Trigonal warping effects on optical properties of anomalous Hall materials

Abstract

The topological nature of topological insulators are related to the symmetries present in the material, for example, quantum spin Hall effect can be observed in topological insulators with time reversal symmetry, while broken time reversal symmetry may give rise to the presence of anomalous quantum Hall effect (AHE). Here we consider the effects of broken rotational symmetry on the Dirac cone of an AHE material by adding trigonal warping terms to the Dirac Hamiltonian. We calculate the linear optical conductivity semi-analytically to show how by breaking the rotational symmetry we can obtain a topologically distinct phase. The addition of trigonal warping terms causes the emergence of additional Dirac cones, which when combined has a total Chern number of $\mp 1$ instead of $\pm 1/2$. This results in drastic changes in the anomalous Hall and longitudinal conductivity. The trigonal warping terms also activates the higher order Hall responses which does not exist in a $\mathcal{R}$ symmetric conventional Dirac material. We found the presence of a non-zero second order Hall current even in the absence of Berry curvature dipole. This shift current is also unaffected by the chirality of the Dirac cone, which should lead to a non-zero Hall current in time reversal symmetric systems.

arXiv comment7 pages, 5 figures

References in corpus (26)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Maximally-localized generalized Wannier functions for composite energy bands
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Optimized norm-conserving Vanderbilt pseudopotentials
• Topological Field Theory of Time-Reversal Invariant Insulators
• Maximally-localized Wannier functions for entangled energy bands
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Monolayer MoS2: trigonal warping, "Γ-valley", and spin-orbit coupling effects
• Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
• Topological flat band models with arbitrary Chern numbers
• Ab initio calculation of the shift photocurrent by Wannier interpolation
• Tuning Chern Number in Quantum Anomalous Hall Insulators
• Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
• Berry Curvature Dipole in Strained Graphene: a Fermi Surface Warping Effect
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Large Bulk Piezophotovoltaic Effect of Monolayer $2H$-MoS${}_2$
• Distant-Neighbor Hopping in Graphene and Haldane Models
• Nonlinear anomalous photocurrents in Weyl semimetals
• Geometric photon-drag effect and nonlinear shift current in centrosymmetric crystals
• Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride
• Intra-cell dynamics and cyclotron motion without magnetic field