Quantized Conductance at the Majorana Phase Transition in a Disordered Superconducting Wire

Akhmerov, A. R.; Dahlhaus, J. P.; Hassler, Fabian; Wimmer, Michael; Beenakker, C. W. J.

doi:10.1103/physrevlett.106.057001

Cited by 322 publications

(379 citation statements)

References 37 publications

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“…(14) and calculate the average |I (ω)| 2 where the average is taken with respect to random realizations of n(t) according to Eqs. (16) and (17). In Fig.…”

Section: Finite-t Crossover In Supercurrent Responsementioning

confidence: 99%

“…(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%

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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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“…(14) and calculate the average |I (ω)| 2 where the average is taken with respect to random realizations of n(t) according to Eqs. (16) and (17). In Fig.…”

Section: Finite-t Crossover In Supercurrent Responsementioning

confidence: 99%

Section: Hamiltonian Tqcp and Phase Diagram At Finite Temperaturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Tewari

Scarola

et al. 2012

Phys. Rev. B

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“…However, conductivity enhancement near zero bias can also be a signature of diverse phenomena in mesoscopic physics, such as the Kondo effect in quantum dots [26,27] or the "0.7 anomaly" in nanowires [28,29]. Fusion of two Majorana modes produces an ordinary fermion and, uniquely to Majorana particles, modifies periodicity of the Josephson relation from 2π (Cooper pairs) to 4π (Majorana particles) [1,4,[30][31][32]. In the dc Josephson effect, fluctuations between filled and empty Majorana modes will mask the 4π periodicity and, indeed, we observe only 2π periodicity in a dc SQUID configuration.…”

mentioning

confidence: 99%

The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles

Rokhinson¹,

2012

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Topological superconductors which support Majorana fermions are thought to be realized in one-dimensional semiconducting wires coupled to a superconductor [1][2][3]. Such excitations are expected to exhibit non-Abelian statistics and can be used to realize quantum gates that are topologically protected from local sources of decoherence [4,5]. Here we report the observation of the fractional a.c. Josephson effect in a hybrid semiconductor/superconductor InSb/Nb nanowire junction, a hallmark of topological matter. When the junction is irradiated with a radio-frequency f 0 in the absence of an external magnetic field, quantized voltage steps (Shapiro steps) with a height ∆V = hf 0 /2e are observed, as is expected for conventional superconductor junctions, where the supercurrent is carried by charge-2e Cooper pairs. At high magnetic fields the height of the first Shapiro step is doubled to hf 0 /e, suggesting that the supercurrent is carried by charge-e quasiparticles. This is a unique signature of Majorana fermions, elusive particles predicted ca. 80 years ago [6].In 1928 Dirac reconciled quantum mechanics and special relativity in a set of coupled equations, which became the cornerstone of quantum mechanics [7]. Its main prediction that every elementary particle has a complex conjugate counterpart -an antiparticle -has been confirmed by numerous experiments. A decade later Majorana showed that Dirac's equation for spin-1/2 particles can be modified to permit real wavefunctions [6,8]. The complex conjugate of a real number is the number itself, which means that such particles are their own antiparticles. While the search for Majorana fermions among elementary particles is ongoing [9], excitations with similar properties may emerge in electronic systems [4], and are predicted to be present in some unconventional states of matter [10][11][12][13][14][15].Ordinary spin-1/2 particles or excitations carry a charge, and thus cannot be their own antiparticles. In a superconductor, however, free charges are screened, and charge-less spin-1/2 excitations become possible. The BCS theory allows fermionic excitations which are a mixture of electron and hole creation operators, γ i = c † i + c i . This creation operator is invariant with respect to charge conjugation, c † i ↔ c i . If the energy of an excitation created in this way is zero, the excitation will be a Majorana particle. However, such zero-energy modes are not permitted in ordinary s-wave superconductors.The current work is inspired by the paper of Sau et al.[15] who predicted that Majorana fermions can be formed in a coupled semiconductor/superconductor system. Superconductivity can be induced in a semiconductor material by the proximity effect. At zero magnetic field electronic states are doubly-degenerate and Majorana modes are not supported. In semiconductors with strong spin-orbit (SO) interactions the two spin branches are separated in momentum space, but SO interactions do not lift the Kramer's degeneracy. However, in * To whom correspondence should be addre...

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“…Recently, systems equivalent to 1D p-wave superconductors have been proposed based on proximity effects in 2D topological insulators 9,10 , or even more close to experimental reality, in 1D semiconducting quantum wires [11][12][13] . To detect MBSs in these systems 14,15 , and possibly to manipulate the MFs therein, is of great interest in current research [16][17][18] . 2D chiral p-wave superconductors 2 , and equivalent systems based on the proximity effect in topological insulators 19,20 or semiconductors 11 , are hosts for chiral Majorana modes (χMMs), which are gapless, charge-neutral edge excitations.…”

Section: Introductionmentioning

confidence: 99%

Scattering theory of chiral Majorana fermion interferometry

Li¹,

Fleury²,

Büttiker³

2012

Phys. Rev. B

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Using scattering theory, we investigate interferometers composed of chiral Majorana fermion modes coupled to normal metal leads. We advance an approach in which also the basis states in the normal leads are written in terms of Majorana modes. Thus each pair of electron-hole states is associated with a pair of Majorana modes. Only one lead Majorana mode couples to the intrinsic Majorana mode whereas its partner is completely reflected. Similarly the remaining Majorana modes are completely reflected but in general mix pair-wise. We demonstrate that the charge current can also be expressed in terms of interference between pairs of Majorana modes. These two basic facts permit a treatment and understanding of current and noise signatures of chiral Majorana fermion interferometry in an especially elegant way. As a particular example of applications, in FabryPerot-type interferometers where chiral Majorana modes form loops, resonances (anti-resonances) from such loops always lead to peaked (suppressed) Andreev differential conductances, and negative (positive) cross-correlations that originate purely from two-Majorana-fermion exchange. These investigations are intimately related to current and noise signatures of Majorana bound states.

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Quantized Conductance at the Majorana Phase Transition in a Disordered Superconducting Wire

Cited by 322 publications

References 37 publications

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles

Scattering theory of chiral Majorana fermion interferometry

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