Abstract
Contents
I Introduction 1
1 Introduction to topological band theory 7
1.1 Topological insulators.............................................................. 8
1.2 Weyl semimetals .................................................................... 15
2 Introduction to non-Hermitian topology 23
2.1 Energy spectra ....................................................................... 25
2.2 Non-Hermitian skin effect....................................................... 26
2.3 Band degeneracies in non-Hermitiansystems ..................... 29
2.4 Non-Hermitian topological classification............................. 31
List of publications 37
11 Weak correlations - topological phases in non-Hermitian quasiparticle Hamiltonians 41
3 Infernal and exceptional edge modes 43
3.1 Infernal edge modes................................................................. 44
3.2 Exceptional edge modes.......................................................... 48
4 Exceptional topological insulators 53
4.1 ETI Tight-binding model....................................................... 54
4.2 Topological invariants.............................................................. 56
4.3 Surface states........................................................................... 58
4.4 Berry flux................................................................................. 61
4.5 Non-Hermitian terms.............................................................. 63
5 Magnetic flux response of non-Hermitian topological phases 67
5.1 Flux defects in non-Hermitian systems................................ 70
5.2 Non-Hermitian flux skin effect............................................. 71
5.3 Non-Hermitian flux spectral jump.......................................... 73
5.4 Non-Hermitian higher-order flux skin effect ....................... 77
5.5 Isolated first- and higher-order flux Majorana modes ... 81
6 Experimental realizations 85
6.1 Electric circuit realizations.................................................... 86
6.2 Non-Hermitian phases from interacting Weyl semimetals . 97
6.3 Experimental realization of non-Hermitian flux response . . 102
7 Conclusion 105
III Strong correlations - symmetry breaking orders in
kagome metals 109
8 Kagome materials 111
8.1 Geometry of the kagomelattice........................................... 112
8.2 Electronic structure of the kagome lattice.......................... 113
8.3 Fermi surface instabilitiesof the kagome lattice.................. 117
8.4 The family of kagome metals AV3Sbs................................ 121
9 Charge order in AV3Sb5 129
9.1 Electronic and magnetic duality of the charge order .... 129
9.2 Analysis of the charge order in AV3Sb5................................ 138
10 Superconductivity in AV3Sb5 147
10.1 Interplay of charge order and superconductivity................ 147
10.2 Superconducting pairing symmetry......................................... 150
10.3 Nature of unconventional pairingin AV3Sbs........................... 152
11 Conclusion 159
IV Summary and Outlook 163
V Appendices 169
A More on infernal and exceptional edge modes 171
A.l Symmetries in NH systems...................................................... 171
A.2 Classification of edge response............................................... 173
A.3 Slab solution for infernal points and connection to the e-
pseudospectrum....................................................................... 187
A.4 Exceptional points in ID...................................................... 190
A. 5 Toy models with nontrivial edge response.......................... 195
B More on exceptional topological insulators 201
B. l Dirac theory for the ETI ...................................................... 201
B.2 Analytical treatment of the ETI tight-binding model . . . 203
B.3 Higher-order exceptional point on the surface of ETI . . . 213
B.4 Bulk invariant.......................................................................... 216
B.5 Non-Hermitian terms due to electron-phonon scattering 227
B. 6 Discussion of two band models with nontrivial w3D .... 232
C More on non-Hermitian magnetic flux response 239
C. l Classification of flux response.....................................................239
C.2 Scaling analysis of flux defect localized modes....................... 264
C.3 More details on the higher-order flux skin effect.................... 267
C. 4 Toy models with nontrivial flux response................................. 275
D More on the charge order in AV3Sb5 283
D. l Nesting instabilities from m-type van Hove singularities . . 283
D. 2 Pressure dependence of the charge order................................. 284
E More on unconventional pairing in AV3Sbs 287
E. l Random phase approximation method.................................... 287
E.2 Two types of van Hove singularity points in the kagome lattice290
E.3 Pairing in real space on the kagome lattice .......................... 293
E.4 Electronic structures and superconducting pairings .... 298
List of acronyms 307
Bibliography 309
Curriculum Vitae 349
Denner, Marco Michael