Novel Topological Features Found in the Non-Bloch Electron Caused by the Precessional Motion of the Rashba Field in the Two-Dimensional Finite System

We focus on an electron confined in the two-dimensional quantum dot (2D QD), and study how the precessional application of Rashba field (Ξ) yields the novel topological features to the non-Bloch states of the 2D finite system. For this aim, we newly propose the new band structure parameterized by those zenith (θ) and azimuthal (φ) angles, because the electronic states are precisely determined by the Rashba field coordinate.

The Rashba field breaks the structure-inversion-symmetry, and causes the spin-orbit interaction, producing the ls- and/or Zeeman-like energy stabilization in accordance with θ. Consequently, a new degenerate state appears at the specific energy and the Weyl point results. Since the precessional application of the Rashba field preserves this degeneracy, the Weyl point is expected to change into the Weyl line, illustrating the Ξ band structure.

To determine the Ξ band, we diagonalize the Hamiltonian by the numerical calculation, in addition to the second-order perturbation approach. Then, we extract the topological properties via the calculations of Berry's parameters (connection, curvature, and phase). The precessional change in Ξ surely changes the Weyl point into the Weyl line at the specific energy, causing sign inversion of the Berry curvature. We also discuss the features of the Berry phase.