Spectral properties of strongly correlated electron systems [Elektronische Ressource] / vorgelegt von Christopher Dahnken

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• Physik

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• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2005
• Nombre de lectures: 26
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

SPECTRAL PROPERTIES OF STRONGLY
CORRELATED ELECTRON SYSTEMS
Dissertation zur Erlangung des
naturwissenschaftlichen Doktorgrades
der Bayerischen Julius-Maximilians-Universitat¨ Wurzb¨ urg
vorgelegt von
Christopher Dahnken
aus Straubing
Wurzb¨ urg 2004ii
Eingericht am:
bei der Fakultat¨ fur¨ Physik und Astronomie
1. Gutachter: Prof. Dr. Werner Hanke
2. Prof. Dr. Enrico Arrigoni
der Dissertation.
1. Prufer:¨ Prof. Dr. Werner Hanke
2. Prufer:¨ Prof. Dr. Rene Matzdorf
der mundlichen¨ Prufung.¨
Tag der mundlichen¨ Prufung:¨ 7. Dezember 2004
Doktorurkunde ausgehandigt:¨iii
¨FUR NOAH, SILAS UND JUDITHAbstract
We investigate the single particle static and dynamic properties at zero temperature within the
Hubbard an three-band-Hubbard model for the superconducting copper oxides. Based on the
recently proposed self-energy functional approach (SFA) [M. Potthoff, Eur. Phys. J. B 32
429 (2003)], we present an extension of the cluster-perturbation theory (CPT) to systems with
spontaneous broken symmetry. Our method accounts for both short-range correlations and
long-range order. Short-range correlations are accurately taken into account via the exact di-
agonalization of finite clusters. Long-range order is described by variational optimization of a
ficticious symmetry-breaking field. In comparison with related cluster methods, our approach is
more flexible and, for a given cluster size, less demanding numerically, especially at zero tem-
perature. An application of the method to the antiferromagnetic phase of the Hubbard model
at half-filling shows good agreement with results from quantum Monte-Carlo calculations. We
demonstrate that the variational extension of the cluster-perturbation theory is crucial to repro-
duce salient features of the single-particle spectrum of the insulating cuprates. Comparison of
the dispersion of the low-energy excitations with recent experimental results of angular resolved
photoemission spectroscopy (ARPES) allows us to fix a consistent parameter set for the one-
0band Hubbard model with an additional hopping parameter t along the lattice diagonal. The
0doping dependence of the single-particle excitations is studied within the t¡ t ¡U Hubbard
model with special emphasis on the electron doped compounds. We show, that the ARPES re-
sults on the band structure and the Fermi surface of Nd Ce CuOCl are naturally obtained2¡x x 4§d
0within the t¡t ¡U Hubbard model without further need for readjustment or fitting of parame-
ters, as proposed in recent theoretical considerations. We present a theory for the photon energy
and polarization dependence of ARPES intensities from the CuO plane in the framework of2
strong correlation models. The importance of surface states for the observed experimental facts
is considered. We show that for electric field vector in the CuO plane the ‘radiation character-2
istics’ of the O 2p and Cu 3d orbitals are strongly peaked along the CuO plane, i.e. most2 2s 2x ¡y
photoelectrons are emitted at grazing angles. This suggests that surface states play an important
role in the observed ARPES spectra, consistent with recent data from Sr CuCl O . We show2 2 2
that a combination of surface state dispersion and Fano resonance between surface state and
the continuum of LEED-states may produce a precipitous drop in the observed photoelectron
ivv
current as a function of in-plane momentum, which may well mimic a Fermi-surface crossing.
This effect may explain the simultaneous ‘observation’ of a hole-like and an electron-like Fermi
surfaces in Bi Sr CaCu O at different photon energies.2 2 2 8+dContents
Introduction 1
I Basics 5
1 Experimental and Theoretical Aspects 6
1.1 Strongly-Correlated Electron Systems and High-T Superconductors . . . . . . 6c
1.2 Microscopic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 The Three-Band Model . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 One-Band Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Angular-Resolved Photoemission Spectroscopy . . . . . . . . . . . . . . . . . 15
2 Exact Diagonalization and Cluster Perturbation Theory 20
2.1 Exact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.1 The Lanczos Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.2 Dynamics of the Ground State . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Cluster Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 An Effective Single-Particle Description of the Hubbard Model . . . . 26
2.2.2 Single-Particle Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.3 A Variational Priciple . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
II The One-Band Hubbard Model 33
3 One-Dimensional Systems 34
3.1 The Ground State Energy of CPT . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Variation of the Hopping Parameters and Additional Bath Sites . . . . . . . . . 39
viCONTENTS vii
4 The Two-Dimensional Systems at Half-Filling 42
4.1 Ground State Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 The Antiferromagnetic Order Parameter . . . . . . . . . . . . . . . . . . . . . 47
4.3 Single Particle Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 The “String” Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Results for the t-U Hubbard model . . . . . . . . . . . . . . . . . . . . 54
4.3.3 Comparison with Experimental Results . . . . . . . . . . . . . . . . . 59
5 The Two-Dimensional Hubbard Model at Finite Doping 64
5.1 Evolution of the Spectral Function in the t-U Hubbard Model . . . . . . . . . . 65
5.2 Photoemission of N-Type Cuprates . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Doping Dependence of the Fermi Surface . . . . . . . . . . . . . . . . . . . . 80
III The Three-Band Model 84
6 Single Particle Excitations of the Three-Band Model 87
6.1 Application of Self-Energy Functional Approach . . . . . . . . . . . . . . . . 89
6.2 Bilayer Splitting - The Bi Sr CaCu O Fermi Surface . . . . . . . . . . . . 912 2 2 8+d
7 Matrix-Element Effects in Photoemission Studies of the CuO Plane 942
7.1 Photoemission Intensities for Strong Correlation Models . . . . . . . . . . . . 95
7.2 Calculation of the Radial Matrix Elements . . . . . . . . . . . . . . . . . . . . 99
7.3 Application to the Three-Band Model . . . . . . . . . . . . . . . . . . . . . . 100
7.4 to Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8 Waveguide Effects and Fake Fermi Surfaces 112
8.1 Surface Resonances and the Energy Dependence of the Intensity . . . . . . . . 112
8.2 Apparent Fermi Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9 Summary 122
10 Appendix 128
Bibliography 130
Zusammenfassung 140
Lebenslauf 146
Publikationen 148
Danksagung 150viiiIntroduction
The discovery of high temperature superconductors (HTSC) [1] almost 20 years ago has at-
tracted great interest in these materials, along with the general physics of transition metal com-
pounds. Despite the great efforts spent in trying to understand the unusual physical properties
of these materials, a microscopic theory of high temperature superconductivity is still lacking.
The HTSC show many differences to the well understood BCS superconductors, e.g. the
high critical temperature T , the lack of an isotope effect on T and the d-wave symmetry of thec c
order parameter. This led to the believe that the pairing force driving the superconductivity must
be of different nature in these materials. Unlike the conventional superconductors, the mech-
anism in the HTSC seems to be of purely electronic nature, and the strong coulomb repulsion
between two electrons in the copper 3d orbital has been proposed as a responsible for thex 2x ¡y
pairing. The remarkably strong interaction in this orbital is caused by its small spatial “exten-
sion”, i.e. the concentration of the wave function in a relative small area around the nucleus.
This has severe consequences for our understanding of solid state physics. Most important,
Fermi-liquid theory, which is only correct in the limit of weak coupling between electrons, fails
to describe the properties of the HTSC correctly. Most prominent, Fermi-liquid theory predicts
a metal with a half filled conduction band for the case of the parent compounds of the HTSC. In
reality we find an antiferromagnetic insulator instead. Systems in which the electron-electron
interaction has such dramatic consequences are called strongly correlated electron systems.
This thesis is devoted to the study of the single-particle properties of strongly correlated
electron models. In particular, we are interested in the spectral function as it is experimentally
measured in angular resolved photoemission (ARPES) experiments. We develop new numerical
methods for the study of strongly correlated electron systems in general and propose theories
for the photoemission intensity from the CuO plane in particular.2
This thesis is organized as follows:
In chapter 1 we give a brief overview about the known facts about the high temperature
superconductor