Shot noise of spin current

Abstract

We report an exact solution for the noise spectrum of spincurrent without charge-current in a spin field effect transistor (SFET). For the SFET with two leads, it is found that both auto-and cross-correlation functions are needed to characterize the noise of spin-current. A shot noise is also generated for the charge-current even though the net chargecurrent is identically zero. The noise spectra of spin-current and charge-current depends on the coupling strength between the SFET and the leads, and they may behave qualitatively differently. We also present results of noise spectra in the adiabatic regime.73.23. Ad,73.40.Gk,72.10.Bg Due to the particle nature of carriers, the fluctuation of charge-current gives rise to the notion of shot noise 1 . For a normal system, the current correlation between different probes (cross correlation) is negative for Fermions and positive for Bosons 2,4 . The correlation can be more complicated if superconducting leads are present 6-12 . Importantly, the correlation properties provide further information, in addition to those contained in conductance or charge-current, for mesoscopic conductors 2 . So far all theoretical and experimental attention have been devoted to correlations of charge-current.In this paper, we theoretically investigate the correlation of spin-current in the absence of charge-current in a two-probe device. Indeed, to be able to generate and control spin-current is of great importance for spintronics 13 , but the noise spectra of spin-current has never been studied before. A pure spin-current can behave qualitatively differently from charge-current because spins can flip so that spin-current may not be conserved. Therefore the cross correlation of currents may not be directly related to the auto-correlation. On the other hand, the conservation of charge forces the cross correlation and autocorrelation of charge-current noise spectra to differ by just a minus sign in a two-probe system. This difference necessarily indicates that the noise spectra of spincurrent is more complicated. To be more specific, we will investigate the spin-current correlation in a twoprobe quantum spin field effect transistor (SFET) 14 . The detailed working principle of the SFET is summarized elsewhere 14 and we refer interested readers there: this device delivers an instantaneous spin-current but without generating a net charge-current by the help of a rotating magnetic field. Roughly, if all the spin-up electrons in a conductor move to one direction while an equal number of spin-down electrons move to the opposite direction, the net charge-current vanishes because I e = e(I ↑ + I ↓ ) = 0; and a finite spin-current results because I s =h/2(I ↑ − I ↓ ) = 0. Here (I ↑ , I ↓ ) are the electron current for spin-up and spin-down electrons respectively. The SFET provides a mechanism for this effect, and there are a number of other possibilities to produce I s = 0 with I e = 0 which is the subject of several recently studies both theoretically 15-17 and experimentally 18 .For a two-lead...

Magnetotransport through a ring conductor with Rashba spin-orbit interaction

“…For instance, the shot noise of spin current in a spin pump device was analyzed based on the Keldysh nonequilibrium Green-function method. 18 It is shown that the spincurrent shot noise can also be used to probe quantum correlation effect in a four terminal geometry with Rashba effect. 19 The possibility of using the spin-current shot noise to measure the spin-relaxation time has been theoretically proposed.…”

Shot noise in magnetic tunneling structures with two-level quantum dots

“…It should be also noted that the problem of spin shot noise has been already considered in many papers [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and for various systems. The main interest of these works was focused on how the discreteness of spin affects the current fluctuations.…”

Shot noises of spin and charge currents in a ferromagnet-quantum-dot-ferromagnet system

“…Since electrons carry spin, the discreteness of spin carriers fluctuates during their transport and the statistical behavior results in the spin current noise. The theoretical investigation on spin current without an accompanying charge current has been reported recently for the system under a rotating magnetic field [38]. The shot noise of spin polarized electrons has been shown to be dependent on spin-flip processes [39].…”