Tomczak, Jan Martin (2007) Spectral and Optical Properties of Correlated Materials. PhD thesis CPHT, CPHT, EP/X p.226.

Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Tomczak.pdf

Abstract

The major concern of this thesis is the calculation and interpretation
of spectral and optical properties of correlated materials.

We extend the variety of physcial quantities that can be accessed by
modern many-body techniques for realistic materials, such as LDA+DMFT. We introduce an analytical continuation scheme that enables us to derive the real-frequency self-energy from imaginary time quantum Monte Carlo calculations in the most general (cluster) context.
This furthermore allows for the calculation of the optical conductivity
We have devised a formalism that relies on a formulation of the solid
in terms of a localized basis set. The commonly used Peierls
substitution approach is generalized to the case of multi-atomic
unit-cells. This results in an approach of great versatility, since
the entire formulation is independent of the underlying electronic
structure method.

We have applied these novel techniques to several compounds of interest:

*Vanadium dioxide VO2*
We find that while the metallic phase is characterized by strong
signatures of correlations, the insulator is, as concerns its excitation
spectrum, close to a description within a one-particle approach, that
we define. Our picture of the insulator emerges as a "many-body
Peierls" scenario. In a full-orbital setup, we calculate
the optical conductivity of both phases, and find our theoretical
result in satisfactory agreement with recent experiments.
From the conductivity we, in particular, deduce the colour of the compound.

*Vanadium sesquioxide V2O3*
In our analysis, we find a correlation enhanced crystal-field
splitting at the origin of its metal to insulator transition that
occurs upon Cr-doping. Besides making predictions for angle-resolved photoemission experiments, we further evidence an orbital selectivity in the quasi-particle coherence temperature, which in particular allows for an understanding of the temperature dependence of recent optical measurements.

*Rare-earth sesquioxides RE2O3 (RE=Ce, Pr, Nd, Pm)*
These compounds are wide-gap Mott insulators that are not well
described in density functional theory, due to the localized character
of the RE4f orbitals. In our analysis, we, in particular, track the
influence of these localized 4f orbitals as a function of the filling
along the rare-earth series and find quantitative agreement for the evolution of the optical gap and a reasonable overall shape of the optical conductivity.

Table of content

I Introduction
1 Correlated Materials
A Physics of strongly correlated materials
B The Hubbard model
2 The Many-Body Problem
A Density Functional Theory (DFT)
B GW
C Dynamical Mean Field Theory (DMFT)
II Technical Advances
3 Spectral Properties
A Technical development and general points
4 Optical Properties
A Introduction
B A formalism for realistic calculations
C Sum rules
D Downfolding of Fermi velocity matrix elements
E Colour Calculations
F Technicalities : Examples
III Applications
5 Vanadium Dioxide – VO2
A Experiments and Theory
B LDA+(C)DMFT – Insights by analytical continuation
C GW – Model and First Principles Calculations
D The Optical Conductivity of VO2
6 Vanadium Sesquioxide – V2O3
A Experiments and Theory
B LDA+DMFT results and discussion
7 Rare Earth Sesquioxides – RE2O3
A Experimental work – a brief review
B Theoretical work – a brief review
C RE2O3 within LDA+DMFT
D Conclusions
8 Conclusions and Outlook
IV Appendices
A Analytical Continuation of off-diagonal Self-Energies
B The Hubbard Molecule
Acknowledgments
Bibliography

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