Abstract:
The presence of spin-orbit coupling affects the spontaneously flowing persistent currents in mesoscopic conducting rings. Here we analyze their dependence on magnetic flux with emphasis on identifying possibilities to prove the presence and extract the strength of Rashba spin splitting in low-dimensional systems. Effects of disorder and mixing between quasi-onedimensional ring subbands are considered. The spin-orbit coupling strength can be inferred from the values of flux where sign changes occur in the persistent charge current. As an important consequence of the presence of spin splitting, we identify a nontrivial persistent spin current that is not simply proportional to the charge current. The different flux dependences of persistent charge and spin currents are a unique signature of spin-orbit coupling affecting the electronic structure of the ring.

Abstract:
We investigate theoretically the spin transport in two-terminal mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI). We find that the interplay between the RSOI and DSOI breaks the original cylindric symmetry of mesoscopic ring and consequently leads to the anisotropic spin transport, i.e., the conductance is sensitive to the positions of the incoming and outgoing leads. The anisotropic spin transport can survive even in the presence of disorder caused by impurity elastic scattering in a realistic system.

Abstract:
We present calculations of the frequency-dependent spin susceptibility tensor of a two-dimensional electron gas with competing Rashba and Dresselhaus spin-orbit interaction. It is shown that the interplay between both types of spin-orbit coupling gives rise to an anisotropic spectral behavior of the spin density response function which is significantly different from that of vanishing Rashba or Dresselhaus case. Strong resonances are developed in the spin susceptibility as a consequence of the angular anisotropy of the energy spin-splitting. This characteristic optical modulable response may be useful to experimentally probe spin accumulation and spin density currents in such systems.

Abstract:
Electronic transport in a one-dimensional mesoscopic ring threaded by a magnetic flux is studied in presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in presence of the spin-orbit interactions and leads to a method of determining the strength of the Dresselhaus interaction. In addition to this, the persistent currents for ordered and disordered rings have been investigated numerically. It is observed that, the presence of the spin-orbit interaction, in general, leads to an enhanced amplitude of the persistent current. Numerical results corroborate the respective analytical findings.

Abstract:
The influence of electron--phonon (EP) scattering on spin polarization of current output from a mesoscopic ring with Rashba spin--orbit (SO) interaction is numerically investigated. There are three leads connecting to the ring at different positions; unpolarized current is injected to one of them, and the other two are output channels with different bias voltages. The spin polarization of current in the outgoing leads shows oscillations as a function of EP coupling strength owing to the quantum interference of EP states in the ring region. As temperature increases, the oscillations are evidently suppressed, implying decoherence of the EP states. The simulation shows that the magnitude of polarized current is sensitive to the location of the lead. The polarized current depends on the connecting position of the lead in a complicated way due to the spin-sensitive quantum interference effects caused by different phases accumulated by transmitting electrons with opposite spin states along different paths.

Abstract:
The electronic states of a mesoscopic ring are assessed in the presence of Rashba Spin Orbit coupling and a $U(1)$ gauge field. Spin symmetric coupling to an ideal lead is implemented following B\"uttiker's voltage probe. The exact density of states is derived using the reservoir uncoupled eigenstates as basis functions mixed by the reservoir coupling. The decay time of uncoupled electron eigenstates is derived by fitting the broadening profiles. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but nonuniformly in temperature, the latter due to the fact that currents emerge from different depths of the Fermi sea, and thus for some regimes of flux, they are provided with a protective gap. Such flux regimes can be tailored by the SO coupling for both charge and spin currents.

Abstract:
We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual state currents together with net current based on second-quantized approach. A significant enhancement of current is observed in presence of spin-orbit coupling and sometimes it becomes orders of magnitude higher compared to the interaction free Fibonacci ring. We also establish a scaling relation of persistent current with ring size, associated with the Fibonacci generation, from which one can directly estimate current for any arbitrary flux, even in presence of spin-orbit interaction, without doing numerical simulation. The present analysis indeed gives a unique opportunity of determining persistent current and has not been discussed so far.

Abstract:
We study theoretically the statistical properties of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized magnetic moments in a disordered two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit couplings. Averaging over disorder, the static spin susceptibility tensor is evaluated diagrammatically in the mesoscopic (phase-coherent) regime. The disorder-averaged susceptibility leads to a twisted exchange interaction suppressed exponentially with distance, whereas the second-order correlations, which determine the fluctuations (variance) of the RKKY energy, decay with the same power-law as in the clean case. We obtain analytic expressions in the limits of large/small spin orbit interactions and for equal Rashba and Dresselhaus couplings. Beside these limiting cases, we study numerically the variance of the RKKY interaction in the presence of pure Rashba spin-orbit coupling. Our results are relevant for magnetic impurities or nuclear moments embedded in III-V two-dimensional heterostructures or in contact with surface states of metals and metal alloys, which can display a sizable Rashba spin-orbit coupling.

Abstract:
Because of the peculiar coupling of spatial and spin degrees of freedom effected by the Rashba spin-orbit interaction, lateral confinement of a two dimensional electronic system leads to a finite transverse spin polarization near the longitudinal edges of a current carrying quantum wire. The sign of this component of the polarization is opposite at the two edges and can be reversed upon inversion of the current. Interestingly for small spin orbit coupling this is the largest contribution to the total polarization, its magnitude being of second order in the coupling constant. As a consequence this phenomenon cannot be revealed in lowest order perturbative approaches. An in plane spin polarization component is also present that is perpendicular to the current. Within the same model this component would be also present in the bulk. On the other hand while in the latter case its magnitude is linear in the coupling constant, we find that it only represents a third order effect in the wire geometry. Our results are consistent with a general rigorous argument on the parity of the components of the spin polarization with respect to the sign of the spin orbit coupling constant.

Abstract:
Electronic transport in closed loop structures is addressed within a tight-binding formalism and in the presence of both the Rashba and Dresselhaus spin-orbit interactions. It has been shown that any one of the spin-orbit fields can be estimated precisely if the other one is known, by observing either the transmission resonance or anti-resonance of unpolarized electrons. The result is obtained through an exact analytic calculation for a simple square loop, and through a numerically exact formulation for a circular ring. The sensitivity of the transport properties on the geometry of the interferometer is discussed in details.