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The comment by O. Entin-Wohlman, A. Aharony, and Y. Utsumi, on our paper S. Varela, I. Zambrano, B. Berche, V. Mujica, and E. Medina, Phys. Rev. B 101, 241410(R) (2020) makes a few points related to the validity of our model, especially in the light of the interpretation of Bardarsons theorem: in the presence of time reversal symmetry and for half-integral spin the transmission eigenvalues of the two terminal scattering matrix come in (Kramers) degenerate pairs. The authors of the comment first propose an ansatz for the wave function in the spin active region and go on to show that the resulting transmission does not show spin dependence, reasoning that spin dependence would violate Bardarsons assertion. Here we clearly show that the ansatz presented assumes spin-momentum independence from the outset and thus just addresses the spinless particle problem. We then find the appropriate eigenfunction contemplating spin-momentum coupling and show that the resulting spectrum obeys Bardarsons theorem. Finally we show that the allowed wavevectors are the ones assumed in the original paper and thus the original conclusions follow. We recognize that the Hamiltonian in our paper written in local coordinates on a helix was deceptively simple and offer the expressions of how it should be written to more overtly convey the physics involved. The relation between spin polarization and torque becomes clear, as described in our paper. This response is a very important clarification in relation to the implications of Bardarsons theorem concerning the possibility of spin polarization in one dimensional systems in the linear regime.
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Electron transfer (ET) in biological molecules such as peptides and proteins consists of electrons moving between well defined localized states (donors to acceptors) through a tunneling process. Here we present an analytical model for ET by tunneling in DNA, in the presence of Spin-Orbit (SO) interaction, to produce a strong spin asymmetry with the intrinsic atomic SO strength in meV range. We obtain a Hamiltonian consistent with charge transport through $pi$ orbitals on the DNA bases and derive the behavior of ET as a function of the injection state momentum, the spin-orbit coupling and barrier length and strength. A highly consistent scenario arises where two concomitant mechanisms for spin selection arises; spin interference and differential spin amplitude decay. High spin filtering can take place at the cost of reduced amplitude transmission assuming realistic values for the spin-orbit coupling. The spin filtering scenario is completed by addressing the spin dependent torque under the barrier, with a consistent conserved definition for the spin current.
We consider a two-dimensional magnetic tunnel junction of the FM/I/QW(FM+SO)/I/N structure, where FM, I and QW(FM+SO) stand for a ferromagnet, an insulator and a quantum wire (QW) with both magnetic ordering and Rashba spin-orbit (SOC), respectively. The tunneling magneto-resistance (TMR) exhibits strong anisotropy and switches sign as the polarization direction varies relative to the QW axis, due to interplay among the one-dimensionality, the magnetic ordering, and the strong SOC of the QW. The results may provide a possible explanation for the sign-switching anisotropic TMR recently observed in the LaAlO$_3$/SrTiO$_3$ interface.
The effect of an ac electric field on quantum transport properties in a system of three quantum dots, two of which are connected in parallel while the third is coupled to one of the other two, is investigated theoretically. Based on the Keldysh nonequilibrium Greens function method, the spin-dependent current, occupation number and spin accumulation can be obtained in our model. An external magnetic flux, Rashba spin orbit coupling (SOC) and intradot Coulomb interactions are considered. The magnitude of the spin-dependent average current and the positions of the photon assisted tunneling (PAT) peaks can be accurately controlled and manipulated by simply varying the strength of the coupling and the frequency of the ac field. A particularly interesting result is the observation of a new kind of PAT peak and a multiple electron-photon pump effect that can generated and controlled by the coupling between the quantum dots. In addition, the spin occupation number and spin accumulation can be well controlled by the Rashba SOC and the magnetic flux.
In this technical note, we address the comments on the energy estimates for Magnetoelectric Spin-orbit (MESO) Logic, a new logic device proposed by the authors. We provide an analytical derivation of the switching energy, and support it with time-domain circuit simulations using a self-consistent ferroelectric (FE) compact model. While the energy to charge a capacitor is dissipated in the interconnect and transistor resistance, we note that the energy to switch a capacitor and a FE is independent of the interconnect resistance value to the first order. Also device design can mitigate the parasitic energy losses. We further show the circuit simulations for a sub 10 aJ switching operation of a MESO logic device comprehending: a) Energy stored in multiferroic; b) Energy dissipation in the resistance of the interconnect, Ric ; c) Energy dissipation in the inverse spin-orbit coupling (ISOC) spin to charge converter Risoc; d) Supply, ground resistance, and transistor losses. We also identify the requirements for the resistivity of the spin-orbit coupling materials and address the effect of internal resistance of the spin to charge conversion layer. We provide the material parameter space where MESO (with a fan-out of 1 and interconnect) achieves sub 10 aJ switching energy with path for scaling via ferroelectric/magnetoelectric/spin-orbit materials development.
Within an effective Dirac theory the low-energy dispersions of monolayer graphene in the presence of Rashba spin-orbit coupling and spin-degenerate bilayer graphene are described by formally identical expressions. We explore implications of this correspondence for transport by choosing chiral tunneling through pn and pnp junctions as a concrete example. A real-space Greens function formalism based on a tight-binding model is adopted to perform the ballistic transport calculations, which cover and confirm previous theoretical results based on the Dirac theory. Chiral tunneling in monolayer graphene in the presence of Rashba coupling is shown to indeed behave like in bilayer graphene. Combined effects of a forbidden normal transmission and spin separation are observed within the single-band n to p transmission regime. The former comes from real-spin conservation, in analogy with pseudospin conservation in bilayer graphene, while the latter arises from the intrinsic spin-Hall mechanism of the Rashba coupling.
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