Lecture 2.2, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare
LDA band structures of
transition-metal oxides
and what electronic
correlations may do to them
The metal-insulator transition in V2O3
Is it really the prototype Mott transition?
[1] T. Saha-Dasgupta, O.K. Andersen, J. Nuss, A.I. Poteryaev, A.
Georges, A.I. Lichtenstein; arXiv: 0907.2841.
[2] A.I. Poteryaev, J.M. Tomczak, S. Biermann, A. Georges, A.I.
Lichtenstein, A.N. Rubtsov, T. Saha-Dasgupta, O.K. Andersen; Phys.
Rev. B 76, 085127 (2007)
[3] F. Rodolakis, P. Hansmann, J.-P. Rueff, A. Toschi, M.W. Haverkort,
G. Sangiovanni, A. Tanaka, T. Saha-Dasgupta, O.K. Andersen, K.
Held, M. Sikora, I. Alliot, J.-P. Itié, F. Baudelet, P.Wzietek, P. Metcalf,
M. Marsi; Phys. Rev. Lett. 104, 047401 (2010).
[4] S. Lupi, L. Baldassarre, B. Mansart, A. Perucchi, A. Barinov, P.
Dudin, E. Papalazarou, F. Rodolakis, J.-P. Rueff, J.-P. Itié, S. Ravy, D.
Nicoletti, P. Postorino, G. Sangiovanni, A. Toschi, P. Hansmann,
N.
Parragh, T. Saha-Dasgupta, O.K. Andersen, K. Held, M. Marsi;
(accepted)
Doped Mott Insulators
have rich physical properties
and controlling them is one of
the major challenges for
developing Advanced Materials
High-Temperature Superconductors
Colossal Magneto-Resistance Materials
Intelligent Windows, Field-effect Transistors
Wannier orbital Conduction band
(LDA)
Hubbard model LDA+DMFT
1/2 filling
U =2.1 eV
T. Saha-Dasgupta and OKA 2002
T=2000K,
U = 3.0 eV
A. Georges et al, Rev Mod Phys 1996:
Georges and Kotliar
1992:
The single-band
Hubbard Model in the
d=∞ limit can be
mapped exactly onto
the Anderson impurity
model supplemented
by a CPA-like selfconsistency condition
for the dynamical
coupling to the noninteracting medium.
Hence, the Kondoresonance may
develop into a quasiparticle peak.
For general hopping,
the Georges-Kotliar
mapping leads to the
dynamical mean-field
approximation(DMFT).
LDA
O.K.
U/W = 1
W=1
DMFT
needed
U/W = 2
DMFT
needed
U/W = 2.5
DMFT
needed
QP
U/W = 3
Mott transition
LDA+U
LHB
O.K.
UHB
Gap
U/W = 4
Electronic-structure calculations for
materials with strong correlations
Current approximations to ab inito Density-Functional Theory
(LDA) are insufficient for conduction bands with strong electronic
correlations, e.g. they do not account for the Mott metal-insulator
transition.
On the other hand, LDA Fermi surfaces are accurate for most
metals, including overdoped high-temperature superconductors.
Presently, we therefore start with the LDA. For the few correlated
bands, we then construct localized Wannier orbitals (NMTOs) and a
corresponding low-energy Hubbard Hamiltonian: HLDA + Uon-site.
This is solved in the dynamical mean-field approximation (DMFT).
V 3d2
M
AFI
I
AFI
M
M
AFI monoclinic
Paramagnetic M and I corundum str
I
LDA+U: Ezhov, Anisimov,
Khomskii, Sawatzky 1999
LDA band structure
of V2O3 projected
onto various orbital
characters:
EF
EF
Blow up the energy scale
and split the panels:
N=1
N=2
EF
N=2
For the low-energy
Hamiltonian we just
need the t2g set
EF
N=2
Pick various subbands by generating
the corresponding
minimal NMTO
basis set:
(V1-xMx)2O3
V2O3
3d (t2g)2
a1g-egπ crystal-field
splitting = 0.3 eV
Hund's-rule
coupling J=0.7 eV
LDA t2g NMTO Wannier Hamiltonian
LDA+DMFT
U = 4.25 eV, J = 0.7 eV
a1g-egπ crystal-field splitting = 0.3 eV
LDA
a1g
2.0
egπ
Undo hybridization
U-enhancement = 1.85 eV ~ 3J
PM
PM
PM
Crystal-field enhanced
and mass-renormalized
QP bands
390 K
Comparison with PES
(Mo et al. PRL 2004):
PM
eg electrons are "localized" and only coherent below ~250K
a1g electrons are "itinerant" and coherent below ~400K
More important for the temperature dependence of the
conductivity is, however, that internal structural parameters
of V2O3 change with temperature, as we shall see later.
LDA t2g NMTO Wannier Hamiltonian
LDA+DMFT
U = 4.25 eV, J = 0.7 eV
= −0.41
a1g-egπ crystal-field splitting = 0.3 eV
LDA
a1g
2.0
egπ
Undo hybridization
PI
U-enhancement = 1.85 eV ~ 3J
PM
PM
a1g
PM
1.7
a1g
egπ
egπ
Crystal-field enhanced
Undo
and mass-renormalized
hybridization
QP
bands
390 K
PM
U=4.2 eV, 0 % Cr, T=390 K
PI
U=4.2 eV, 3.8% Cr, T=580 K
t = -0.72 eV
t = -0.49 eV
t = -0.49 eV
t = -0.72 eV
T=300K
V2O3
LDA
(V0.96Cr0.04)2 O3
undo a1g-egπ
LDA
undo a1g-egπ
1.7
2.0 eV
Robinson, Acta Cryst. 1975:
V2O3 at 300K ~
LDA
(V0.99Cr0.01)2 O3
undo a1g-egπ
1.9
LDA
~ V2O3 at 900K
undo a1g-egπ
1.6
V2O3 3d (t2g)2
Hund's-rule coupling
This metal-insulator transition in V2O3 is not,
like in the case of a single band, e.g. a HTSC:
Wannier orbital and LDA
conduction band
Hubbard model, LDA+DMFT
Band 1/2 full
U =2.1 eV
T=2000K
U = 3.0 eV
T. Saha-Dasgupta and OKA 2002
caused by disappearance of the quasi-particle peak
and driven by the Coulomb repulsion (U),
i.e. it is not really a Mott transition.
Conclusion
In the (t2g)2 system V2O3, described by an LDA t2g
Hubbard model, the metal-insulator transition calculated
in the DMFT is caused by quasi-particle bands being
separated by correlation-enhanced a1g-egπ crystal-field
splitting and lattice distortion.
The driving mechanism is multiplet splitting (nJ) rather
than direct Coulomb repulsion (U).
The a1g electrons stay coherent to higher temperatures
(~450K) than the egπ electrons (~250K).