Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors

Sau, Jay D.; Tewari, Sumanta; Sarma, S. Das

doi:10.1103/physrevb.84.085109

Cited by 29 publications

(27 citation statements)

References 53 publications

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“…Once the presence of a robust zero energy mode is established, hence the necessary condition for the existence of the Majorana is realized, one must move on to establish the sufficient condition, which would obviously be a harder task. Several ideas for establishing definitively the existence of the Majorana mode (and its non-Abelian braiding statistics nature) have already been suggested in the literature, including experiments involving the fractional Josephson effect [11,14,33,37,78], the quantized differential conductance [76,79], and Majorana interferometry [80][81][82].…”

Section: Discussionmentioning

confidence: 99%

Majorana fermions in semiconductor nanowires

2011

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We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The non-trivial topological state corresponds to a superconducting phase supporting an odd number of pairs of Majorana modes localized at the ends of the wire, whereas the non-topological state corresponds to a superconducting phase with no Majoranas or with an even number of pairs of Majorana modes. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality, but also allows having higher carrier density in the nanowire. Consequently, multiband nanowires are better-suited for stabilizing the topological superconducting phase and for observing the Majorana physics. We present a detailed study of the parameter space for multiband semiconductor nanowires focusing on understanding the key experimental conditions required for the realization and detection of Majorana fermions in solid-state systems. We include various sources of disorder and characterize their effects on the stability of the topological phase. Finally, we calculate the local density of states as well as the differential tunneling conductance as functions of external parameters and predict the experimental signatures that would establish the existence of emergent Majorana zero-energy modes in solid-state systems.

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Section: Discussionmentioning

confidence: 99%

Majorana fermions in semiconductor nanowires

2011

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“…(1) has recently been studied extensively. [8][9][10][11][12][13][14][15][16][17][18][19][20] A TQCP exists in this system as the tuning parameter is varied through the critical value = c = 2 + μ 2 where the quantity C 0 = ( 2 + μ 2 − 2 ) changes sign. For C 0 > 0, the (low-) state is an ordinary, nontopological superconductor (NTS) with only perturbative effects from the Zeeman and spin-orbit couplings.…”

Section: Hamiltonian Tqcp and Phase Diagram At Finite Temperaturesmentioning

confidence: 99%

“…This system has recently been studied extensively after it was pointed out by Sau et al 8 that for greater than a critical value c this system supports novel non-Abelian topological states. [9][10][11][12][13][14][15][16][17][18][19][20] For > c , defects in the (proximity-induced) s-wave pair potential can support localized topological zero-energy excitations called Majorana fermions. Majorana fermions, with second-quantized operators γ satisfying γ † = γ , follow non-Abelian exchange statistics under pair-wise exchange of the coordinates.…”

Section: Introductionmentioning

confidence: 99%

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Tewari

Scarola

et al. 2012

Phys. Rev. B

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Quantum ground states on the nontrivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.

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“…The 1D electron-or holedoped wires in the TS state can be arranged in a quasi-1D network geometry 8 to test non-Abelian statistics 8 and perform topological quantum computation (TQC) 9,10 in the Bravyi-Kitaev (BK) scheme. 11 In principle, TQC in the BK scheme is also possible with the 2D semiconductor TS states using Majorana fermion interferometry 12 analogous to that in the ν = 5/2 fractional quantum Hall (FQH) states, 13 chiral p-wave superconductors, 14 and TS states on the surface of topological insulators. 15,16 Efforts to realize a semiconductor TS state with Majorana fermions in proximity to s-wave superconductors are currently underway in many laboratories world-wide, concentrating on both 1D semiconducting nanowires and 2D semiconductor heterostructures in close proximity to a regular bulk s-wave superconductor (e.g.…”

Section: Introductionmentioning

confidence: 99%

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

2012

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In proximity to an s-wave superconductor, a one-or two-dimensional, electron-or hole-doped semiconductor with a sizable spin-orbit coupling and a Zeeman splitting can support a topological superconducting (TS) state. The semiconductor TS state has Majorana fermions as localized zeroenergy excitations at order parameter defects such as vortices and sample edges. Here we examine the effects of quenched disorder from the semiconductor surface on the stability of the TS state in both electron-and hole-doped semiconductors. By considering the interplay of broken time reversal symmetry (due to Zeeman splitting) and disorder we derive an expression for the disorder suppression of the superconducting quasiparticle gap in the TS state. We conclude that the effects of disorder can be minimized by increasing the ratio of the spin-orbit energy with the Zeeman splitting. By giving explicit numbers we show that a stable TS state is possible in both electron-and holedoped semiconductors for experimentally realistic values of parameters. We discuss possible suitable semiconductor materials which should be the leading candidates for the Majorana search in solid state systems.

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Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors

Cited by 29 publications

References 53 publications

Majorana fermions in semiconductor nanowires

Majorana fermions in semiconductor nanowires

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

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