Spatiotemporal characteristics of spin transport in compensated metals with electron–hole exchange interaction

Abstract

We develop a theory describing spatiotemporal behavior of spin transport in two-band metals by postulating a spin–exchange interaction between electrons and holes. Starting with the semiclassical Boltzmann equation, we derive a system of coupled diffusion equations and solve them analytically under steady-state conditions. The solutions reveal two types of electron–hole coupled-spin transport modes: a dissipative mode and a nondissipative mode with an infinite spin diffusion length. The two modes are the manifestations of two types of spin coupling channels. Besides the exchange interaction, we incorporate into our derivation the relaxation caused by the spin–orbit interaction to show how it affects the spin transport characteristics of the two modes.

Long-distance spin communication via ambipolar conductor with electron–hole spin exchange interaction

“…The nondissipative spin mode disappears when the spin relaxation due to the SOI is present because, as described in appendix D, the collision integrals for the SOI in the ambipolar conductor case violate the CPT invariance whereas those for the Baber collision show the CPT invariance, where C, P and T are the charge conjugation operation, the time-reversal operation and the inversion operation, respectively [22,31]. The importance of the CPT invariance is theoretically argued for zigzag-edge graphene ribbons, in which a nondissipative spin-valley current is assured by the CPT invariance [32].…”

“…ν ∆µ ν (ν =↑, ↓), which is used for the holes [22], into (17) and (18) yields the same equation as (9). Therefore, the simultaneous equations determining F ↑ , F ↓ , D ↑ , D ↓ , E 1 and E 2 are identical to those used when the carriers of the N region are electrons.…”

“…In the presence of this sort of Baber collision, the individual modes with pure electron and hole characters are no longer eigenmodes. Instead, two types of electron-hole coupled-spin transport modes are eigenmodes, namely, a dissipative mode and a nondissipative mode with an infinite spin diffusion length, each of which has an out-of-phase character D h n [22]. The spin diffusion length ℓ out for the out-of-phase mode is given by…”

“…Value Units Temperature Reference where r 1 , r 2 and r amb are the spin resistances of the F1, F2 and N regions, respectively; they are defined by (C. 22) and show that r amb is proportional to L. The V SC of a singleheterojunction structure can be derived by substituting p 2 = 0 and L → ∞ into (51) to obtain (50). Accordingly, the proportionality of r amb to L directly causes the absence of N region characteristics in (50).…”

“…Because ambipolar conductors include approximately 10 types of elemental metals and approximately 60 types of metal alloys [19], they are not special materials. When an electron-hole collision, which is called Baber scattering [20], is accompanied by spin exchange [21], the two type of electron-hole coupled-spin modes, one having a finite ℓ N and the other having an infinite ℓ N , are eigenmodes instead of individual modes with pure electron and hole characters [22]. The present theory incorporates these characteristics into the conventional boundary conditions associated with charge transport, spin angular momentum transport and electrochemical potentials to formulate V SC and ∆V SC as functions of spin polarizations of the F regions.…”