Spintronics is an emerging paradigm with the aim to replace conventional electronics by using electron spins as information carriers. Its utility relies on the magnitude of the spin-relaxation, which is dominated by spin-orbit coupling (SOC). Yet, SOC induced spin-relaxation in metals and semiconductors is discussed for the seemingly orthogonal cases when inversion symmetry is retained or broken by the so-called Elliott-Yafet and D'yakonov-Perel' spin-relaxation mechanisms, respectively. We unify the two theories on general grounds for a generic two-band system containing intra-and inter-band SOC. While the previously known limiting cases are recovered, we also identify parameter domains when a crossover occurs between them, i.e. when an inversion symmetry broken state evolves from a D'yakonov-Perel' to an Elliott-Yafet type of spin-relaxation and conversely for a state with inversional symmetry. This provides an ultimate link between the two mechanisms of spin-relaxation.A future spintronics device would perform calculations and store information using the spin-degree of freedom of electrons with a vision to eventually replace conventional electronics [1][2][3] . A spin-polarized ensemble of electrons whose spin-state is manipulated in a transistor-like configuration and is read out with a spin-detector (or spin-valve) would constitute an elemental building block of a spin-transistor. Clearly, the utility of spintronics relies on whether the spin-polarization of the electron ensemble can be maintained sufficiently long. The basic idea behind spintronics is that coherence of a spin-ensemble persists longer than the coherence of electron momentum due to the relatively weaker coupling of the spin to the environment. The coupling is relativistic and has thus a relatively weak effect known as spin-orbit coupling (SOC).The time characterizing the decay of spin-polarization is the so-called spin-relaxation time (often also referred to as spin-lattice relaxation time), t s . It can be measured either using electron spin-resonance spectroscopy (ESR) 4 or in spin-transport experiments 5,6 . Much as the theory and experiments of spin-relaxation measurements are developed, it remains an intensively studied field for novel materials; e.g. the value of t s is the matter of intensive theoretical studies 7-13 and spin-transport experiments [14][15][16][17] in graphene at present. The two most important spin-relaxation mechanisms in metals and semiconductors are the so-called ElliottYafet (EY) and the D'yakonov-Perel' (DP) mechanisms. These are conventionally discussed along disjoint avenues, due to reasons described below. Although the interplay between these mechanisms has been studied in semiconductors 3,[18][19][20] , no attempts have been made to unify their descriptions. We note that a number of other spin-relaxation mechanisms, e.g. that involving nuclear-hyperfine interaction, are known 2,3 . The EY theory 21,22 describes spin-relaxation in metals and semiconductors with inversion symmetry. Therein, the SOC does not spl...
Recent experiments on silicon nanostructures have seen breakthroughs toward scalable, long-lived quantum information processing. The valley degree of freedom plays a fundamental role in these devices, and the two lowest-energy electronic states of a silicon quantum dot can form a valley qubit. In this work, we show that a single-atom high step at the silicon/barrier interface induces a strong interaction of the qubit and in-plane electric fields, and analyze the consequences of this enhanced interaction on the dynamics of the qubit. The charge densities of the qubit states are deformed differently by the interface step, allowing non-demolition qubit readout via valley-tocharge conversion. A gate-induced in-plane electric field together with the interface step enables fast control of the valley qubit via electrically driven valley resonance. We calculate single-and two-qubit gate times, as well as relaxation and dephasing times, and present predictions for the parameter range where the gate times can be much shorter than the relaxation time and dephasing is reduced.
Topological properties of quantum systems could provide protection of information against environmental noise, and thereby drastically advance their potential in quantum information processing. Most proposals for topologically protected quantum gates are based on many-body systems, e.g., fractional quantum Hall states, exotic superconductors, or ensembles of interacting spins, bearing an inherent conceptual complexity. Here, we propose and study a topologically protected quantum gate, based on a one-dimensional single-particle tight-binding model, known as the Su-Schrieffer-Heeger chain. The proposed Y gate acts in the two-dimensional zero-energy subspace of a Y junction assembled from three chains, and is based on the spatial exchange of the defects supporting the zeroenergy modes. With numerical simulations, we demonstrate that the gate is robust against hopping disorder but is corrupted by disorder in the on-site energy. Then we show that this robustness is topological protection, and that it arises as a joint consequence of chiral symmetry, time-reversal symmetry and the spatial separation of the zero-energy modes bound to the defects. This setup will most likely not lead to a practical quantum computer, nevertheless it does provide valuable insight to aspects of topological quantum computing as an elementary minimal model. Since this model is non-interacting and non-superconducting, its dynamics can be studied experimentally, e.g., using coupled optical waveguides. arXiv:1902.01358v2 [cond-mat.mes-hall]
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