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Register a new userIn-plane Zeeman field induced Majorana corner and hinge modes in an $s$-wave superconductor heterostructure
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Second-order topological superconductors host Majorana corner and hingemodes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions or layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an $s$-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses between adjacent boundaries, leading to one Majorana mode at each corner. A similar paradigm also applies to 3D topological insulators with the emergence of Majorana hinge states. Avoiding complex superconductor pairing and material structure, our scheme provides an experimentally realistic platform for implementing Majorana corner and hinge states.
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SnTe materials are one of the most flexible material platforms for exploring the interplay of topology and different types of symmetry breaking. We study symmetry-protected topological states in SnTe nanowires in the presence of various combinations of Zeeman field, s-wave superconductivity and inversion-symmetry-breaking field. We uncover the origin of robust corner states and hinge states in the normal state. In the presence of superconductivity, we find inversion-symmetry-protected gapless bulk Majorana modes, which give rise to quantized thermal conductance in ballistic wires. By introducing an inversion-symmetry-breaking field, the bulk Majorana modes become gapped and topologically protected localized Majorana zero modes appear at the ends of the wire.
We identify three-dimensional higher-order superconductors characterized by the coexistence of one-dimensional Majorana hinge states and gapless surface sates. We show how such superconductors can be obtained starting from the model of a spinful quadrupolar semimetal with two orbitals and adding an s-wave superconducting pairing term. By considering all the possible s-wave pairings satisfying Fermi-Dirac statistics we obtain six different superconducting models. We find that for two of these models a flat-band of hinge Majorana states coexist with surface states, and that these models have a non-vanishing quadrupole-like topological invariant. Two of the other models, in the presence of a Zeeman term, exhibit helical and dispersive hinge states localized only at two of the four hinges. We find that these states are protected by combinations of rotation and mirror symmetries, and that the pair of corners exhibiting hinge states switches upon changing the sign of the Zeeman term. Furthermore, we show that these states can be localized to a single hinge with suitable perturbations. The remaining two models retain gapless bulk and surface states that spectroscopically obscure any possible hinge states.
We propose a realization of chiral Majorana modes propagating on the hinges of a 3D antiferromagnetic topological insulator, which was recently theoretically predicted and experimentally confirmed in the tetradymite-type $mathrm{MnBi_2Te_4}$-related ternary chalgogenides. These materials consist of ferromagnetically ordered 2D layers, whose magnetization direction alternates between neighboring layers, forming an antiferromagnetic order. Besides surfaces with a magnetic gap, there also exsist gapless surfaces with a single Dirac cone, which can be gapped out when proximity coupled to an $s$-wave superconductor. On the sharing edges between the two types of gapped surfaces, the chiral Majorana modes emerge. We further propose experimental signatures of these Majoana hinge modes in terms of two-terminal conductance measurements.
Exotic states of topological materials are challenging or impossible to create under ambient conditions.1-4 Moreover, it is unclear whether topological superconductivity, as a critical element for topological quantum computing, exists in any naturally occurring materials.5-7 Although these problems can be overcome through the combination of materials in heterostructures, there are still many requisites, such as low temperatures and specific magnetic fields.8,9 Herein, an intrinsic topological superconductor that does not depend on particular external conditions is demonstrated. It is accomplished utilizing the unique properties of polyaromatic hydrocarbons (PAHs), which have been proposed to have persistent ring current.10-12 According to the Su-Schrieffer-Heeger(SSH)13 and Kitaev14 models, PAHs can have a non-trivial edge mode, so that perpendicularly stacked PAHs are expected to have Majorana hinge and corner modes.15 Intrinsic persistent ring current of HYLION-12 is demonstrated by MPMS.16 Coherent Quantum Phase Slip(CQPS), the Constant Conductance Plateau (CCP) and the zero bias conductance peak(ZBP) which is signatures of hinge modes are confirmed through the Josephson junction device of pelletized orthorhombic phase organic crystals of HYLION-12 by transport spectroscopy.17,18 They are signatures of Majorana hinge and corner modes. In addition, the braidinglike operation by transport spectroscopy shows the emergence of the most important and critical elements of quantum computers that can be realized without an external magnetic field at room temperature.
Contrary to the widespread belief that Majorana zero-energy modes, existing as bound edge states in 2D topological insulator (TI)-superconductor (SC) hybrid structures, are unaffected by non-magnetic static disorder by virtue of Andersons theorem, we show that such a protection against disorder does not exist in realistic multi-channel TI/SC/ferromagnetic insulator (FI) sandwich structures of experimental relevance since the time-reversal symmetry is explicitly broken locally at the SC/FI interface where the end Majorana mode (MM) resides. We find that although the MM itself and the emph{bulk} topological superconducting phase inside the TI are indeed universally protected against disorder, disorder-induced subgap states are generically introduced at the TI edge due to the presence of the FI/SC interface as long as multiple edge channels are occupied. We discuss the implications of the finding for the detection and manipulation of the edge MM in realistic TI/SC/FI experimental systems of current interest.
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