Critical currents and supercurrent oscillations in Josephson field-effect transistors

Chrestin, A.; Matsuyama, T.; Merkt, U.

doi:10.1103/physrevb.49.498

Cited by 72 publications

(68 citation statements)

References 16 publications

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“…As was discovered in studies of Andreev reflection at Nb-InAs interfaces 40,44 , FWVM modifies the CPR of Superconductor/Semiconductor/Superconductor junctions. In the general case, where FWVM and barriers are included at the S-N interfaces, the bound state energies and the continuum current must be calculated from the transmission matrix formalism 46 , in which the transmission matrix includes a normal (specular) reflection coefficient as well as an Andreev (retro) reflection coefficient.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Orbital Josephson interference in a nanowire proximity-effect junction

Gharavi

Baugh

2015

Phys. Rev. B

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“…Figure 1 shows the current-voltage characteristic ͑I-V͒ of the Wϭ4 m junction at 10 mK, which has a current density of almost 100 nA/m. For ballistic Nb-2DEG-Nb junctions of similar electron density, junction length, and effective mass, Chrestin et al 4 calculated a critical current density of approximately 20 times the experimental value. Even after taking into account the small differences between the experimental and theoretical device parameters, there still remains an order-of-magnitude difference between theory and experiment.…”

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confidence: 96%

“…1 We focus on transport properties of InAs-based superconductor two-dimensional electron gas superconductor junctions ͑S-2DEG-S͒, where the 2DEG is in the ballistic regime. Several theoretical [2][3][4] and experimental papers [5][6][7] describing these devices have been published. However, presently there is no agreement between the predicted and observed value of the critical current I c nor of its temperature dependence I c (T).…”

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confidence: 99%

“…Two temperature regimes can be distinguished by comparing L to the thermal coherence length T ϭបv F /2k B T. In the high-temperature limit, T ϽL, I c (T) is predicted 2,4 to be proportional to exp(ϪL/ T ). This limit is experimentally obtained when TϾ1 K. However, thermal rounding of the I-V curves and the smallness of I c in this regime hamper its accurate determination ͑wider junctions make this regime more accessible͒.…”

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Experimental indication for supercurrents carried by opened transport channels

et al. 1996

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Electrical-transport properties of mesoscopic junctions consisting of a ballistic two-dimensional electron gas coupled at two sides to overlaying superconducting contacts are presented. The properties suggest that, despite the presence of transport limiting barriers in the sample, supercurrents are carried by a few modes that have near-unity transmission probability. We can qualitatively account for the presence of these resonances by the theory of disorder-induced opening of tunnel channels. ͓S0163-1829͑96͒51028-3͔Over the past few years, transport properties of phasecoherent normal ͑N͒ conductors coupled to superconducting ͑S͒ electrodes have received considerable interest. In such structures the interaction between the superconducting condensate and a normal electron gas can be studied on a mesoscopic scale. The process responsible for this interaction is Andreev reflection: an electron incident from N on a N-S interface can be backscattered as a hole, which has the phase of the incident electron shifted by an amount depending on energy and the macroscopic phase of S. As a result of this scattering process transport properties of such hybrid structures can change drastically.

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“…Thus, the large difference between ξ S and ξ 0 means that there is a substantial Fermi velocity mismatch (typically an order of magnitude 7,9 ), which must generate normal scattering at the SN interface in addition to Andreev reflection. This, together with other possible sources of scattering at the SN boundary, like imperfect interfaces 4,11,12 or charge accumulation layers 14 (typical of Nb/InAs contact), cannot be detected by only observing the independence of I c and R N on interelectrode separation (for intermediate 7 L). Nevertheless, this is frequently the criterion used in experiments 7 to ensure that the transport is ballistic.…”

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confidence: 99%

Intrinsic reduction of Josephson critical current in short ballistic SNS weak links

2001

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We present fully self-consistent calculations of the thermodynamic properties of three-dimensional clean SN S Josephson junctions, where S is an s-wave short-coherence-length superconductor and N is a clean normal metal. The junction is modeled on an infinite cubic lattice such that the transverse width of the S is the same as that of the N , and its thickness is tuned from the short to long limit. Both the reduced order parameter near the SN boundary and the short coherence length depress the critical Josephson current Ic, even in short junctions. This is contrasted with recent measurements on SN S junctions finding much smaller IcRN products than expected from the standard (non-self consistent and quasiclassical) predictions. We also find unusual current-phase relations, a "phase anti-dipole" spatial distribution of the self-consistently determined contribution to the macroscopic phase, and an "unexpected" minigap in the local density of states within the N region.PACS numbers: 74.50.+r, 74.80.Fp Over the past decade, both experimental and theoretical interest in the superconductivity of inhomogeneous systems have been rekindled, thereby leading to a reexamination of even well-charted areas from the mesoscopic point of view.1 For example, the Josephson effect in a superconductor-normal-metal-superconductor (SN S) weak link was known to be the result of the macroscopic condensate wave function leaking from the S into the N region. The induction of such superconducting correlations in the N , the so-called proximity effect, has been given a new real-space interpretation through the relative phase-coherence of quasiparticles, correlated by Andreev reflection at the SN interface.2 Moreover, the realization of the importance of tracking the phase-coherence of single particle wave-functions in proximity-coupled metals of mesoscopic size has also unearthed new phenomena, such as quantization of the critical current in ballistic mesoscopic short SN S junctions at low enough temperature.3,4 In short clean junctions, as T → 0, the critical supercurrent I c = e∆/ carried by a single conducting channel depends only on the superconducting energy gap ∆ as the smallest energy scale ∆ < E Th = v N F /L (in the long junction limit I c ∼ E Th is set 5 by the "ballistic" Thouless energy E Th < ∆, which is a single quasiparticle property determined by the Fermi velocity v N F in the N interlayer of length L). Thus, both mesoscopic and "classical" clean point-contact SN S junctions, with ballistic transport ℓ > L (ℓ is the mean free path), are predicted to exhibit the same I c R N = π∆/e product at T = 0. This has been known for quite some time as the KulikOmelyanchuk (KO) formula, 6 where R N is the Sharvin point contact resistance R N = h/2e 2 M of the ballistic N region containing M conducting channels.Recent experimental activity 7 on highly transparent 8 ballistic short SN S junctions, where both I c and R N are independent of the junction length, reveals much lower values of I c R N than the KO formula (similarly, the cri...

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Critical currents and supercurrent oscillations in Josephson field-effect transistors

Cited by 72 publications

References 16 publications

Orbital Josephson interference in a nanowire proximity-effect junction

Orbital Josephson interference in a nanowire proximity-effect junction

Experimental indication for supercurrents carried by opened transport channels

Intrinsic reduction of Josephson critical current in short ballistic SNS weak links

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