Quantum geometric scattering of a Dirac particle by a Berry curvature domain wall

TL;DR

This work addresses the scattering of 3D massless Dirac particles at a Berry-curvature domain wall separating regions with identical spectra but different Berry dipoles. Using a three-band tight-binding model with tunable Berry curvature dipole and a continuum Dirac description, the authors derive an explicit transmission formula that depends on incidence angles and dipole mismatch, and show that the transmission is energy-independent in the continuum limit. The key result is a partial reflection induced purely by a quantum geometric mismatch, with perfect transmission at normal incidence and at certain oblique incidences, as well as valley-dependent transmission. A lattice description corroborates the continuum result and reveals two propagation modes due to Brillouin-zone folding; intermode scattering is suppressed at low energy, highlighting the role of geometry in controlling Dirac transport.

Abstract

We investigate the scattering of a three-dimensional massless Dirac particle through a domain wall separating two regions with identical energy spectra but distinct Berry curvature dipoles. We demonstrate that the quantum geometric mismatch induces partial reflection and transmission despite identical incident and refracted momenta. These results highlight the role of engineered quantum geometric interfaces as key tools to control Dirac particle scattering.

Figures (7)

• Figure 1: Top panel: Schematic representation of the $AB$ stacking of layers of 2D Lieb lattice. Bottom panel: Cut of the lattice at $x=a/2$ on the left and at $y=a/2$ on the right. The hopping amplitudes between $B$ and $A$ sites is $t/2$ along $x$ direction and alternating alternating hoppings $\pm c_\alpha t/4$ along $z$ direction. The hopping amplitudes between $B$ and $C$ sites is $t/2$ along $y$ direction and alternating hoppings $\pm s_\alpha t/4$ along $z$ direction. $\vec{a}_1=a(2,0,0)$, $\vec{a}_2=a(0,2,0)$ and $\vec{a}_3=a(1,1,1)$ are the Bravais lattice vectors.
• Figure 2: Energy band spectrum along the path $\Gamma(0,0,0)\rightarrow D(\pi/2,\pi/2,0)\rightarrow M(\pi,\pi,0)\rightarrow R(\pi,\pi,\pi)$.
• Figure 3: Vector field plots of the Berry curvature (blue arrows) and Berry dipole (Green arrows for $\xi_x\xi_y=1$, red arrows for $\xi_x\xi_y=-1$) of the conduction band near the four Dirac points ${\bm D}_{\xi_x=\pm 1,\xi_y=\pm 1,\xi_z=1}$.
• Figure 4: Transmission probability $T_{\xi_x\xi_y}(\theta,\varphi)$ through the Berry dipole domain wall. $\alpha_L=0$ and $\alpha_R=\pi/3$. (a) $\xi_x\xi_y=1$ and (b) $\xi_x\xi_y=-1$
• Figure 5: Effective one-dimensional model picture of the domain walls.