Hollow nanocylinder: Multisubband superconductivity induced by quantum confinement

Chen, Yajiang; Shanenko, A. A.; Peeters, F. M.

doi:10.1103/physrevb.81.134523

Cited by 26 publications

(41 citation statements)

References 41 publications

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“…The use of Anderson's recipe is well justified because (i) corrections were found to be less than a few percent for nanofilms (see, e.g., Ref. 15) and (ii) resulting equations are much easier for numerical implementation. In terms of the particleand hole-like amplitudes, the Anderson approximation reads…”

Section: Formalismmentioning

confidence: 99%

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Superconducting transition temperature of Pb nanofilms: Impact of thickness-dependent oscillations of the phonon-mediated electron-electron coupling

Chen¹,

Shanenko²,

Peeters³

2012

Phys. Rev. B

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To date, several experimental groups reported measurements of the thickness dependence of Tc of atomically uniform single-crystalline Pb nanofilms. The reported amplitude of the Tc-oscillations varies significantly from one experiment to another. Here we propose that the reason for this unresolved issue is an interplay of the quantum-size variations in the single-electron density of states with thickness-dependent oscillations in the phonon mediated electron-electron coupling. Such oscillations in the coupling depend on the substrate material, the quality of the interface, the protection cover and other details of the fabrication process, changing from one experiment to another. This explains why the available data do not exhibit one-voice consistency about the amplitude of the Tc-oscillations. Our analyses are based on a numerical solution of the Bogoliubovde Gennes equations for a superconducting slab.

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Section: Formalismmentioning

confidence: 99%

“…II A byḡ given by Eq. (15). It is worth noting that one should distinguish oscillations of g from those of the electron-phonon mass enhancement parameter λ.…”

Section: Formalismmentioning

confidence: 99%

Superconducting transition temperature of Pb nanofilms: Impact of thickness-dependent oscillations of the phonon-mediated electron-electron coupling

Chen¹,

Shanenko²,

Peeters³

2012

Phys. Rev. B

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“…2, is zero in the N -section, and so it does not mix the (n, l) states (see Ref. 34 ). In the S-sections, Cooper pairing generally mixes subbands with different radial quantum numbers p, but the orbital angular momentum number l remains a good quantum number 33 .…”

Section: B Andreev Bound Statesmentioning

confidence: 99%

“…The most general solutions u(r), v(r) to Eq. 3 are expansions over these single-particle solutions 33,34 . However, since ∆ * (r) = 0 in the N -section, (k, n, l) are good quantum numbers and the single particle energies are given by:…”

Section: A Bogoliubov-de Gennes Equationsmentioning

confidence: 99%

Orbital Josephson interference in a nanowire proximity-effect junction

Gharavi

Baugh

2015

Phys. Rev. B

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A semiconductor nanowire based superconductor-normal-superconductor (SN S) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N -section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N -section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mechanical result is shown to reduce to an intuitive, semi-classical model when the Andreev approximation holds. Numerical calculations of the critical current versus axial field reveal flux-aperiodic oscillations that we identify as a novel form of Josephson interference due to this orbital subband effect. This behavior is studied as a function of junction length and chemical potential. Finally, we discuss extensions to the model that may be useful for describing realistic devices.The Josephson effect is characterized by a currentphase relationship (CPR) linking macroscopic current flow to the phase gradient of the superconducting order parameter1 . The precise form of the CPR for a superconducting weak link depends on intrinsic factors such as junction geometry, material properties, coherence lengths, etc., in addition to extrinsic variables like temperature and magnetic field. In superconductor-normalsuperconductor (SN S) junctions in which the N -section is long enough to suppress direct tunnelling of Cooper pairs, but shorter than the N -section phase coherence length, a supercurrent may be carried by quasiparticles undergoing Andreev reflection at the S-N interfaces 2-5 . Planar SN S junctions of width large compared to the S-section superconducting coherence length have been studied in great detail 6 (width refers to the dimension perpendicular to the current). These have revealed, for example, Fraunhofer oscillations of the critical current I c with respect to an externally applied out-of-plane magnetic field 7-9 . For junction widths comparable to the S-section coherence length, i.e. the narrow junction limit, this becomes a quasi-Gaussian, monotonic decay of the critical current 7,10,11 . Recently, attention has been given to nanoscale, quasi one-dimensional (1D) SN S junctions, such as those readily engineered by contacting semiconductor nanowires with superconducting leads [12][13][14][15][16] . Gating the semiconducting N -section allows for modulating the supercurrent by controlling the chemical potential 12,15 . The oscillations of the magnetoresistance of a nanowire SN S junction in the voltage-biased state (i.e. no dc supercurrent) versus an axial magnetic field have been studied 16 . Efforts to realize Majorana fermion quasiparticles in 1D semiconductors with strong spin-orbit interaction and proximity coupling to a superconductor 17-20 have further raised interest in this type of junction. Theoretical resul...

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“…However, in the nanoscale regime, the confinement affects not only the electronic spectrum but also the phononic degrees of freedom which for nanofilms strongly deviates from that in the bulk (). The quantization of the phononic spectra in nanofilms and its influence on superconducting properties have been considered in many papers . Moreover, the effect of the confinement on the electron–phonon coupling strength has been recently studied by Saniz et al.…”

Section: Discussionmentioning

confidence: 99%

Orbital effect on the in‐plane critical field in free‐standing superconducting nanofilms

Wójcik

Zegrodnik

2015

Physica Status Solidi (b)

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The superconductor to normal metal phase transition induced by the in‐plane magnetic field is studied in free‐standing Pb(111) nanofilms. In the considered structures, the energy quantization induced by the confinement leads to the thickness‐dependent oscillations of the critical field (the so‐called “shape resonances”). In this paper, we examine the influence of the orbital effect on the in‐plane critical magnetic field in nanofilms. We demonstrate that the orbital term suppresses the critical field and reduces the amplitude of the thickness‐dependent critical field oscillations. Moreover, due to the orbital effect, the slope Hnormalc,false|false|−Tc at Tcfalse(0false) becomes finite and decreases with increasing film thickness in agreement with recent experiments. The temperature t* at which the superconductor to normal metal phase transition becomes of the first order is also analyzed.

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Hollow nanocylinder: Multisubband superconductivity induced by quantum confinement

Cited by 26 publications

References 41 publications

Superconducting transition temperature of Pb nanofilms: Impact of thickness-dependent oscillations of the phonon-mediated electron-electron coupling

Superconducting transition temperature of Pb nanofilms: Impact of thickness-dependent oscillations of the phonon-mediated electron-electron coupling

Orbital Josephson interference in a nanowire proximity-effect junction

Orbital effect on the in‐plane critical field in free‐standing superconducting nanofilms

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