Higher-order topological superconductivity of spin-polarized fermions

Ahn, Junyeong; Yang, Bohm‐Jung

doi:10.1103/physrevresearch.2.012060

Cited by 71 publications

(25 citation statements)

References 72 publications

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“…We remark that alternative formulas relating the signs of the pairing order parameters on different Fermi surfaces and topological invariants also exist in the literature, but this approach requires more detailed knowledge on the system than just the symmetry representations (24). Furthermore, the extension of these formulas for other crystalline and higher-order TSCs has only been achieved for specific examples (25)(26)(27).…”

Section: Introductionmentioning

confidence: 99%

Refined symmetry indicators for topological superconductors in all space groups

Ono

Watanabe

2020

Sci. Adv.

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Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing fourfold symmetric superconductors with or without inversion symmetry and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.

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Section: Introductionmentioning

confidence: 99%

Refined symmetry indicators for topological superconductors in all space groups

Ono

Watanabe

2020

Sci. Adv.

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“…In particular, a 2D second-order topological superconductor (SOTSC) hosts MBSs at the corners of a rectangular sample. [189][190][191][192][193][194][195][196][197][198][199][200][201][202][203][204][205] One particular way to obtain such Majorana corner states is to start from a conventional (first-order) TI or TSC with helical edge states, which are then perturbatively gapped out by small additional terms. Depending on the symmetries of the model as well as the sample geometry, the gap acquired by the edge states is not necessarily of the same size or type for different edges.…”

Section: Majorana Corner Statesmentioning

confidence: 99%

Majorana bound states in semiconducting nanostructures

Laubscher,

Klinovaja

2021

Preprint

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In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple 'minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional s-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students-both theorists and experimentalists-seeking to familiarize themselves with some of the basic concepts in the field.

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“…Superconductors with odd-parity pairing (Yan 2019) can be used, too. Here, the early ideas about the first-order topological superconductivity with oddparity pairing (Sato 2009, Sato 2010, Fu & Berg 2010 have been generalized to higher-order topology (Ahn & Yang 2020). For instance, a second-order topological superconducting phase arises when the (p x + ip y )wave pairing is induced in a Dirac semimetal (Wang, Lin & Hughes 2018); a two-dimensional (p x + iσp y )wave superconductor is transformed into a secondorder topological superconductor hosting Majorana corner modes upon applying an in-plane magnetic field (Zhu 2018).…”

Section: Topological Superconductivity In Other Helical Systemsmentioning

confidence: 99%

Helical Liquids in Semiconductors

Hsu,

Stano,

Klinovaja

et al. 2021

Preprint

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One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator, also known as a two-dimensional topological insulator, and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in semiconductors. Our focus is on the theory, though we confront it with existing experiments. We discuss various aspects of the helical states, such as their realization, topological protection and stability, or possible experimental characterization. We lay emphasis on the hallmark of these states, being the prediction of a quantized electrical conductance. Since so far reaching a well-quantized conductance remained challenging experimentally, a large part of the review is a discussion of various backscattering mechanisms which have been invoked to explain this discrepancy. Finally, we include topics related to proximity-induced topological superconductivity in helical states, as an exciting application towards topological quantum computation with the resulting Majorana bound states.

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Higher-order topological superconductivity of spin-polarized fermions

Cited by 71 publications

References 72 publications

Refined symmetry indicators for topological superconductors in all space groups

Refined symmetry indicators for topological superconductors in all space groups

Majorana bound states in semiconducting nanostructures

Helical Liquids in Semiconductors

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