Majorana corner flat bands in two-dimensional second-order topological superconductors

Kheirkhah, Majid; Nagai, Yuki; Chen, Chun; Marsiglio, F.

doi:10.1103/physrevb.101.104502

Cited by 31 publications

(8 citation statements)

References 60 publications

(65 reference statements)

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“…Exploiting the high critical temperature of the parent superconductor and quantum spin Hall state in, for instance, WTe 2 monolayer, this setup provides a high-temperature platform for Kramers pairs of MBS at the corners of the two-dimensional structure (Yan et al 2018, Wang, Liu, Lu & Zhang 2018. Upon confinement, this setting can form flat bands of Majorana corner modes with a harmonic trapping potential (Kheirkhah et al 2020). Alternatively, Majorana corner modes can be induced using a two-dimensional magnetic topological insulator proximitized by either d x 2 −y 2 -wave or s ± -wave superconductors (Liu et al 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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Section: Topological Superconductivity In Other Helical Systemsmentioning

confidence: 99%

Helical Liquids in Semiconductors

Hsu,

Stano,

Klinovaja

et al. 2021

Preprint

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“…SOTIs have been realized in various experiments, most notably in artificial settings such as mechanical [21], electrical [22], microwave [23], and photonic [24] devices, but they have also been shown to occur in Nature [25]. A similar phenomenology has been predicted to occur in non-Hermitian systems [26], topological superconductors [27][28][29][30][31][32] and QSLs [33]. In the latter two, corner states can be Majorana particles.…”

mentioning

confidence: 94%

Majorana edge and corner states in square and kagome quantum spin- 32 liquids

Wang

Principi

2021

Phys. Rev. B

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Quantum spin liquids hosting Majorana excitations have recently experienced renewed interest for potential applications to topological quantum computation. Performing logical operations with reduced poisoning requires to localize such quasiparticles at specific point of the system, with energies that are well defined and inside the bulk energy gap. These are two defining features of second order topological insulators (SOTIs). Here, we show two spin models that support quantum spin liquid phases characterised by Majorana excitations and that behave as SOTIs, one of which is analytically solvable thanks to a theorem by Lieb. We show that, depending on the values of spin couplings, it is possible to localize either fermions or Majorana particles at their corners.

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“…Up to now, several interesting ideas have been proposed to realize 2D second-order TSCs in various different settings, such as using the superconducting proximity effect on quantum Hall insulators [14], quantum spin Hall insulators [12,15,16], second-order TSCs [17], Rashba semiconductors [18] and nanowires [19]; breaking time reversal symmetry of TSCs with helical Majorana edge states by applying external magnetic field [8,[20][21][22][23] or attaching antiferromagnets [24]; and some other ideas [12,22,[25][26][27]. In 3D, on the other hand, there are only few mechanisms proposed for realizing a third-order TSC such as applying magnetic field to a 3D second-order TSC with helical hinge modes [8].…”

mentioning

confidence: 99%

Higher-order topological superconductivity of spin-polarized fermions

Ahn

Yang

2020

Phys. Rev. Research

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We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. Here, we derive generalized parity formulae for the topological invariants characterizing higherorder topology of centrosymmetric superconductors. Based on the formulae, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal line semimetals generates a nodal line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up a new avenue for future topological quantum computations using Majorana zero modes. arXiv:1906.02709v2 [cond-mat.mes-hall]

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Majorana corner flat bands in two-dimensional second-order topological superconductors

Cited by 31 publications

References 60 publications

Helical Liquids in Semiconductors

Helical Liquids in Semiconductors

Majorana edge and corner states in square and kagome quantum spin- 32 liquids

Higher-order topological superconductivity of spin-polarized fermions

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