† 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...

We propose a lattice scale two-band generalized Hubbard model as a caricature of the electronic structure of twisted bilayer graphene. Various possible broken symmetry phases can arise, including a nematic phase (which is a form of orbital ferromagnet) and an orbital-triplet spin-singlet superconducting phase. Concerning the mechanism of superconductivity -we propose an analogy with superconductivity in alkali-doped C60 in which a violation of Hund's first rule plays a central role.arXiv:1804.03162v3 [cond-mat.supr-con]

We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called "point-gap" and "line-gap" schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from Z winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups Z n (rather than Z Chern number). We interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.