Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>

Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi

doi:10.1103/physrevlett.111.087002

Cited by 158 publications

(200 citation statements)

References 77 publications

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“…Already, detailed topological classification schemes for all point-group symmetries have been proposed, 166) and also the mirror topology has been expanded to superconductors. [167][168][169] Experimentally, elucidating the interplay between Z 2 topology and mirror topology in materials like SnTe under uniaxial strain would be an interesting issue.…”

Section: Topological Crystalline Insulatormentioning

confidence: 99%

“…4,250) Recently, as mentioned in Sect. 4.5, new topological classifications based on pointgroup symmetry of the crystal lattice is attracting significant interest, [166][167][168][169] particularly after the new type of topological materials called topological crystalline insulators 61,161) have been experimentally discovered. 62,162,164) Also, whereas it was thought to be necessary for topological materials to have a fully-gapped energy spectrum for a topological invariant to be well defined, 4) it is becoming possible to conceive a nontrivial topology for gapless systems.…”

Section: New Types Of Topologiesmentioning

confidence: 99%

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Topological Insulator Materials

2013

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Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussed in detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identify surface Dirac fermions through transport measurements. The prospects of topological insulator materials for elucidating novel quantum phenomena that await discovery conclude the review.

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Section: Topological Crystalline Insulatormentioning

confidence: 99%

Section: New Types Of Topologiesmentioning

confidence: 99%

Topological Insulator Materials

2013

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“…Although the original concept of the topological phase in the quantum Hall system is independent of the symmetry, it has recently been emphasized that the interplay between the topology and symmetry enriches the topological properties of the ordered state [15,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]. The important step was the proposal of the topological table that categorizes topological insulators and superconductors to ten Altland-Zirnbauer (AZ) symmetry classes in terms of time-reversal, particle-hole, and chiral (sub-lattice) symmetries [34,36].…”

mentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

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158

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Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

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“…[55][56][57][58][59][60][61][62][63][64] For instance, consider the mirror reflection symmetry with respect to the xy-plane,…”

Section: Topological Crystalline Superconductorsmentioning

confidence: 99%

Majorana Fermions and Topology in Superconductors

2016

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type of quantum statistics referred to as non-Abelian statistics, which is distinct from bose and fermi statistics, and can be utilized for application to topological quantum computation. Also, Majorana fermions give rise to various exotic phenomena such as "fractionalization", nonlocal correlation, and "teleportation". A pedagogical review of these subjects is presented.We also discuss interaction effects on topological classification of superconductors, and the basic properties of Weyl superconductors.

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Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application toSr2RuO4

Cited by 158 publications

References 77 publications

Topological Insulator Materials

Topological Insulator Materials

Symmetry protected topological superfluid³He-B

Majorana Fermions and Topology in Superconductors

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Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application toSr2RuO4

Cited by 158 publications

References 77 publications

Topological Insulator Materials

Topological Insulator Materials

Symmetry protected topological superfluid3He-B

Majorana Fermions and Topology in Superconductors

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Symmetry protected topological superfluid³He-B