Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

Liu, Tao; He, James Jun; Nori, Franco

doi:10.1103/physrevb.98.245413

Cited by 169 publications

(99 citation statements)

References 77 publications

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“…Finally, the edge Hamiltonians are obtained by projecting the remaining parts of Eqs. (26) and (31) with the projectors formed of states we have found. We are interested in their zero-energy states that have to be of the same form if there exists a simultaneous eigenstate of both domain walls.…”

Section: Appendix 4: Proof That the Corner-localized Zero-energy Statmentioning

confidence: 83%

An anomalous higher-order topological insulator

2018

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Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. A new invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs. arXiv:1807.09050v2 [cond-mat.mes-hall]

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Section: Appendix 4: Proof That the Corner-localized Zero-energy Statmentioning

confidence: 83%

An anomalous higher-order topological insulator

2018

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“…This can be understood as a result of the reduction of |∆ R | by µ R , see Eq. (5). Strikingly, increasing µ R further, we observe a clear 0-π transition for the parameters satisfying inequality (8).…”

Section: Arxiv:190509308v1 [Cond-matsupr-con] 22 May 2019mentioning

confidence: 74%

“…Introduction.-The second-order topological superconductor (SOTS) is a novel topological phase of matter and features Majorana zero-dimensional (0D) corner or 1D hinge states which are two dimensions lower than the gapped bulk [1][2][3][4][5][6][7][8][9][10][11][12] and may provide stable qubits for topological quantum computation [13][14][15][16][17][18][19][20][21]. Recently, the SOTS has been discovered in a variety of realistic materials and triggered tremendous interest [3][4][5][6][7][8][9][10][22][23][24][25][26][27]. One way to mimic SOTSs in 2D is given by quantum spin Hall insulators (QSHIs) in proximity to unconventional superconductors with d x 2 −y 2 -wave or s ± -wave pairing order [3][4][5].…”

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confidence: 99%

Detection of second-order topological superconductors by Josephson junctions

Zhang

Trauzettel

2020

Phys. Rev. Research

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We study Josephson junctions based on a second-order topological superconductor (SOTS) which is realized in a quantum spin Hall insulator with a large inverted gap in proximity to an unconventional superconductor. We find that tuning the chemical potential in the superconductor strongly modifies the pairing gap of the helical edge states and leads to topological phase transitions. As a result, the supercurrent in the junction is controllable and a 0-π transition is realized by tuning the chemical potentials in the superconducting leads. These striking features are stable in junctions with different sizes, doping in the normal region, and in the presence of disorder. We propose them as novel experimental signatures of SOTSs. Moreover, the 0-π transition can serve as a fully electric way to create or annihilate Majorana bound states in the junction without magnetic manipulation.Introduction.-The second-order topological superconductor (SOTS) is a novel topological phase of matter and features Majorana zero-dimensional (0D) corner or 1D hinge states which are two dimensions lower than the gapped bulk [1-12] and may provide stable qubits for topological quantum computation [13][14][15][16][17][18][19][20][21]. Recently, the SOTS has been discovered in a variety of realistic materials and triggered tremendous interest [3][4][5][6][7][8][9][10][22][23][24][25][26][27]. One way to mimic SOTSs in 2D is given by quantum spin Hall insulators (QSHIs) in proximity to unconventional superconductors with d x 2 −y 2 -wave or s ± -wave pairing order [3][4][5]. The proximity effect of unconventional superconductivity in 2D systems has also been intensively explored in theory [28][29][30][31][32][33][34][35][36][37] and experiment [38][39][40][41][42][43]. To date, however, the only way proposed to detect 2D SOTSs is a tunneling experiment without a concrete calculation of the observable signature. An alternative or complementary approach to probe SOTSs and manipulate the Majorana corner modes is thus desirable. In QSHIs, a finite doping is usually inevitable, and the chemical potential can be far away from the Dirac points. Therefore, it is interesting and relevant to explore the influence of the chemical potential in SOTSs.

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“…In second-order TSCs these MZMs have been studied at the corners of a two-dimensional (2D) system and hinges of a three-dimensional (3D) system where neighboring hinges have different chiralities 27,28 . These zero-energy corner modes are known as Majorana corner states (MCSs) which have been studied in various kinds of system such as high-temperature superconductors (SCs) [29][30][31][32][33][34] , s-wave superfluid 28,35 , systems with an external magnetic field [36][37][38] , and 2D and 3D second-order TSCs 39 .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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In this paper we find that confining a second-order topological superconductor with a harmonic potential leads to a proliferation of Majorana corner modes. As a consequence, this results in the formation of Majorana corner flat bands which have a fundamentally different origin from that of the conventional mechanism. This is due to the fact that they arise solely from the one-dimensional gapped boundary states of the hybrid system that become gapless without the bulk gap closing under the increase of the trapping potential magnitude. The Majorana corner states are found to be robust against the strength of the harmonic trap and the transition from Majorana corner states to Majorana flat bands is merely a smooth crossover. As a harmonic trap can potentially be realized in heterostructures, this proposal paves a way to observe these Majorana corner flat bands in an experimental context.

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Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

Cited by 169 publications

References 77 publications

An anomalous higher-order topological insulator

An anomalous higher-order topological insulator

Detection of second-order topological superconductors by Josephson junctions

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

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