Enhancement of spin polarization by chaos in graphene quantum dot systems

Abstract

When graphene is placed on a substrate of heavy metal, Rashba spin-orbit interaction of substantial strength can occur. In an open system such as a quantum dot, the interaction can induce spin polarization. Would classical dynamics have any effect on the spin polarization? Here we consider the quantum-dot setting, where the Rashba interaction is confined within the central scattering region whose geometrical shape can be chosen to yield distinct types of dynamics, e.g., regular or chaotic, in the classical limit. We find that, as compared with regular or mixed dynamics, chaos can lead to significantly smooth fluctuation patterns of the spin polarization in its variation with the Fermi energy. Strikingly, in the experimentally feasible range of the Rashba interaction strength, the average polarization for a chaotic dot can be markedly larger than that for a regular or mixed dot. From the semiclassical viewpoint, a key quantity that determines the average spin polarization is the angle distribution of the outgoing electrons at the interface between regions with and without the Rashba interaction, respectively. Classical chaos generates a different distribution which, in turn, leads to higher average spin polarization. There was little previous work on the interplay between classical chaos and electron spin, and the phenomenon of chaos-enhanced spin polarization uncovered here can be exploited for spintronics applications.

Effect of chaos on two-dimensional spin transport

“…It has been noted that with spin-orbit interactions only circular billiard is integrable 57,58 , but in our case, integrable or chaos are referred to the corresponding classical dynamics only. Since it is assumed that the orbital motion is not affected by spin, the orbital motion is purely determined by the classical trajectories [33][34][35][36] , and the cavity shape determines the classical integrability of the system. For the purpose of comparison, the leads attached to the cavities in all cases have the same width so that, for a given energy, there are an equal number of transmitting modes in the lead.…”

“…Quantum mechanically, there can be residuals of the x or y component of spin polarization. In this case, classical chaos or edge roughness of the underlying quantum confinement structure can reduce the cancellation of the spin of the pair of electrons with initial opposite spins, leading to an enhancement in the residual polarization 33,34 .…”

Relativistic quantum chaos

“…In RQC, topics that have been studied so far include energy level-spacing statistics in graphene systems [115][116][117][118][119][120], relativistic quantum scarring [121][122][123][124], relativistic quantum chaotic scattering and transport [125][126][127][128][129][130][131][132][133], quantum resonant tunneling in Dirac fermion and graphene systems [134][135][136], effects of chaos and random disorder on persistent currents in Dirac fermion sys-tems [137][138][139], the role of classical dynamics in confinement of massless Dirac fermions [140][141][142][143], chaos and spin transport in graphene quantum dot systems [144], and the interplay among chaos, relativistic quantum mechanics, and many body interaction in graphene billiards [136,145].…”

Relativistic quantum chaos—An emergent interdisciplinary field

“…At the level of basic science, a new field has emerged: Relativistic Quantum Chaos (RQC), which aims to uncover, understand, and exploit relativistic quantum manifestations of classical nonlinear dynamical behaviors including chaos. Topics studied so far include relativistic quantum scarring, 121,134,136,153 energy level spacing statistics in graphene systems, 123,[125][126][127]130 relativistic quantum chaotic scattering and transport, 128,131,139,142,145,149,150,154 relativistic quantum tunneling, 133,141,143 effects of chaos on persistent currents in Dirac fermion systems, 146,148 the role of classical dynamics in confinement of massless Dirac fermions, 122,129,135,144 the interplay between chaos and spin transport in graphene quantum dot systems, 151 and the role of many body interactions in chaotic graphene quantum billiards. 143,152 From an applied point of view, due to the underlying physics being effectively governed by the Dirac equation, purely relativistic quantum phenomena such as Klein tunneling, Zitterbewegung, and pair creations can potentially occur in solid state devices and be exploited for significantly improving or even revolutionizing conventional electronics and spintronics.…”