x=0.18
x=0.21
x=0.24
T-x phase diagram
Inhomogeneous
of model cuprate
EHBL phase
Signatures of the EHBL phase in
manganites
Electronic phase separation and
physical properties of nominally
stoichiometric LaMnO3
1.0
fEH
O’ orthorhombic
JT ordering
A-type AFM
dynamic
EH droplets
O orthorhombic
FM-EHBL
static
0
200
TNTC
400
Tg?
600*
T1
800
Tdisp=TJT
1000*
T2 T (K)
A. S. Moskvin,
Phys. Rev. B 79,
115102 (2009).
EHBL in YBaMn2O6?
Susceptibility in manganites behaves in a
fundamentally different way at high
temperatures than is usually observed in
magnetic
materials
with
dominant
superexchange interactions.
Magnetic moment observed in YBaMn2O6 by
ESR can be explained only, if to assume that all
Mn ions are in a tetravalent state (!?). This
points to EHBL phase with triplet local bosons
eg2 moving in the lattice formed by Mn4+
centers. ESR contribution of the boson spin
system cannot be detected when the hopping
time becomes short compared to a Larmor
period and prevents the occurrence of the
precessional motion of the spin.
D. V. Zakharov, J. Deisenhofer, H.-A. Krug von
Nidda et al., PHYS. REV. B 78, 235105 (2008)
EHBL in YBaMn2O6?
• The linewidth for T>520 K
appears to follow a
classical Korringa-type
behavior, typical for the
localized spins coupled to
the quasifree spin and
charge carriers.
* Dr. Joachim Deisenhofer (Uni-Augsburg), private communication
EHBL in manganites
• The very idea of using multiple-valence
atoms as an active element electronically
involved in the conduction mechanism
namely, the Mn2+ and Mn4+ in manganites
opens unexplored scenarios in the study
of physical properties of CMR materials.
Thank you!