Nonreciprocal transverse currents in Rashba metal junctions under out-of-plane Zeeman fields

Abstract

We study charge transport across a junction between a normal metal and a Rashba metal in the presence of a Zeeman field applied to the spin--orbit coupled region. While an out-of-plane Zeeman field does not generate a transverse response in a homogeneous Rashba system, we show that such a junction exhibits a finite transverse conductivity that is inherently nonreciprocal, i.e., it depends on the direction of the applied bias. We demonstrate that this effect originates from the breaking of the $k_y \to -k_y$ symmetry of the Hamiltonian in the presence of the Zeeman field, which prevents cancellation of transverse current contributions from opposite transverse momenta. We further show that evanescent modes in the spin--orbit coupled region play a crucial role by carrying a finite spin polarization that gives rise to a transverse current localized near the junction. The transverse conductivity exhibits a peak at an energy scale set by the Zeeman field, displays distinct behavior for opposite bias directions, and shows spatial dependence governed by the nature of the contributing modes. We also identify bound states at the junction for attractive barrier strengths, which enhance conductivity when their energies lie near the transport window. Our results reveal a mechanism for nonreciprocal transverse charge transport in Rashba systems without requiring in-plane magnetic fields or ferromagnetic contacts, and should be experimentally accessible in semiconductor heterostructures.

Figures (5)

• Figure 1: Schematic of the system: a junction between a normal metal (NM) and a spin--orbit coupled (SOC) region subjected to an out-of-plane Zeeman field. The dispersion relations are drawn in NM and SOC regions.
• Figure 2: Longitudinal ($G_{xx}$) and transverse ($G_{yx}$) conductivities as functions of bias. While $G_{xx}$ is identical for left-to-right (L$\to$R) and right-to-left (R$\to$L) bias, $G_{yx}$ differs for the two directions. Note the strong non-reciprocity in $G_{yx}$. Parameters: $c=1$, $q_0=0.5E_F/\alpha_0$, $\alpha=2\alpha_0$, $b=0.25E_F$, evaluated at $x=0^{+}$.
• Figure 3: Transverse conductivity $G_{yx}$ as a function of position $x$ for left-to-right bias at $eV=0.1E_F$ (solid line) and $eV=0.4E_F$ (dashed line). Other parameters are the same as in Fig. \ref{['fig:GvsE']}.
• Figure 4: (a) Longitudinal conductivity $G_{xx}$ and (b) transverse conductivity $G_{yx}$ versus barrier strength $q_0$ for two bias values. For small bias, the peak occurs at negative $q_0$.
• Figure 5: Logarithm of $|{\rm det}M|$ plotted as a function of energy $E$ and transverse momentum $k_y$ for $q_0=-E_F/\alpha_0$. Bound states correspond to solutions of $\det M=0$ and appear as pronounced minima (large negative values) in the plot. The dispersion of these minima in the $(k_y,E)$ plane reflects the $k_y$ dependence of the bound-state energies. Other parameters are the same as in Fig. \ref{['fig:GvsE']}.