Absence of the Aharonov-Bohm effect of chiral Majorana fermion edge states

Park, Sunghun; Moore, Joel E.; Sim, Hyun Sub

doi:10.1103/physrevb.89.161408

Cited by 13 publications

(11 citation statements)

References 37 publications

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“…The factor Φ B 2π in (56) is the magnetic field inside the solenoid, while the change of signs in front the δ-function when passing from H′ − to H′ + , shows that the system is a topological invariant (for a study from a different point of view see for example [23,24]). The complete solution of the problem is the superposition of different n (±) , that is, different winding numbers for spin components up and down.…”

Section: Let Us Consider First the H′mentioning

confidence: 99%

Topological Insulators Quantum Mechanics

Gamboa¹,

Méndez²

2021

Preprint

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Topological insulators in three dimensions are studied as a problem of supersymmetric quantum mechanics. The spin-orbit coupling is induced as a consequence of the supersymmetrization procedure and we show that it is equivalent to the appearance of a SU (2) connection. The procedure presented in this letter is general and valid for any three-dimensional quantum system. The approach allows -in principle-to study a wide range of topological insulators as standard quantum mechanical problems. As an illustration the three-dimensional harmonic oscillator and the Aharonov-Bohm effect are studied in detail.

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Section: Let Us Consider First the H′mentioning

confidence: 99%

Topological Insulators Quantum Mechanics

Gamboa¹,

Méndez²

2021

Preprint

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“…A comprehensive theoretical scheme of low-energy electric transport for a Coulomb-Majorana junction was put forward by Zazunov et al, they obtained the general Keldysh functional integral formulas and provided the detailed analysis of the current-voltage relation under weak Coulomb blockade regime [28]. One theoretically explored an interferometry of a chiral Majorana edge channel formed at the interface between a superconductor and a topological insulator under an external magnetic field, quantum-transport properties can manifest the obvious signatures of Majorana modes [29]. Since quantum dots(QDs) as the artificial granules can provide an excellent model system to study quantum transport behaviors, very recently, the searches for Majorana quasi-particles have become a focus of intense attention based on the granular QD devices [20,[31][32][33][34].…”

Section: Introductionmentioning

confidence: 98%

Detecting the existence of Majorana fermions via the Dicke-like effect in a triple quantum-dot system

Zhang

Duan

et al. 2015

Physica B: Condensed Matter

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“…As shown in ref. [21], the chiral Majorana mode existing within the zeroth LL at q = 0 for TIs does not exist for graphene. However, we expect the neutral fermionic edge mode predicted here (for q = 0) to survive in graphene.…”

mentioning

confidence: 93%

Neutral edge modes in a superconductor–topological-insulator hybrid structure in a perpendicular magnetic field

Tiwari

Zülicke

Bruder

et al. 2014

EPL

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PACS 73.20.At -Surface states, band structure, electron density of states PACS 73.25.+i -Surface conductivity and carrier phenomena PACS 74.45.+c -Proximity effects; Andreev effect; SN and SNS junctions Abstract -We study the low-energy edge states of a superconductor -3D topological-insulator hybrid structure (NS junction) in the presence of a perpendicular magnetic field. The hybridization of electron-like and hole-like Landau levels due to Andreev reflection gives rise to chiral edge states within each Landau level. We show that by changing the chemical potential of the superconductor, this junction can be placed in a regime where the sign of the effective charge of the edge state within the zeroth Landau level changes more than once resulting in neutral edge modes with a finite value of the guiding-center coordinate. The appearance of these neutral edge modes is related to the level repulsion between the zeroth and the first Landau levels in the spectra. We also find that these neutral edge modes come in pairs, one in the zeroth Landau level and its corresponding pair in the first. Unlike ordinary neutral bogolon excitations in superconductors, the neutral modes found by us have a finite speed and, thus, the potential to carry a heat current.Introduction. -The integer quantum Hall (QH) state [1] represented the first example of a many-body state whose nontrivial properties do not stem from a spontaneously-broken symmetry, but rather its topological character [2]. The precise quantisation of the Hall conductance in integer multiples of e 2 /h was initially studied using a two-dimensional electron gas at a low temperature and in a strong perpendicular magnetic field, receiving a renewed attention with the discovery of graphene and its peculiar Dirac-like energy spectrum [3,4]. At the heart of transport in integer-QH systems -which based on their energy spectra could be expected to be insulating if the chemical potential lies in the gap between the neighbouring Landau levels (LLs) -is the existence of edge states. These LLs acquire dispersion as the guiding centers approach the physical edges of the sample (Hall bar), which gives rise to a current along the edges. The net current, resulting from a voltage (or chemical potential) drop in the direction perpendicular to the Hall-bar edges, is determined by the number of edge channels, i.e., of LLs occupied in the bulk.

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Absence of the Aharonov-Bohm effect of chiral Majorana fermion edge states

Cited by 13 publications

References 37 publications

Topological Insulators Quantum Mechanics

Topological Insulators Quantum Mechanics

Detecting the existence of Majorana fermions via the Dicke-like effect in a triple quantum-dot system

Neutral edge modes in a superconductor–topological-insulator hybrid structure in a perpendicular magnetic field

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