Andreev Reflection at High Magnetic Fields: Evidence for Electron and Hole Transport in Edge States

Eroms, Jonathan; Weiss, Dieter; Boeck, J. De; Borghs, Gustaaf; Zülicke, U.

doi:10.1103/physrevlett.95.107001

Cited by 57 publications

(62 citation statements)

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“…The setup we propose here differs in one essential aspect: before reaching the beam splitter, the electrons are partially Andreev reflected at a superconducting electrode. Andreev reflection in the quantum Hall effect regime has been reported in InAs quantum wells [32,33] and in graphene monolayers [34][35][36]. In graphene, which has small spinorbit coupling, the Andreev reflected hole is in the opposite spin band as the electron (spin-singlet pairing).…”

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Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

Beenakker

2014

Phys. Rev. Lett.

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The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a 1 AE cos ϕ dependence on the phase difference ϕ of the superconductors from which the excitations originated (with the AE sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent. DOI: 10.1103/PhysRevLett.112.070604 PACS numbers: 05.60.Gg, 03.75.Lm, 74.45.+c, 74.78.Na Condensed matter analogies of concepts from particle physics are a source of much inspiration, and many of these involve superconductors or superfluids [1]. Majorana's old idea [2] that a spin-1=2 particle (such as a neutrino) might be its own antiparticle has returned [3] in the context of low-dimensional superconductors, inspiring an intense theoretical and experimental search for condensed matter realizations of Majorana fermions [4]. The search has concentrated on Majorana zero modes [5][6][7]-midgap states (at the Fermi level E ¼ 0) bound to a defect in a superconductor with broken spin-rotation and time-reversal symmetry (a so-called topological superconductor [8,9]). The name Majorana zero mode (or Majorino [10]) is preferred over Majorana fermion, since they are not fermions at all but have a non-Abelian exchange statistics [11].Majorana fermions, in the original sense of the word, do exist in superconductors. In fact they are ubiquitous: the time-dependent four-component Bogoliubov-de Gennes wave equation for quasiparticle excitations (so-called Bogoliubov quasiparticles) can be brought to a real form by a 4 × 4 unitary transformation U [12], in direct analogy to the real Eddington-Majorana wave equation of particle physics [2,13]. A real wave equation implies the linear relation Ψ † ðr; tÞ ¼ UΨðr; tÞ between the particle and antiparticle field operators, which is the hallmark of a Majorana fermion. As argued forcefully by Chamon et al. [14], fermionic statistics plus superconductivity by itself produces Majorana fermions, irrespective of considerations of dimensionality, topology, or broken symmetries.Here we propose an experiment to probe the Majorana nature of Bogoliubov quasiparticles in conventional, nontopological, superconductors. Existing proposals apply to topological superconductors [15][16][17][18][19][20][21][22][23][24][25], where Majorana fermions appear as charge-neutral edge states with a distinct signature in DC transport experiments. In contrast, the Bogoliubov quasiparticles of a nontopological superconductor have charge expectation valueq ≠ 0, so their Majorana nature remains hidden in the energy domain probed by DC transport.It is in the time domain that the wave equation takes on a real form and that particle and antiparticle operators are linearly related. We will show that...

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Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

Beenakker

2014

Phys. Rev. Lett.

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“…3,4 Weak links formed by a two-dimensional ͑2D͒ electron gas ͑2DEG͒ in semiconductor quantum wells 5 are of particular interest because here the ballistic transport can be studied. In very high magnetic field perpendicular to the 2DEG, theory 6 and experiments 7,8 have demonstrated Andreev transport via edge states. Indirect evidence for a strong magneticfield effect on AR was experimentally found in antidot billiards.…”

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“…The electron density was 7.8ϫ 10 15 m −2 , resulting in a Fermi wavelength F =2 / k F = 28 nm. 7 First, a constriction of width W with a four-terminal ͑4t͒ lead struc- …”

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Doppler shift in Andreev reflection from a moving superconducting condensate in Nb/InAs Josephson junctions

et al. 2009

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We study narrow ballistic Josephson weak links in a InAs quantum wells contacted by Nb electrodes and find a dramatic magnetic-field suppression of the Andreev reflection amplitude, which occurs even for in-plane field orientation with essentially no magnetic flux through the junction. Our observations demonstrate the presence of a Doppler shift in the energy of the Andreev levels, which results from diamagnetic screening currents in the hybrid Nb/InAs banks. The data for conductance, excess, and critical currents can be consistently explained in terms of the sample geometry and the McMillan energy, characterizing the transparency of the Nb/InAs interface. DOI: 10.1103/PhysRevB.80.220507 PACS number͑s͒: 74.45.ϩc In recent years a detailed microscopic understanding of the proximity effect has emerged. There is now agreement that in highly transparent Josephson junctions formed by a metallic weak link in good contact with two superconducting ͑SC͒ banks the supercurrent is carried by Andreev bound states ͑ABSs͒. 1 These come in pairs corresponding to the opposite directions of Cooper-pair transfer mediated by multiple Andreev reflection ͑MAR͒ at the SC/metal interfaces provided that the acquired quasiparticle phase is a multiple of 2 . 2 At currents exceeding the critical current I C ͑T , B͒ MAR between the SC banks manifests itself in the currentvoltage characteristics as subharmonic gap structures at voltages eV n =2⌬ / n, where ⌬ is the SC energy gap and n =1,2,.... At higher voltage eV ӷ 2⌬, I͑V͒ becomes linear with an excess current I exc = I͑V͒ − G N V determined by a single Andreev reflection ͑AR͒ probability ͉a͑ ͉͒ 2 ͑G N is the normal-state conductance͒. 3,4 Weak links formed by a two-dimensional ͑2D͒ electron gas ͑2DEG͒ in semiconductor quantum wells 5 are of particular interest because here the ballistic transport can be studied. In very high magnetic field perpendicular to the 2DEG, theory 6 and experiments 7,8 have demonstrated Andreev transport via edge states. Indirect evidence for a strong magneticfield effect on AR was experimentally found in antidot billiards. 9 The case of parallel field, with respect to the 2DEG, is equally intriguing: as ideally no magnetic flux threads the 2DEG, one may naively expect the Josephson current to survive up to the critical fields of the SC leads. This is not the case, but the underlying mechanism of the supercurrent suppression is still unclear. This question, also relevant for other 2D hybrid systems, 10 is among the issues this Rapid Communication focuses on.In this Rapid Communication, Nb/InAs Josephson junctions of different width are studied in a four-terminal lead configuration within the 2DEG. This allows us to separately determine the transparencies of the InAs weak link and Nb/ InAs interfaces and identify an additional energy scale in the electronic spectrum of the hybrid SC terminals. We observe a very strong suppression of both the AR probability and supercurrent in weak magnetic fields of 4 and 100 mT for perpendicular and parallel orientations, r...

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“…In addition, the high carrier mobility attainable in semiconductors in combination with the phase-coherent Andreev reflection leads to novel unique phenomena in the magnetotransport. [5][6][7] Usually for these devices the semiconductor is patterned by conventional lithography. As an elegant alternative one can also directly create semiconductor nanostructures, i.e.…”

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Josephson supercurrent in Nb/InN-nanowire/Nb junctions

Frielinghaus

Batov

Weides

et al. 2010

Applied Physics Letters

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We experimentally studied the Josephson supercurrent in Nb/InN-nanowire/Nb junctions. Large critical currents up to 5.7 µA have been achieved, which proves the good coupling of the nanowire to the superconductor. The effect of a magnetic field perpendicular to the plane of the Josephson junction on the critical current has been studied. The observed monotonous decrease of the critical current with magnetic field is explained by the magnetic pair-breaking effect in planar Josephson junctions of ultra-narrow width [J. C. Cuevas and F. S. Bergeret, Phys. Rev. Lett. 99, 217002 (2007)] Superconductor/normal-conductor/superconductor (SNS) junctions with a semiconductor employed as the N-weak link material offer the great advantage that here the Josephson supercurrent can be controlled by means of the field effect. 1,2 Gate-controlled superconductor/semiconductor hybrid devices such as superconducting field effect transistors 3 or split-gate structures 4 have been fabricated which find no counterpart in conventional SNS structures. In addition, the high carrier mobility attainable in semiconductors in combination with the phase-coherent Andreev reflection leads to novel unique phenomena in the magnetotransport. 5-7 Usually for these devices the semiconductor is patterned by conventional lithography. As an elegant alternative one can also directly create semiconductor nanostructures, i.e. nanowires, by epitaxial growth. 8 By using InAs nanowires connected to superconducting electrodes tunable Josephson supercurrents, supercurrent reversal, and Kondo-enhanced Andreev tunneling have been realized. [9][10][11] Among the various materials used for semiconductor nanowires InN is of particular interest for semiconductor/superconductor hybrid structures, since the surface accumulation layer in InN can provide a sufficiently low resistive contact to superconducting electrodes. 12-14 Due to almost ideal crystalline properties of InN nanowires electronic transport along the wires, contacted by normal metal electrodes, shows quantization phenomena, i.e. flux periodic magnetoconductance oscillations. 15 Furthermore, the carrier concentration in the surface electron gas is of the order of 10 13 cm −2 and thus about a factor of ten larger than in InAs. Consequently when combined with superconducting electrodes one can expect low resistive SNS junctions.Here, we report on transport studies of Nb/InNnanowire/Nb junctions. We succeeded in observing a pronounced Josephson supercurrent and a relatively large I c R N product of up to 0.44 mV. The latter factor, the critical current times the normal resistance, is an important figure of merit for Josephson junctions. We devoted special attention to the dependence of the critical current I c on an external magnetic field B, where a monotonous decrease of I c with B was found. This experimental finding is interpreted in the framework of a recent theoretical model for the proximity effect in narrow-width junctions with dimensions comparable or smaller than the magnetic length ξ B = Φ 0 /B,...

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Andreev Reflection at High Magnetic Fields: Evidence for Electron and Hole Transport in Edge States

Cited by 57 publications

References 28 publications

Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

Doppler shift in Andreev reflection from a moving superconducting condensate in Nb/InAs Josephson junctions

Josephson supercurrent in Nb/InN-nanowire/Nb junctions

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