Critical supercurrent and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>φ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> state for probing a persistent spin helix

Abstract

We theoretically study the profile of a supercurrent in two-dimensional Josephson junctions with Rashba-Dresselhaus spin-orbit interaction (RDSOI) in the presence of a Zeeman field. Two types of RDSOIs are considered that might be accessible in $\mathrm{GaAs}$ quantum wells and zinc-blende materials. Through investigating self-biased supercurrent (so called ${\ensuremath{\varphi}}_{0}$-Josephson state), we obtain explicit expressions for the functionality of the ${\ensuremath{\varphi}}_{0}$ state with respect to RDSOI parameters $(\ensuremath{\alpha},\ensuremath{\beta})$ and in-plane Zeeman field components $({h}_{x},{h}_{y})$. Our findings reveal that when the chemical potential $(\ensuremath{\mu})$ is high enough compared to the energy gap $(\mathrm{\ensuremath{\Delta}})$ in superconducting electrodes, i.e., $\ensuremath{\mu}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$, RSOI and DSOI with equal strengths $(|\ensuremath{\alpha}|=|\ensuremath{\beta}|)$ cause vanishing ${\ensuremath{\varphi}}_{0}$ states independent of magnetization and the type of RDSOI. A Zeeman field with unequal components, i.e., $|{h}_{x}|\ensuremath{\ne}|{h}_{y}|$, however, can counteract and nullify the destructive impact of equal-strength RDSOIs (for one type only), where $\ensuremath{\mu}\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}$, although $|{h}_{x}|=|{h}_{y}|$ can still eliminate the ${\ensuremath{\varphi}}_{0}$ state. Remarkably, in the $\ensuremath{\mu}\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}$ limit, the ${\ensuremath{\varphi}}_{0}$ state is proportional to the multiplication of both components of an in-plane Zeeman field, i.e., ${h}_{x}{h}_{y}$, which is absent in the $\ensuremath{\mu}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$ limit. Furthermore, our results of critical supercurrents demonstrate that the persistent spin helices can be revealed in a high enough chemical potential regime $\ensuremath{\mu}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$, while an opposite regime, i.e., $\ensuremath{\mu}\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}$, introduces an adverse effect. In ballistic regime, the ``maximum'' of the critical supercurrent occurs at $|\ensuremath{\alpha}|=|\ensuremath{\beta}|$ and the Zeeman field can boost this feature. The presence of disorder and nonmagnetic impurities change this picture drastically so the ``minimum'' of the critical supercurrent occurs at and around the symmetry lines $|\ensuremath{\alpha}|=|\ensuremath{\beta}|$. We show that the signature of persistent spin helices explored in disordered systems originate from the competition of short-range spin-singlet and long-range spin-triplet supercurrent components. Our study uncovers delicate details of how the interplay of RDSOI and a Zeeman field manifests in the ${\ensuremath{\varphi}}_{0}$ state and critical supercurrent. Relying on the fact that the ${\ensuremath{\varphi}}_{0}$ state is accessible regardless of the amount of nonmagnetic impurities and disorder, our results can provide guidelines for future experiments to confirm the presence of persistent spin helices, determine the type of SOI, and reliably extract SOI parameters in a system, which might be helpful in devising spin-orbit-coupled spintronics devices and ultrasensitive spin-transistor technologies.

Topics & Concepts