Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields

Marra, Pasquale; Inotani, Daisuke; Nitta, Muneto

doi:10.48550/arxiv.2106.09047

Cited by 3 publications

(3 citation statements)

References 109 publications

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“…Following references [127,128] we define the Majorana pseudospin operator T = τ /2 as the analogous of the spin operator S = σ/2. The expectation values of the Majorana pseudospin are given by T(x) = ψ(x)|T|ψ(x) with Cartesian components given by…”

Section: Majorana Pseudospinmentioning

confidence: 99%

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Marra

Nigro

2022

J. Phys.: Condens. Matter

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Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: Indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.

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Section: Majorana Pseudospinmentioning

confidence: 99%

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Marra

Nigro

2022

J. Phys.: Condens. Matter

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“…Therefore they may be considered as spin-locked 1D excitations. If they open a superconducting gap originating from the proximity effect of a superconducting substrate it is natural to expect [30][31][32][33][34][35][36] the possible creation of Majorana zero modes (MZM) at the end of the step line which would lead to a zero-bias conductance peak in transport and tunneling experiments [27,37,38]. Due to the locking of opposite spins in the helical state an underlying conventional singlet or s-wave superconductor with gap ∆ 0 may be used instead of the difficult to realize p-wave superconductor necessary in spinless models [25,30,36].…”

Section: Majorana Zero Modes In the Sc Proximity Induced Gap Of 1d St...mentioning

confidence: 99%

Surface step states and Majorana end states in profiled topological insulator thin films

Thalmeier,

Akbari

2021

Preprint

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The protected helical surface states in thin films of topological insulators (TI) are subject to inter-surface hybridisation. This leads to gap opening and spin texture changes as witnessed in photoemission and quasiparticle interference investigations. Theoretical studies show that universally the hybridisation energy exhibits exponential decay as well as sign oscillations as function of film thickness, depending on the effective band parameters of the material. When a step is introduced in the TI film e.g. by profiling the substrate such that the hybridisation has different signs on both sides of the step, 1D bound states appear within the hybridisation gap which decay exponentially with distance from the step. The step bound states have linear dispersion and inherit the helical spin locking from the surface states and are therefore non-degenerate. When the substrate becomes an s-wave superconductor Majorana zero modes located at the step ends are created inside the superconducting gap. The proposed scenario involves just a suitably stepped interface of superconductor and TI and therefore may be a most simple device being able to host Majorana zero modes.

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“…Under the influence of these magnetic fields and the phase-biased superconducting proximity effect, the chiral edge modes transform into a massive Majorana particle [38,49], which leads to Majorana zero modes (MZMs) at the edges of the system or at mass domain walls. Our analysis identifies the parameter regime in which such a pyramidal SC/CI/SC structure behaves as a MZM track.…”

Section: Introductionmentioning

confidence: 99%

Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids

Wang,

Zhou,

Kotetes

2021

Preprint

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Recent experiments have provided evidence for chiral charge order in Kagome superconductors (SCs). This intriguing possibility motivates us to unveil the first pathway to engineer topological superconductivity by harnessing the interplay of charge Chern insulators (CIs) and conventional SCs. We here identify under which conditions a pyramidal SC/CI/SC heterostructure induces an effective 1D spinless p-wave SC that allows pinning Majorana zero modes (MZMs) at termination edges and domain walls. As we reveal, such a MZM track is controlled by the phase difference of the two SCs involved and additional magnetic fields which are required for generating Rashba-like spin-orbit coupling. Further, we show that a SC/CI/SC/CI/SC double-pyramidal hybrid defines a double MZM track, in which braiding occurs by varying the two superconducting phase differences in space and adiabatically in time. Given the geometry of the MZM racetrack, we propose to employ the time-averaged quadrupolar differential conductance to confirm the here-termed MZM track exchange process which is pivotal for braiding. In addition, we identify experimental knobs which enable the fusion of MZM pairs, and the detection of the underlying non-Abelian topological order and twofold many-body ground state degeneracy by encoding it in a topological invariant.

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Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields

Cited by 3 publications

References 109 publications

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Surface step states and Majorana end states in profiled topological insulator thin films

Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids

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