A solid case for Majorana fermions

Reich, Eugenie Samuel

doi:10.1038/483132a

Cited by 19 publications

(9 citation statements)

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“…Majorana zero-energy modes (MZMs) have recently attracted enormous theoretical and experimental attention [1][2][3][4] due to their exotic non-Abelian braiding statistics [5][6][7] and potential application to fault-tolerant topological quantum computation [8]. A large number of theoretical proposals has been put forward to realize MZMs in topological superconductors (TSCs) [9][10][11][12][13][14][15][16][17], see also reviews [4,18,19] for more details.…”

Section: Introductionmentioning

confidence: 99%

Majorana zero modes choose Euler numbers as revealed by full counting statistics

2015

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We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly, the full counting statistics is qualitatively different in the presence of the Majorana coupling.

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Section: Introductionmentioning

confidence: 99%

Majorana zero modes choose Euler numbers as revealed by full counting statistics

2015

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“…Introduction. The search for topological superconductors hosting non-Abelian quasiparticles (defects binding Majorana zero modes) has become an active and exciting pursuit in condensed matter physics [1][2][3]. There has been enormous theoretical and experimental activity in this direction recently [4] fueled, in part, by the potential application of topological superconductors for the faulttolerant topological quantum computation schemes [5].…”

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confidence: 99%

Probing Majorana physics in quantum-dot shot-noise experiments

2015

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We consider a quantum dot coupled to a topological superconductor and two normal leads and study transport properties of the system. Using Keldysh path-integral approach, we study current fluctuations (shot noise) within the low-energy effective theory. We argue that the combination of the tunneling conductance and the shot noise through a quantum dot allows one to distinguish between the topological (Majorana) and non-topological (e.g., Kondo) origin of the zero-bias conduction peak. Specifically, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or Kondo physics, the shot noise is qualitatively different in the presence of Majorana zero modes.PACS numbers: 73.21. Hb, 71.10.Pm, 74.78.Fk, 72.70.+m Introduction. The search for topological superconductors hosting non-Abelian quasiparticles (defects binding Majorana zero modes) has become an active and exciting pursuit in condensed matter physics [1][2][3]. There has been enormous theoretical and experimental activity in this direction recently [4] fueled, in part, by the potential application of topological superconductors for the faulttolerant topological quantum computation schemes [5]. A large number of theoretical proposals for engineering topological superconductors in the laboratory has been put forward [6][7][8][9][10][11][12][13][14][15], and there has been a significant amount of experimental activity in this area recently [16][17][18][19][20][21][22][23][24][25]. One of the simplest ways to detect the presence of Majorana zero modes (MZMs) in topological superconductors (TSC) is tunneling spectroscopy. Indeed, the presence of MZMs leads to a quantized zero-bias conductance G = 2e 2 /h [26-33]. The pioneering Majorana experiment based on a semiconductor/superconductor heterostructure proposal [10,11] was performed in Delft [16] where the observation of zero-bias peak in a finite magnetic field was reported, consistent with the theoretical predictions [31]. However, other effects might also lead to the zero-bias anomaly which spurred the debate [34][35][36][37][38][39][40][41] as to the precise origin of the (un-quantized) zerobias conduction peak observed in recent tunneling experiments [16][17][18][19][20][21]. Therefore, additional experiments testing other properties on MZMs [17,36,37,[42][43][44][45][46][47][48][49][50][51][52][53][54] are necessary in order to reach a consensus.

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“…The search for solid state Majorana modes, which are localized quasiparticles with non-Abelian braiding statistics and a direct realization of the Majorana operator, has created a great deal of recent interest in the whole physics community, 6 partly because of the great mystique associated with Majorana and partly because of the prospects for topological quantum computation using solid state Majorana quasiparticles. The most experimentally promising among the many theoretical proposals for solid state Majorana fermions is the semiconductor-superconductor hybrid structures [2][3][4][5] where the ordinary s-wave superconducting proximity effect induced in the semiconductor is modified by the intrinsic spin-orbit coupling in the semiconductor and an externally applied Zeeman spin splitting.…”

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confidence: 99%

Zero-bias conductance peak in Majorana wires made of semiconductor/superconductor hybrid structures

Lin

Sau²,

Sarma³

2012

Phys. Rev. B

111

125

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Motivated by a recent experimental report Mourik et al. [Science 336, 1003] claiming the likely observation of the Majorana mode in a semiconductor-superconductor hybrid structure, we study theoretically the dependence of the zero-bias conductance peak associated with the zero-energy Majorana mode in the topological superconducting phase as a function of temperature, tunnel barrier potential, and a magnetic field tilted from the direction of the wire for realistic wires of finite lengths. We find that higher temperatures and tunnel barriers as well as a large magnetic field in the direction transverse to the wire length could very strongly suppress the zero-bias conductance peak as observed in recent experiments. We also show that a strong magnetic field along the wire could eventually lead to the splitting of the zero bias peak into a doublet with the doublet energy splitting oscillating as a function of increasing magnetic field. Our results based on the standard theory of topological superconductivity in a semiconductor hybrid structure in the presence of proximity-induced superconductivity, spin-orbit coupling, and Zeeman splitting show that the recently reported experimental data are generally consistent with the existing theory that led to the predictions for the existence of the Majorana modes in the semiconductor hybrid structures in spite of some apparent anomalies in the experimental observations at first sight. We also make a prediction for the future observation of Majorana splitting in finite wires used in the experiments.

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A solid case for Majorana fermions

Cited by 19 publications

References 1 publication

Majorana zero modes choose Euler numbers as revealed by full counting statistics

Majorana zero modes choose Euler numbers as revealed by full counting statistics

Probing Majorana physics in quantum-dot shot-noise experiments

Zero-bias conductance peak in Majorana wires made of semiconductor/superconductor hybrid structures

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