Magnetic devices are a leading contender for the implementation of memory and logic technologies that are non-volatile, that can scale to high density and high speed, and that do not wear out. However, widespread application of magnetic memory and logic devices will require the development of efficient mechanisms for reorienting their magnetization using the least possible current and power. There has been considerable recent progress in this effort; in particular, it has been discovered that spin-orbit interactions in heavy-metal/ferromagnet bilayers can produce strong current-driven torques on the magnetic layer, via the spin Hall effect in the heavy metal or the Rashba-Edelstein effect in the ferromagnet. In the search for materials to provide even more efficient spin-orbit-induced torques, some proposals have suggested topological insulators, which possess a surface state in which the effects of spin-orbit coupling are maximal in the sense that an electron's spin orientation is fixed relative to its propagation direction. Here we report experiments showing that charge current flowing in-plane in a thin film of the topological insulator bismuth selenide (Bi2Se3) at room temperature can indeed exert a strong spin-transfer torque on an adjacent ferromagnetic permalloy (Ni81Fe19) thin film, with a direction consistent with that expected from the topological surface state. We find that the strength of the torque per unit charge current density in Bi2Se3 is greater than for any source of spin-transfer torque measured so far, even for non-ideal topological insulator films in which the surface states coexist with bulk conduction. Our data suggest that topological insulators could enable very efficient electrical manipulation of magnetic materials at room temperature, for memory and logic applications.
Despite much interest in engineering new topological surface (edge) states using structural defects, such topological surface states have not been observed yet. We show that recently imaged tilt boundaries in gated multilayer graphene should support topologically protected gapless edge states. We approach the problem from two perspectives: the microscopic perspective of a tight-binding model and an ab initio calculation on a bilayer, and the symmetry-protected topological (SPT) state perspective for a general multilayer. Hence, we establish the tilt-boundary edge states as the first concrete example of the edge states of symmetry-protected Z-type SPT, protected by no-valley mixing, electron-number conservation, and time-reversal T symmetries. Further, we discuss possible phase transitions between distinct SPTs upon symmetry changes. Combined with a recently imaged tilt-boundary network, our findings may explain the long-standing puzzle of subgap conductance in gated bilayer graphene. This proposal can be tested through future transport experiments on tilt boundaries. In particular, the tilt boundaries offer an opportunity for the in situ imaging of topological edge transport.
In this paper, we introduce a two-dimensional fractional topological superconductor (FTSC) as a strongly correlated topological state which can be achieved by inducing superconductivity into an Abelian fractional quantum Hall state, through the proximity effect. When the proximity coupling is weak, the FTSC has the same topological order as its parent state and is thus Abelian. However, upon increasing the proximity coupling, the bulk gap of such an Abelian FTSC closes and reopens resulting in a new topological order: a non-Abelian FTSC. Using several arguments we will conjecture that the conformal field theory (CFT) that describes the edge state of the non-Abelian FTSC is U (1)/Z2 orbifold theory and use this to write down the ground-state wave function. Further, we predict FTSC based on the Laughlin state at ν = 1/m filling to host fractionalized Majorana zero modes bound to superconducting vortices. These zero modes are non-Abelian quasiparticles which is evident in their quantum dimension of dm = √ 2m. Using the multi-quasi-particle wave function based on the edge CFT, we derive the projective braid matrix for the zero modes. Finally, the connection between the non-Abelian FTSCs and the Z2m rotor model with a similar topological order is illustrated. arXiv:1204.6245v4 [cond-mat.str-el]
† These authors contribute to the work equally. Chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain two-dimensonal topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions lead to the same unitary transformation as that in the braiding of Majorana zero modes, and propose a new platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can utilize quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state. Chiral Majorana fermion, also known as Majorana-Weyl fermion, is a massless fermionic particle being its 1 arXiv:1712.06156v3 [cond-mat.mes-hall] 26 Sep 2018 own antiparticle proposed long ago in theoretical physics. The simplest chiral Majorana fermion is predicted in 1 dimensional (1D) space, where it propagates unidirectionally. In condensed matter physics, 1D chiral Majorana fermions can be realized as quasiparticle edge states of a 2D topological state of matter (1). A celebrated example is the p + ip chiral topological superconductor (TSC), which carries a Bogoliubov-de Gennes (BdG) Chern number N = 1, and can be realized from a quantum anomalous Hall insulator (QAHI) with Chern number C = 1 in proximity with an s-wave superconductor (2-5). A QAHI-TSC-QAHI junction implemented this way is predicted to exhibit a half quantized conductance plateau induced by chiral Majorana fermions (3,4), which has been recently observed in the Cr doped (Bi,Sb) 2 Te 3 thin film QAHI system in proximity with Nb superconductor (6). Chiral Majorana fermion could also arise in the Moore-Read state of fractional quantum Hall effect (7) and topologically ordered states of spin systems (8). A closely related concept, Majorana zero modes (MZMs) which emerge in the bulk vortices of a p+ip TSC (9) or at the endpoints of a 1D p-wave TSC (10, 11), are known to obey non-Abelian braiding statistics and can be utilized in fault-tolerant topological quantum computations (12-17). Despite the theoretical progress made during the past decade on employing MZMs in universal quantum computation (14-17), due to the localized and pointlike nature of MZMs, all existing proposed architectures inevitably require nano-scale design and control of the coupling among MZMs. As an essential step towards topological quantum computing, the braiding of MZMs has not yet been experimentally demonstrated.In this paper, we propose a novel platform to implement topologically protected quantum gates at mesoscopic scales, which utilizes propagation of chiral Majorana fermions with purely electrical manipulations in...
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