LDA band structures of LDA band structures of transition-metal oxidestransition-metal oxides
Is it really the prototype Mott transition?Is it really the prototype Mott transition?
The metal-insulator transition in VThe metal-insulator transition in V22OO33
and what electronic and what electronic correlations may do to themcorrelations may do to them
Lecture 2.2, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare
[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. ParraghN. 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
Hubbard model LDA+DMFT1/2 filling T=2000K,
U = 3.0 eVU =2.1 eV
T. Saha-Dasgupta and OKA 2002
Wannier orbital Conduction band (LDA)
U/W = 1
U/W = 2
U/W = 2.5
U/W = 3
U/W = 4
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 self-consistency condition for the dynamical coupling to the non-interacting medium. Hence, the Kondo-resonance may develop into a quasi-particle peak.
For general hopping, the Georges-Kotliar mapping leads to the dynamical mean-field approximation(DMFT).
A. Georges et al, Rev Mod Phys 1996:
QP
Gap
LHB UHB
W = 1
LDA O.K.
LDA+U O.K.
DMFT needed
DMFT needed
DMFT needed
Mott transition
Electronic-structure calculations for Electronic-structure calculations for materialsmaterials with strong correlations 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 3dV 3d22
AFI monoclinic
Paramagnetic M and I corundum str
LDA+U: Ezhov, Anisimov, Khomskii, Sawatzky 1999
MM
IIMM
AFI
AFI
II
MM
LDA band structure LDA band structure of Vof V22OO3 3 projected projected
onto various orbital onto various orbital characters:characters:
N=2
N=2
N=2
N=1
Blow up the energy scale Blow up the energy scale and split the panels:and split the panels:
EEFF
EEFF
EEFF
Pick various sub-Pick various sub-bands by bands by generating the generating the corresponding corresponding minimal minimal NNMTO MTO basis set: basis set:
EEFF
For the low-energy For the low-energy Hamiltonian we Hamiltonian we just need the just need the tt2g2g set set
(V(V1-x1-xMMxx))22OO33
VV22OO33
3d (3d (tt2g2g))22
Hund's-rule coupling J=0.7 eV
a1g-egπ crystal-field
splitting = 0.3 eV
Undo Undo hhybridizationybridization
aa1g1g
eeggππ
PMPM
LDA t2g NMTO Wannier Hamiltonian
2.0
LDALDA
PMPM
a1g-e
gπ c
rys
tal-
fie
ld s
pli
ttin
g =
0.3
eV
U-e
nh
an
ce
me
nt
= 1
.85
eV
~ 3J
LDA+DMFT
U = 4.25 eV, J = 0.7 eV
Crystal-field enhanced Crystal-field enhanced and mass-renormalized and mass-renormalized QP bandsQP bands
PM
390 K
PM
eg electrons are "localized" and only coherent below ~250K
a1g electrons are "itinerant" and coherent below ~400K"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.
Undo Undo hhybridizationybridization
aa1g1g
eeggππ
PMPM
LDA t2g NMTO Wannier Hamiltonian
2.0
LDALDA
PMPM
a1g-e
gπ c
rys
tal-
fie
ld s
pli
ttin
g =
0.3
eV
U-e
nh
an
ce
me
nt
= 1
.85
eV
~ 3J
LDA+DMFT
U = 4.25 eV, J = 0.7 eV
Crystal-field enhanced Crystal-field enhanced and mass-renormalized and mass-renormalized QP bandsQP bands
PM
eeggππ
aa1g1g
PIPI
= −0.41
1.7
UndoUndo hhybridizationybridization
aa1g1g
eeggππ
390 K
2.0 eV2.0 eV
1.61.61.91.9
1.71.7
V2O3
T=300K(V0.96Cr0.04)2 O3
LDALDA
LDALDA
LDALDA
LDALDA
undo undo aa1g1g--eeggππ
undo undo aa1g1g--eeggππundo undo aa1g1g--eegg
ππ
undo undo aa1g1g--eeggππ
Robinson, Acta Cryst. 1975:
(V(V0.990.99CrCr0.010.01))2 2 OO33 V2O3 at 300K ~ ~ V2O3 at 900K
This metal-insulator transition in V2O3 is not,not, like in the case of a single band, e.g. a HTSC:
Hubbard model, LDA+DMFTHubbard model, LDA+DMFTBand 1/2 fullBand 1/2 full
U = 3.0 eV
T=2000KT=2000K
Wannier orbital and LDA Wannier orbital and LDA conduction bandconduction band
U =2.1 eV
T. Saha-DasguptaT. Saha-Dasgupta and OKA 2002 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.it is not really a Mott transition.
ConclusionConclusion
In the (t2g)2 system V2O3, described by an LDA tt2g2g
Hubbard model, the metal-insulator transition calculated in the DMFT is caused by quasi-particle bands being
separated by correlation-enhanced correlation-enhanced aa1g1g-e-eggππ crystal-field crystal-field
splitting and lattice distortionsplitting and lattice distortion.
The driving mechanism is multiplet splitting (nJ) rather
than direct Coulomb repulsion (U).
The aa1g1g electrons stay coherentcoherent to higher temperatures
(~450K) than the eeggππ electrons (~250K).