Conversion of spin current into charge current in a topological insulator: Role of the interface

Abstract

Three dimensional spin current density injected onto the surface of a topological insulator (TI) produces a two dimensional charge current density on the surface of the TI, which is the so-called inverse Edelstein effect (IEE). The ratio of the surface charge current density on the TI to the spin current density injected across the interface defined as the IEE length was shown to be exactly equal to the mean free path in the TI determined to be independent of the electron transmission rate across the interface [Phys. Rev. B 94, 184423 (2016)]. However, we find that the transmission rate across the interface gives a non-zero contribution to the transport relaxation rate in the TI as well as to the effective IEE relaxation rate (over and above any surface hybridization effects), and the IEE length is always less than the original mean free path in the TI without the interface. We show that both the IEE relaxation time and the transport relaxation time in the TI are modified by the interface transmission time. The correction becomes significant when the transmission time across the interface becomes comparable to or less than the original momentum scattering time in the TI. This correction is similar to experimental results in Rashba electron systems in which the IEE relaxation time was found shorter in case of direct interface with metal in which the interface transmission rate will be much higher, compared to interfaces incorporating insulating oxides. Our results indicate the continued importance of the interface to obtain a better spin-to-charge current conversion and a limitation to the conversion efficiency due to the quality of the interface.

Mapping spin–charge conversion to the band structure in a topological oxide two-dimensional electron gas

“…In the experiments, however, the electrons have in principle the possibility to leak out of the 2DEG through a tunneling barrier (in this case, the AlO x layer), and scatter in the metal with very short relaxation times (typically tens of fs). This can be considered as a second scattering channel 33,34 characterized by an escape time τ esc through the tunneling barrier, in addition to the scattering between the STO states with characteristic time τ 2DEG . The two scattering channels lead to an effective relaxation time τ eff =(τ 2DEG -1 + τ esc -1 ) -1 that will set the efficiency of the conversion process.…”

Theory of spin detection on the surface of diffusive topological insulators by means of ferromagnets: Establishing Onsager reciprocity and the importance of tunnel contact

“…, where we obtain the momentum relaxation time τ tr to be τ tr = 2τ p because of the spin-momentum locking of the TI surface states 24,34,36 (note that τ s = 2τ p = τ tr ). We refer to τ tr as "the transport relaxation time" consistent with Schwab et al 24 .…”

“…where n ± = n ↑ ± n ↓ . We define the dimensionless parameter ξ = γN + τ tr = 2γN + τ p , which is the normalized tunneling rate with respect to the momentum scattering rate on the TI surface, 36 and ξ is proportional to the tunnel conductance. In case of weak tunneling, ξ 1, the conditions |∆ x | |Ω| 1 Ω so remains valid, and f 2 given in Eq.…”

“…The potential drop due to the NM contact can be calculated considering the transport on the TI surface under the NM contact. Previously 36 , we calculated the modified transport equations on the TI surface due to tunneling from the NM contact. In the 1D case, considering the transport on the TI surface along the x-direction, the modified continuity equation of the TI surface states due to tunneling to and from the NM is given by 36…”

“…where, N m is the per spin DOS of the NM at the Fermi energy, and µ c is the charge electrochemical potential in the NM. In our previous work 36 , we defined the interface transmission time τ t by 1/τ t = γN m . The modified diffusion equation for the charge current density on the TI surface due to tunneling from the NM is given by 36…”