Orbital-related gyrotropic responses in Cu$_2$WSe$_4$ and chirality indicator

TL;DR

The paper addresses how gyrotropy and crystal chirality manifest in orbital transport by studying the gyrotropic yet achiral Cu$_2$WSe$_4$ with first-principles and Wannier-based modeling. It shows that the orbital Edelstein effect dominates the magnetization response and that nonlinear transport (NCTE Hall and nonlinear Hall effects) is controlled primarily by the Berry curvature dipole, while spin–orbit coupling plays only a minor role. A chirality indicator based on the trace of the gyrotropic tensor $\mathcal{G}$ is proposed to distinguish gyrotropy from chirality and to probe chiral phase transitions. The results highlight Cu$_2$WSe$_4$ as a promising platform for orbitronics and for disentangling gyrotropy from chirality in transport phenomena.

Abstract

In recent years, counterparts of phenomena studied in spintronics have been actively explored in the orbital sector. The relationship between orbital degrees of freedom and crystal chirality has also been intensively investigated, although the distinction from gyrotropic properties has not been fully clarified. In this work, we investigate spin and orbital Edelstein effects as well as the nonlinear responses in the ternary transition-metal chalcogenide Cu$_2$WSe$_4$, which has a gyrotropic but achiral crystal structure. We find that in the Edelstein effect, magnetization is dominated by the orbital contribution rather than the spin contribution. On the other hand, both the nonlinear chiral thermoelectric (NCTE) Hall effect--a response to the cross product of the electric field and the temperature gradient--and the nonlinear Hall effect--conventional second-order response to the electric field--are found to be dominated by the Berry curvature dipole. We further find that spin-orbit coupling plays only a minor role in these effects, whereas the orbital degrees of freedom are essential. Finally, we demonstrate that the orbital magnetic-moment contributions to both the Edelstein effect and the NCTE Hall effect are closely linked to chirality, and we discuss the possibility of using them as a chirality indicator.

Figures (4)

• Figure 1: (a) Crystal structure of Cu$_2$WSe$_4$. The cuboid indicates the conventional unit cell, which contains two primitive cells. (b) Band structure with SOC (red) and without SOC (black). The inset shows the Brillouin zone and high‑symmetry points. (c) Projected partial density of states (DOS) from the relativistic calculation for each atomic species.
• Figure 2: Orbital Edelstein magnetization without (black line) and with (red line) SOC and the spin Edelstein magnetization (blue line).
• Figure 3: [(a) and (b)] NCTE charge Hall current (a) with SOC and (b) without SOC. [(c) and (d)] NCTE thermal Hall current (c) with SOC and (d) without SOC. Berry curvature (BC) contribution (red lines), orbital magnetic moment (OM) contribution (blue lines), and total value (black lines) are plotted in each panel.
• Figure 4: Normalized nonlinear Hall conductivity $\sigma_{ijk}/(e^3/h)$ ($h$: Planck constant) calculated using (a,b) Eq. \ref{['eq:NLC']} (full) and (c,d) Eq. \ref{['eq:nlbcd']} (BCD), in the (a,c) presence and (b,d) absence of SOC. $xyz$ (red solid lines) and $zxy$ (blue solid lines) are plotted, and $-\sigma_{zxy}/2$ (black dotted lines) is also shown to compare with $xyz$ component.