PDF《Pure spin current in graphene NS》

arXiv:cond-mat/0610750v3 [cond-mat.

mes-hall]

30 May

2007 Pure spin current in graphene NS structures D. Greenbaum,1 S. Das,1 G. Schwiete,1 and P. G. Silvestrov2

1 Department of Condensed Matter Physics, Weizmann Institute of Science,

76100 Rehovot, Israel

2 Theoretische Physik III, Ruhr-Universit¨ at Bochum,

44780 Bochum, Germany (Dated: August 30, 2018) We demonstrate theoretically the possibility of producing a pure spin current in graphene by ?ltering the charge from a spin-polarized electric current. To achieve this e?ect, which is based on the recently predicted property of specular Andreev re?ection in graphene, we propose two possible device structures containing normal-superconductor (NS) junctions. PACS numbers: 74.45.+c, 73.23.-b, 85.75.-d, 81.05.Uw I. INTRODUCTION The recent experimental realization of conducting two dimensional monolayers of graphite [1, 2, 3, 4], also known as graphene, o?ers the promise for new electronic devices. One conceivable use for graphene is in spintron- ics [5], where the lack of nuclear spin interaction (12 C has no nuclear spin) could o?er the ability to maintain spin coherence over larger distances than in conventional semiconductors. For progress towards this goal, it is es- sential to have simple and reliable means to transport spin in graphene. We address this issue by proposing a prescription for producing a pure spin current in ballistic bulk graphene. Spin currents have already been predicted to arise in graphene due to spin-orbit coupling [6] and the Quan- tum Hall E?ect [7]. In both cases, the spin currents are due to counter-propagating edge states of opposite spin. Our proposal makes use of the recently predicted specu- larity [8] of Andreev re?ection [9] in graphene to produce a pure spin current in bulk. This is accomplished us- ing structures containing normal-superconducting (NS) boundaries, which ?lter the charge out of a current of spin-polarized quasiparticles, leaving behind a pure spin current. To be speci?c, we consider two device paradigms: 1) a V-junction geometry with opening angle appropriately tuned, 2) a channel with a superconductor at one boundary and a normal edge at the other. An ad- vantage of such devices is the large number of transmit- ting channels in the bulk, o?ering the possibility of rapid spin accumulation. Also, our proposal does not require a magnetic ?eld, nor does it rely on the spin-orbit gap. In the present case, however, it is crucial to ?rst generate a spin-polarized electric current, which could conceivably be done by contacting the system to a ferromagnetic lead, as has been done with carbon nanotubes [10]. Our description of proximity e?ects in graphene fol- lows that of Ref. [8]. Later publications, Refs. [11, 12], used this approach to discuss the Andreev spectrum and Josephson e?ect in NS (SNS) structures in graphene. A very recent paper [13] makes explicit use of the specu- larity of Andreev re?ection in graphene by considering the neutral excitations propagating along a narrow SNS channel. These authors propose a device that is similar to e h e y x S α F FIG. 1: V-junction with NS interface. Polarized electrons are injected through the lower arm and the same polarization is transferred to the upper arm by the electron-hole beam. the one considered below in Sec. IV, but suggest investi- gating the thermoelectric e?ect to observe the chargeless excitations. In contrast, we analyze the spin transport. Our approach also lends itself to an analysis of the de- viations from perfect charge ?ltering in a channel, which is done in Sec. V. Finally, an elegant method to pro- duce pure spin currents in conventional semiconductors was suggested in Ref. [14], where the spatial separation of electron and hole trajectories is caused by tunneling through a superconductor. II. ANDREEV REFLECTION IN GRAPHENE The electron wave function in graphene is described by a two component (pseudo-)spinor ψ. Its spin-up and spin-down components correspond to the quantum me- chanical amplitudes of ?nding the particle on one of the two sublattices of the honeycomb lattice. The low energy physics of graphene is governed by two so-called Dirac points in the spectrum, located at the two inequivalent corners K, K′ of the Brillouin zone. The spinor wave function for low energy excitations in (lightly-doped) graphene decomposes into a sum of two waves oscillat- ing with di?erent wave vectors ψ = eiKr φ+ + eiK′r φ?. The smooth envelope functions φ± satisfy the two- dimensional Dirac equation [15] described by the Hamil-