Majorana Fermions and Topology in Superconductors

Sato, Masatoshi; Fujimoto, Satoshi

doi:10.7566/jpsj.85.072001

Cited by 384 publications

(296 citation statements)

References 278 publications

(467 reference statements)

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“…Correspondingly, an occupied state in (a1) is even under reflection, 5) but that in (a2) is odd under reflection,…”

Section: Representation Dependence and R(p )-Module Structurementioning

confidence: 99%

“…[1][2][3][4][5][6] Whereas only fully gapped systems had been regarded as topological phases in the early stage of the study, recent developments have clarified that bulk gapless materials like Weyl semimetals also exhibit non-trivial topological phenomena. The existence of surface Fermi arcs and related anomalous transports are typical topological phenomena in the latter case.…”

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confidence: 99%

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Topological crystalline materials: General formulation, module structure, and wallpaper groups

2017

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We formulate topological crystalline materials on the basis of the twisted equivariant K-theory. Basic ideas of the twisted equivariant K-theory are explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an application of our formulation, we present a complete classification of topological crystalline surface states, in the absence of time-reversal invariance. The classification works for gapless surface states of three-dimensional insulators, as well as full gapped two-dimensional insulators. Such surface states and two-dimensional insulators are classified in a unified way by 17 wallpaper groups, together with the presence or the absence of (sublattice) chiral symmetry. We identify the topological numbers and their representations under the wallpaper group operation. We also exemplify the usefulness of our formulation in the classification of bulk gapless phases. We present a new class of Weyl semimetals and Weyl superconductors that are topologically protected by inversion symmetry. CONTENTS

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“…Correspondingly, an occupied state in (a1) is even under reflection, 5) but that in (a2) is odd under reflection,…”

Section: Representation Dependence and R(p )-Module Structurementioning

confidence: 99%

mentioning

confidence: 99%

Topological crystalline materials: General formulation, module structure, and wallpaper groups

2017

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“…Nontrivial topology embedded in bulk brings about topological quantization in transport and anomalous electromagnetic responses [1,2]. The topological viewpoint has also shed light on a new facet of unconventional superconductors/superfluids [3][4][5][6][7][8][9][10]. The key ingredient is Majorana fermions, which behave as non-abelian anyons [11,12] and possess Ising spins [13][14][15][16].…”

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confidence: 99%

P23superfluids are topological

2017

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We clarify topology of 3 P2 superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors.3 P2 phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and cyclic phases. We here show that all the phases are accompanied by different types of topologically protected gapless fermions: Surface Majorana fermions in nematic phases and a quartet of (single) itinerant Majorana fermions in the cyclic (ferromagnetic) phase. Using the superfluid Fermi liquid theory, we also demonstrate that dihedral-two and -four biaxial nematic phases are thermodynamically favored in the weak coupling limit under a magnetic field. It is shown that the tricritical point exists on the phase boundary between these two phases and may be realized in the core of realistic magnetars. We unveil the intertwining of symmetry and topology behind mass acquisition of surface Majorana fermions in nematic phases.

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“…In the case of a topological superconductor, zero energy Majorana modes are predicted to appear and great effort has been devoted to prove their existence. Methods that provide signatures of their presence have been proposed and experimentally tested via for instance tunneling experiments 55,56 , interferometry 3 , point contacts using the Andreev reflection 57 through the detection of zero-bias peaks 58 , using the quantum waveguide theory 59 which gives the correct bulk-edge correspondence 35 and fractional Josephson currents 1,3,60 . Also signatures of the Majorana states may be found in bulk measurements such as the imaginary part of frequency dependent Hall conductance 61 and the d.c. Hall conductivity itself 62 .…”

Section: Introductionmentioning

confidence: 99%

4π Josephson currents in junctions of hybridized multiband superconductors

2017

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We study two-band one-dimensional superconducting chains of spinless fermions with inter and intra-band pairing. These bands hybridize and, depending on the relative angular momentum of their orbitals, the hybridization can be symmetric or anti-symmetric. The self-consistent competition between intra and inter-band superconductivity and how it is affected by the symmetry of the hybridization is investigated. In the case of anti-symmetric hybridization the intra and inter-band pairings do not coexist while in the symmetric case they do coexist and the interband pairing is shown to be dominant. The topological properties of the model are obtained through the topological invariant winding number and the presence of edge states. We find the existence of a topological phase due to the inter-band superconductivity and induced by symmetric hybridization. In this case we find a characteristic 4π-periodic Josephson current. In the case of anti-symmetric hybridization we also find a 4π-periodic Josephson current in the gapless inter-band superconducting phase, recently identified to be of Weyl-type.

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Majorana Fermions and Topology in Superconductors

Cited by 384 publications

References 278 publications

Topological crystalline materials: General formulation, module structure, and wallpaper groups

Topological crystalline materials: General formulation, module structure, and wallpaper groups

P23superfluids are topological

4π Josephson currents in junctions of hybridized multiband superconductors

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