Higher-order Van Hove singularities in kagome topological bands Public

Abstract

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from C = ±1 to ±4. We perform analytical and numerical analysis of the energy bands near the high-symmetry points Γ, ±K, and M_i (i = 1, 2, and 3), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), ρ(ϵ) ∼ |ϵ|^(−ν), with exponents ν = 1/2, 1/3, 1/4, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands C = ±2, ±4 in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points M_i (i = 1, 2, and 3) on the Brillouin zone boundary. This classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

Table of Contents

1 Introduction 1

2 Background 5

2.1 Kagome systems 5

2.2 Van Hove singularities 6

2.1 Berry curvature 7

3 Model 9

4 Analysis 11

4.1 Higher-order Van Hove Singularities 11

4.1.1 Critical points at ±K 13

4.1.2 Critical points at Γ 14

4.1.3 Critical points at M_i 15

4.1.4 HOVHS Phase Diagrams 16

4.2 Band topology 19

4.3 Sublattice Interference 22

5 Conclusion 24

A Analytical Expressions of the HOVHS Lines 26

Bibliography 29

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, Condensed Matter
Mot-clé	Kagome lattice Van Hove singularity Quantum anomalous Hall effect
Committee Chair / Thesis Advisor	Luiz H. Santos, Emory University
Committee Members	Wladimir Benalcazar, Emory University Ajit Srivastava, Emory University

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