Unconventional properties of non-centrosymmetric superconductors [Elektronische Ressource] / vorgelegt von Ludwig Klam

Ludwig Klam

Sujets

• Physik

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2010
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Unconventional properties of
non–centrosymmetric superconductors
Von der Fakultät Mathematik und Physik der Universität Stuttgart
zur Erlangung der Würde eines Doktors der Naturwissenschaften
(Dr. rer. nat.) genehmigte Abhandlung
Vorgelegt von
Ludwig Klam
aus Heidenheim an der Brenz
Hauptberichter: Prof. Dr. Walter Metzner
Mitberichter: Prof. Dr. Alejandro Muramatsu
Mitberichter: PD Dr. Dirk Manske
Tag der mündlichen Prüfung: 28. Oktober 2010
Max-Planck-Institut für Festkörperforschung
Stuttgart, 2010Contents
1 Introduction 15
1.1 Antisymmetric spin–orbit coupling in NCS . . . . . . . . . . . . . . . . . . . . 18
1.2 Phenomenological theory of Cooper–pairing . . . . . . . . . . . . . . . . . . . . 21
2 Response and transport in the presence of ASOC 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Derivation of the transport equations . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Solution by Bogoliubov transformation . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Gauge invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Normal and superfluid density . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 New gauge modes 41
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Role of phase fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Results for the gauge modes in NCS . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Theory of Raman response 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Raman vertices and pure triplet response . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Mixed–parity results: determination of the singlet–triplet ratio . . . . . . . . . . 56
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Dynamical spin and charge responses in CePt Si 673
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Spin–susceptibility with ASOC . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Role of band structure in CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . 723
5.3.1 Tight–binding model and DoS . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.2 Fermi surface nesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.1 Inelastic neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.2 Consequences for the Cooper–pairing . . . . . . . . . . . . . . . . . . . 85
2Contents
5.4.3 Kohn anomalies in CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . 913
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 Summary 99
A Smallq–expansion 103
B Derivation of the Raman vertices 107
C Tight–binding fit 113
D Algorithms to calculate the DoS and susceptibility 119
D.1 Numerical convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
D.2 Trilinear interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
D.3 DoS in 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Acknowledgments 139
Curriculum vitae 141
3List of Figures
1.1 Crystal and magnetic structure of CePt Si . . . . . . . . . . . . . . . . . . . . . 163
1.2 Spin–orbit coupling for tetragonal and cubic point group . . . . . . . . . . . . . 19
1.3 Phase diagram of the phenomenological theory . . . . . . . . . . . . . . . . . . 21
3.1 Gauge modes in NCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Slope of the gauge modes in NCS . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 Raman spectra for a pure triplet order parameter . . . . . . . . . . . . . . . . . . 55
4.2 Raman spectra for the point groupC . . . . . . . . . . . . . . . . . . . . . . . 574v
4.3 Power laws for the Raman response onΔ of the point groupC . . . . . . . . 59− 4v
4.4 Power laws for the Raman response onΔ of the point groupC . . . . . . . . 59+ 4v
4.5 Raman spectra for E and T symmetry of the point groupO . . . . . . . . . . . . 622
4.6 Raman spectra for A symmetry of the point groupO . . . . . . . . . . . . . . . 631
4.7 Area on the Fermi–surface that contributes to the triplet Raman response . . . . . 64
5.1 Brillouin zone for CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733
5.2 Tight–binding fit to the LDA band structure of CePt Si . . . . . . . . . . . . . . 743
5.3 Fermi surfaces of CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753
5.4 Band structure model with spin–orbit coupling for CePt Si . . . . . . . . . . . . 763
5.5 Cuts through theβ band of CePt Si . . . . . . . . . . . . . . . . . . . . . . . . 763
5.6 Density of states for CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773
5.7 Nesting function band of CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . 783
5.8 Nesting vectors for theβ band of CePt Si . . . . . . . . . . . . . . . . . . . . . 793
5.9 Real part of the susceptibility for theβ band of CePt Si . . . . . . . . . . . . . . 803
5.10 Calculated INS alongq for CePt Si . . . . . . . . . . . . . . . . . . . . . . . . 82z 3
5.11 Calculated INS spectra for CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . 843
5.12 Pairing interaction for the singlet channel in CePt Si . . . . . . . . . . . . . . . 863
5.13 Pairing interaction for the triplet channel in CePt Si . . . . . . . . . . . . . . . . 873
5.14 Projections of superconducting pairing states on theβ band of CePt Si . . . . . . 893
5.15 Important nesting vector for the pairing interaction in CePt Si . . . . . . . . . . 903
5.16 Feynman diagram for Kohn anomalies . . . . . . . . . . . . . . . . . . . . . . . 91
5.17 RPA enhancement ofℜχ for CePt Si alongΓZ . . . . . . . . . . . . . . . . . . 930 3
5.18 Phonon dispersion for CePt Si . . . . . . . . . . . . . . . . . . . . . . . . . . . 943
5.19 Kohn anomalies for theβ band of CePt Si alongΓZ . . . . . . . . . . . . . . . . 953
5.20 Kohn anomalies for theβ band of CePt Si alongΓX . . . . . . . . . . . . . . . 953
5.21 Kohn anomalies for theβ band of CePt Si alongΓM . . . . . . . . . . . . . . . 963
5List of Figures
D.1 Schematic data flow of the susceptibility algorithm . . . . . . . . . . . . . . . . 120
D.2 Data alignment for a symmetric convolution . . . . . . . . . . . . . . . . . . . . 123
D.3 Data alignment for an antisymmetric convolution . . . . . . . . . . . . . . . . . 124
6List of Tables
2.1 External perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
B.1 Raman vertices forG =C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114v
B.2 Raman vertices forG =O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7Acronyms
ABM Anderson–Brinkman–Morel
AFM Antiferromagnetism
ARPES Angle-resolved photoemission spectroscopy
ASOC Antisymmetric spin–orbit coupling
BCS Bardeen–Cooper–Schrieffer
BQP Bogoliubov quasiparticle
BW Balian–Werthamer
DCT Discrete cosine transformation
DFT Density functional theory
DoS Density of states
DST Discrete sine transformation
INS Inelastic neutron scattering
LDA Local-density approximation
MKE Matrix–kinetic equation
NCS Non–centrosymmetric superconductors
pha Particle–hole asymmetric
RPA Random phase approximation
SBSOS Spontaneously broken spin orbit symmetry
SOC Spin–orbit coupling
9