Scattering of a Dirac particle by a Berry phase domain wall

TL;DR

We address how massless Dirac particles scatter from a Berry-phase domain wall in the α-T3 model, where two regions share the same energy spectrum but differ in quantum geometry. By combining a low-energy continuum description with lattice tight-binding analysis on the dice lattice, we show that a Berry-phase mismatch at the wall yields partial reflection even when incident and transmitted momenta are identical; Klein tunneling persists at normal incidence for straight walls. Straight walls exhibit Klein tunneling and strong agreement between continuum and lattice results at low energy, while zigzag walls suppress Klein tunneling and can support propagation along the wall, with the low-energy theory recoverable via a generalized interface-matching matrix. The results reveal a geometric mechanism for Dirac scattering and suggest phononic-crystal platforms as feasible experimental tests of Berry-phase domain-wall scattering.

Abstract

Massless Dirac particles are characterized by an effective pseudospin-momentum locking, which is the origin of the peculiar scattering properties of Dirac particles through potential barriers. This pseudospin-momentum locking also governs the quantum geometric properties (such as the Berry phase and Berry curvature) of Dirac particles. In the present work, we demonstrate that a domain wall separating two regions with distinct quantum geometric properties can serve as an alternative to potential barriers. Specifically, using the three-band $α-T_3$ model of two-dimensional Dirac particles, we show that a Berry phase domain wall results in partial reflection and transmission of the Dirac particles, despite the fact that the incident and refracted momenta are identical.

Figures (8)

• Figure 1: Schematic representation of scattering through the Berry phase domain wall (left) versus through a potential step in the $\alpha-T_3$ model with a step height $V_0$ for an incident energy $E=V_0/2$ (right).
• Figure 2: Transmission probability $T_{\textrm{cont}}(\theta)$ through the Berry phase domain wall for increasing value of the Berry phase jump $\Delta_{R L}$: green line $\Delta_{R L}=0.055$, blue line $\Delta_{R L}=0.22$ and red line $\Delta_{R L}=0.5$.
• Figure 3: Lattice description of the straight domain wall. Bravais lattice vectors ${\bm a}_1,{\bm a}_2$. The green dotted line is the virtual domain-wall line (parallel to ${\bm a}_2$) that separates the regions $\alpha=\alpha_L$ for $n\le 0$ and $\alpha=\alpha_R$ for $n>0$. In each region, the nearest-neighbor hopping amplitudes are $t_{AB}=c_{\alpha}t$ (black continuous line) and $t_{CB}=s_{\alpha}t$ (black dashed line).
• Figure 4: Lattice description of the zigzag domain wall. The green dotted line is the virtual domain-wall line.
• Figure 5: Effective one-dimensional model picture of the straight (a) and zigzag (b) domain walls.