It is well known that non-Abelian Majorana zero modes (MZM) harbor at vortex cores in a px +ipy topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an s-wave superconductor. Here we show that existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can be resulted in much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces and gapped out by superconducting pairings, we show that at least a single MZM survives if there are only odd number of Fermi surfaces of which the corresponding superconducting orders have vortices, and such MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result may enrich new experimental schemes for realizing non-Aelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on the recent cold atom experiments.The quest for realization of non-Abelian Majorana zero modes (MZMs), driven by the pursuit of both fundamental physics and their potential application to faulttolerant topological quantum computation [1, 2], has been spearheaded by the developments in p-wave superconductors. Early studies predicted that MZMs exist in ν = 5/2 fractional quantum Hall state [3], at the vortex cores in 2D spinless p x + ip y topological superconductors (SCs) [4], and at ends of a 1D p-wave SC [5]. More recently, it has been proposed that the hybrid systems of s-wave SC and spin-orbit (SO) coupled matters with odd number of Fermi surfaces (FSs) can favor effective p-wave pairing states, bringing the realization of MZMs to realistic solid state experiments [6][7][8][9][10][11][12][13][14][15]. Motivated by these proposals, numerous experimental studies have been performed to observe Majorana induced zero bias conductance anomalies with different heterostructures formed by s-wave SCs and semiconductor nanowires [16][17][18][19], magnetic chains [20], or topological insulators [21][22][23].By far the experimental proposals for MZMs are built on the realization of topological SCs. Note that MZMs in SCs are topological defect modes [24][25][26][27], which correspond to nonlocal extrinsic deformations in the Hamiltonian of the topological system. For example, MZMs in the chiral p x + ip y SC harbor at vortices which exhibit nonlocal phase windings of the SC order (a global deformation in the original uniform Hamiltonian). This feature tells that the MZMs at vortices are not intrinsic topological excitations, but extrinsic modes of a SC. In this regard, one may conjecture that the existence of MZMs is not uniquely corresponding to the bulk topology of a SC, and there might be much broader range of experimental systems which can host such exotic modes, besides those based on topologically nontrivial SCs.In this Letter...

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Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in an experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH) model using the nuclear magnetic resonance processor. Unlike the usual experiments using auxiliary qubits, we develop a stochastic average approach based on the stochastic Schrödinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifying the implementation of quantum gates. We demonstrate the stability of dynamical topology against weak noise and observe two types of dynamical topological transitions driven by strong noise. Moreover, a region where the emergent topology is always robust regardless of the noise strength is observed. Our work shows a feasible quantum simulation approach for dissipative quantum dynamics with stochastic Schrödinger equation and opens a route to investigate non-Hermitian dynamical topological physics.