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General solution for the response of materials under radiation and tilted magnetic field: semi-classical regime

Narjes Kheirabadi, YuanDong Wang

TL;DR

The paper addresses how materials respond to radiation in the presence of a tilted magnetic field within a semiclassical framework, focusing on linear and nonlinear Hall effects driven by Berry-curvature geometry. It extends the Boltzmann kinetic equation to include field-corrected Berry curvature $\tilde{\boldsymbol{\Omega}}$ and Berry-connection–polarizability concepts, deriving DC, linear, and second-harmonic current components for 2D and 3D systems, with particular emphasis on 2D TCIs. It reveals two surviving nonlinear TCIs contributions: (i) a Berry-curvature-dipole–driven quantum term and (ii) a velocity$\times$BC term that scales with the perpendicular field $B_z$ and vanishes at zero tilt ($\alpha=0$), along with a linear intrinsic Hall current from $\int f_0^0 \Omega^B$; numerical SnTe examples illustrate current magnitudes accessible in THz experiments. Overall, the results clarify the geometric and topological origins of Hall responses under tilted fields, guiding experimental exploration and device concepts in THz/microwave regimes for 2D materials and TCIs.

Abstract

The Berry curvature dipole is well-known to cause Hall conductivity. This study expands on previous results to demonstrate how two- and three-dimensional materials react under a tilted magnetic field in the linear and nonlinear regimes. We show how the Hall effect has a quantum origin by deriving the general form of intrinsic and extrinsic currents in materials under a tilted magnetic field. Our focus is on determining the linear and nonlinear response of two-dimensional materials. We also demonstrate that as the result of the perpendicular component of the magnetic field a current resulted by both velocity and Berry curvature can occur in two-dimensional materials and topological crystalline insulators in second harmonic generation and ratchet responses. The findings of this research may provide insight into the transport characteristics of materials in the semi-classical regime and initiate a new chapter in linear and nonlinear Hall effects.

General solution for the response of materials under radiation and tilted magnetic field: semi-classical regime

TL;DR

The paper addresses how materials respond to radiation in the presence of a tilted magnetic field within a semiclassical framework, focusing on linear and nonlinear Hall effects driven by Berry-curvature geometry. It extends the Boltzmann kinetic equation to include field-corrected Berry curvature and Berry-connection–polarizability concepts, deriving DC, linear, and second-harmonic current components for 2D and 3D systems, with particular emphasis on 2D TCIs. It reveals two surviving nonlinear TCIs contributions: (i) a Berry-curvature-dipole–driven quantum term and (ii) a velocityBC term that scales with the perpendicular field and vanishes at zero tilt (), along with a linear intrinsic Hall current from ; numerical SnTe examples illustrate current magnitudes accessible in THz experiments. Overall, the results clarify the geometric and topological origins of Hall responses under tilted fields, guiding experimental exploration and device concepts in THz/microwave regimes for 2D materials and TCIs.

Abstract

The Berry curvature dipole is well-known to cause Hall conductivity. This study expands on previous results to demonstrate how two- and three-dimensional materials react under a tilted magnetic field in the linear and nonlinear regimes. We show how the Hall effect has a quantum origin by deriving the general form of intrinsic and extrinsic currents in materials under a tilted magnetic field. Our focus is on determining the linear and nonlinear response of two-dimensional materials. We also demonstrate that as the result of the perpendicular component of the magnetic field a current resulted by both velocity and Berry curvature can occur in two-dimensional materials and topological crystalline insulators in second harmonic generation and ratchet responses. The findings of this research may provide insight into the transport characteristics of materials in the semi-classical regime and initiate a new chapter in linear and nonlinear Hall effects.
Paper Structure (9 sections, 73 equations, 1 figure, 1 table)

This paper contains 9 sections, 73 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Boltzmann kinetic equation
  3. The form of the currents (linear, ratchet, and second harmonic generation (SHG))
  4. 2D materials example
  5. Conclusion
  6. Acknowledgement
  7. The form of $f$ functions for $a=x$ and $a=y$
  8. Expressions of the response tensors for ratchet or DC current
  9. Constraints on $M$ and $N$ tensors by the generators of the point groups

Figures (1)

  • Figure 1: The absolute values of $M$, $N$ and $O$ prefactors in the $x$ and $y$ directions as a function of the chemical potential $\mu$ for SnTe under a $10$ T perpendicular magnetic field and by considering $\omega \tau=1$.