Subharmonic Gap Structure Research Articles

Coherent Multiple Charge Transfer in a Superconducting NbN Tunnel Junction

We measured shot noise and submillimeter-wave response in a superconducting NbN tunnel junction that had a subharmonic gap structure on the current-voltage (I-V) curve. We found that the observed effective charge, defined from the noise-current ratio, tends to a steplike function of voltage. In the presence of submillimeter-wave radiation of frequency v, novel step structures spaced by hv/2e below and above the half-gap voltage clearly appeared on the I-V curve, overlapping the ordinary photon-assisted tunneling steps spaced by hv/e. Observation of these features provides clear evidence that coherent multiple Andreev reflection processes occur in the NbN tunnel junction with low barrier transparency.

Correlation Between the<tex>$1/f$</tex>Noise Parameter and the Andreev Conductance in Epitaxial NbN/AlN/NbN Junctions

Low-frequency noise properties of epitaxial NbN/AlN/NbN tunnel junctions have been investigated as a function of the bias voltage. The subharmonic gap structures (SGSs) were clearly observed in the differential resistance dV/dI-V curves. The SGSs were explained with Octavio, Tinkham, Blonder, Klapwijk (OTBK) theory based on the multiple-Andreev reflection (MAR) phenomena. To estimate the amplitude of the voltage noise power spectra S/sub V/(f) in the range 1-10/sup 5/ Hz, we extended Rogers and Buhrman empirical theory. The 1/f noise parameter /spl eta/ in this theory is given as /spl eta/=S/sub V/(f)I/sub b//sup 2/R/sub d//sup 2//fA, where A is the junction area, I/sub b/ is the bias current and R/sub d/ is the dynamic resistance. The /spl eta/ values (/spl eta//sub sg/) biased at the sub-gap voltage were larger than that (/spl eta//sub ag/) of the above-gap voltage. In addition, the /spl eta//sub sg/-V curves in the sub-gap region have dip and peak structures related to the SGSs in the dI/dV-V curves. In contrast, for the above-gap bias voltage, the /spl eta//sub ag/ values did not depend on the bias voltage. We concluded from these results that the excess 1/f noise in the sub-gap bias voltage was caused by the fluctuation of the MAR conductance.

Subharmonic Photon-Assisted Tunneling Effect in Superconducting NbN Tunnel Junctions

We investigated subharmonic gap structures in the current-voltage (I-V) characteristics of NbN tunnel junctions by observing frequency response using a quasioptical mixer configuration. We chose a 10.5-/spl mu/m-long by 0.6-/spl mu/m-wide junction for the mixer so that the junction behaved as a distributed element at submillimeter-wave frequencies in wideband observations. In the presence of electromagnetic waves, subharmonic photon-assisted tunneling steps with a voltage width of hf/2e could clearly be observed below and above the half-gap voltage in the I-V curves of junctions at measured frequencies from 600 to 950 GHz, where h is Planck's constant, f is frequency, and e is electron charge. This evidence is consistent with a consequence of multiple Andreev reflection at low transmissions or multiparticle tunneling.

Noise and Full Counting Statistics of Incoherent Multiple Andreev Reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Delta/en. For low voltages V<<Delta/e, the counting statistics results from diffusion of multiple charges in energy space, giving the pth cumulant Q(p) proportional, variantV(2-p), diverging for p> or =3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.

Shot noise of large charge quanta in superconductor/semiconductor/superconductor junctions

We have found experimentally that the noise of ballistic electron transport in a superconductor/semiconductor/superconductor junction is enhanced relative to the value given by the general relation, S_V=2eIR^2coth(eV/2kT), for two voltage regions in which this expression reduces to its thermal and shot noise limits. The noise enhancement is explained by the presence of large charge quanta, with effective charge q*=(1+2Delta/eV)e, that generate a noise spectrum S_V=2q*IR^2, as predicted in Phys. Rev. Lett. 76, 3814 (1996). These charge quanta result from multiple Andreev reflections at each junction interface, which are also responsible for the subharmonic gap structure observed in the voltage dependence of the junction's conductance.

Anomalous behavior near T c and synchronization of Andreev reflection in two-dimensional arrays of SNS junctions

We have investigated low-temperature transport properties of two-dimensional arrays of superconductor--normal-metal--superconductor (SNS) junctions. It has been found that in two-dimensional arrays of SNS junctions (i) a change in the energy spectrum within an interval of the order of the Thouless energy is observed even when the thermal broadening far exceeds the Thouless energy for a single SNS junction; (ii) the manifestation of the subharmonic energy gap structure (SGS) with high harmonic numbers is possible even if the energy relaxation length is smaller than that required for the realization of a multiple Andreev reflection in a single SNS junction. These results point to the synchronization of a great number of SNS junctions. A mechanism of the SGS origin in two-dimensional arrays of SNS junctions, involving the processes of conventional and crossed Andreev reflection, is proposed.

Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.

Current transport and the fluctuation of critical current in high-temperature superconductor interface-engineered Josephson junctions

The mechanisms of current transport in interface-engineered junctions (IEJs) with ramp-edge geometry were investigated to clarify the possible origin of the statistical fluctuation of the Josephson critical current. More than 1000 junctions with a ramp edge aligned either along the [100] or [110] axis of the high-temperature superconductor electrode were fabricated under various process conditions. These junctions exhibited a critical current density ranging from ${10}^{2}$ to ${10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{A}∕\mathrm{cm}}^{2}$ at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ while maintaining a magnetic field modulation of the critical current exceeding 80% without any indication of the peculiar effect of $d$-wave pairing symmetry. The junctions with a critical current density exceeding ${10}^{4}\phantom{\rule{0.3em}{0ex}}{\mathrm{A}∕\mathrm{cm}}^{2}$ exhibited an appreciable amount of excess current that grew rapidly within an approximate voltage range of less than $5\phantom{\rule{0.3em}{0ex}}\mathrm{mV}$. The critical current versus temperature characteristics of these junctions were found to be explained reasonably well by a superconductor-normal-superconductor (SNS) junction model in the diffusive regime. This model is also consistent with our observation of a weak subharmonic gap structure due to multiple Andreev reflections. In addition, we found that the Josephson critical current $({I}_{c})$ exhibited a good correlation with the differential resistance near $0\phantom{\rule{0.3em}{0ex}}\mathrm{V}$, while the normal resistance defined at a current level of two to three times ${I}_{c}$ varied appreciably even for junctions with a similar ${I}_{c}$. This indicates that another conduction channel with little contribution to the Josephson current coexists within the junctions. The $dI∕dV$ measurement for high resistance junctions revealed that resonant tunneling of quasiparticles through localized states in an insulating barrier constitutes this second conduction channel. All these results suggest that IEJs should be regarded as an array of microscopic SNS contacts embedded in an insulating barrier with random orientation. The fluctuation in the number of SNS contacts in a junction restricts the attainable minimum spread of the ${I}_{c}$ value.

Photon-assisted multiple-Andreev reflections in high- Jc NbN/AlN/NbN tunnel junctions

Interplay between microwave field and Andreev current in epitaxial NbN/AlN/NbN tunnel junctions have been investigated. The subharmonic-gap structures (d V/d I dip-structures) were clearly observed for almost all junctions without microwave field, and the voltage positions of d V/d I dips were well explained by Octavio, Tinkham, Blonder and Klapwijk (OTBK) theory based on multiple-Andreev reflection (MAR). In the presence of microwave field, the d V/d I– V curve only in a high- J c (5 kA/cm 2) junction has a rich subgap structure due to photon-assisted MAR. The observed microwave-induced d V/d I structure was qualitatively explained by the OTBK theory with an effective time-dependent voltage model.

Subharmonic gap structure in superconducting scanning tunneling microscope junctions

We observe a subharmonic gap structure (SGS) and the Josephson effect in superconducting scanning tunneling microscope junctions with resistances below 100 kΩ. The magnitude of the n=2 SGS is shown to scale with the square of the junction normal state conductance, in agreement with theory. We show by analyzing the Josephson effect in these junctions that the superconducting phase dynamics are strongly affected by thermal fluctuations. We estimate the linewidth of the Josephson oscillations due to phase fluctuations, a quantity that may be important in modern theories of the subgap structure. While phase fluctuations may smear the SGS current onsets, we conclude that the sharpness of these onsets in our data is not limited by fluctuations.

Multiple Andreev reflections in a carbon nanotube quantum dot.

We report resonant multiple Andreev reflections in a multiwall carbon nanotube quantum dot coupled to superconducting leads. The position and magnitude of the subharmonic gap structure is found to depend strongly on the level positions of the single-electron states which are adjusted with a gate electrode. We discuss a theoretical model of the device and compare the calculated differential conductance with the experimental data.

Characterization of low frequency noise in epitaxial NbN/AlN/NbN tunnel junctions

We measured the low frequency noise characteristics and subharmonic gap structures of epitaxial NbN/AlN/NbN tunnel junctions with different current densities. For all of the junctions, the voltage noise power spectrum S/sub v/(f) showed a frequency dependence that is well described by 1/f behavior. Subharmonic gap structures were clearly observed in the dV/dI-V curves at voltage 2/spl Delta//ne, and the values of n increased with the current density J/sub c/ in the junctions. We estimated the 1/f noise parameter /spl eta/ using the empirical theory of Rogers and Buhrman for the S/sub v/(f), and investigated the correlation between the /spl eta/ and the inverse junction quality 1/Q. We found that the /spl eta/-1/Q relationship for our epitaxial tunnel junctions gave a different behavior for nonepitaxial tunnel junctions. The tunnel barrier properties were investigated by applying a pulse voltage to the junctions at 4.2 K, and measuring the applied voltage dependence of the I-V characteristics and low frequency noise amplitude.

Tunnel Junctions Using Different High- T c Superconductors

We present the results on the measurements of the ramp-edge type hetero-junctions with different high-T c superconductor electrodes, YBa2Cu3O7−δ and Bi2Sr2CaCu2O8+δ. The dynamic conductance dI/dV in junctions showed a two-gap-like structure, which can be explained in terms of the sum and difference of two different superconducting gaps. The BTK model fitting yielded a good agreement with the experimental results. Subharmonic gap structure was also observed in several junctions with lower tunnel resistance.

Scanning tunneling spectroscopy in MgB 2

We present extensive scanning tunneling spectroscopy measurements at low temperatures in the multiband superconductor MgB 2. We find a similar behavior in single crystalline samples and in single grains, which clearly shows the partial superconducting density of states of both the π and σ bands of this material. The superconducting gaps corresponding to both bands are not single valued. Instead, we find a distribution of superconducting gaps centered around 1.9 and 7.5 mV, corresponding respectively to each set of bands. Interband scattering effects, leading to a single gap structure at 4 mV and a smaller critical temperature can be observed in some locations on the surface. S–S junctions formed by pieces of MgB 2 attached to the tip clearly show the subharmonic gap structure associated with this type of junctions. We discuss future developments and possible new effects associated with the multiband nature of superconductivity in this compound.

Subharmonic gap structure ind-wave superconductors

We present a self-consistent theory of current-voltage characteristics of d-wave/d-wave contacts at arbitrary transparency. In particular, we address the open problem of the observation of subharmonic gap structure (SGS) in cuprate junctions. Our analysis shows that: (i) the SGS is possible in d-wave superconductors, (ii) the existence of bound states within the gap results in an even-odd effect in the SGS, (iii) elastic scattering mechanisms, like impurities or surface roughness, may suppress the SGS, and (iv) in the presence of a magnetic field the Doppler shift of the Andreev bound states leads to a very peculiar splitting of the SGS, which is an unambiguous fingerprint of d-wave superconductivity.

Proximity effect and multiple Andreev reflections in chaotic Josephson junctions

We study the dc-current transport in a voltage biased superconductor-chaotic dot-superconductor junction with an induced proximity effect(PE) in the dot. It is found that for a Thouless energy $E_{Th}$ of the dot smaller than the superconducting energy gap $\Delta$, the PE is manifested as peaks in the differential conductance at voltages of order $E_{Th}$ away from the even subharmonic gap structures $eV \approx 2(\Delta\pm E_{Th})/2n$. These peaks are insensitive to temperatures $kT \ll \Delta$ but are suppressed by a weak magnetic field. The current for suppressed PE is independent of $E_{Th}$ and magnetic field and is shown to be given by the Octavio-Tinkham-Blonder-Klapwijk theory.

Hamiltonian approach to the ac Josephson effect in superconducting-normal hybrid systems

The ac Josephson effect in hybrid systems of a normal mesoscopic conductor coupled to two superconducting (S) leads is investigated theoretically. A general formula of the ac components of time-dependent current is derived which is valid for arbitrary interactions in the normal region. We apply this formula to analyze a S-normal-S system where the normal region is a noninteracting single level quantum dot. We report the physical behavior of time-averaged nonequilibrium distribution of electrons in the quantum dot, the formation of Andreev bound states, and ac components of the time-dependent current. The distribution is found to exhibit a population inversion; and all Andreev bound states between the superconducting gap $\Delta$ carry the same amount of current and in the same flow direction. The ac components of time-dependent current show strong oscillatory behavior in marked contrast to the subharmonic gap structure of the average current.

Irradiation-assisted fabrication and properties ofYBa2Cu3O7-x thin-film microbridges

Irradiation-weakened links wereproduced in epitaxial YBa2Cu3O7-x films. The phenomena occurring inmicrobridges with different critical current density jc were studied. Thecharacteristics of the microbridges with jc (77 K)>1×106 A cm-2 are ascertained to be affected by the heating effects andthe heat transfer coefficient value was deduced to be5500-7500 W cm-2 K-1. It is established that the rf properties ofthe microbridges with jc (10 K)~104-106 A cm-2 aredetermined by vortex movement. A subharmonic gap structure correspondingto a higher (49 meV) and a lower (10.3 meV) energy gap at 4.2 K wasregistered in the characteristics of some of the microbridges. Thecharacteristics of microbridges with a completely suppressed criticalcurrent show a zero-bias anomaly which is stable relative totemperature increase and is observed at temperatures close to Tc.

Diffusive single and multiply connectedSNS systems with high-transparentinterfaces

We present low-temperature transport measurementson single and multiply connected SNS systems fabricated on thebasis of superconducting polycrystalline PtSi film. Zero biasanomaly (ZBA) and subharmonic energy gap structure (SGS)originating from the proximity effects and the multiple Andreevreflections were observed and carefully studied. It was foundthat the ZBA is not described by any theories developed forSNS junctions with high-transparent NS interface. The value ofexcess conductance and the width of ZBA for single SNSjunction far exceed values predicted by up-to-date theories.The NS interfaces of our SNS junctions are really high-transparent, for superconducting and normal metal parts aremade of the same material. On the other hand, as we have todeal with long diffusive SNS junctions one might expect thatimpurities could provide the conditions for incoherent multipleAndreev reflections.In comparison with single SNS junctions we observe significant narrowing of the ZBA in multiply connected SNS systems:one-dimensional (1D) and two-dimensional arrays (2D) of SNSjunctions. In 2D arrays an appreciable SGS appears, with up to n = 16(eV = ±2Δ/n) and some numbers being lost. One of themost interesting results obtained on 1D arrays consists in theappearance of symmetrical dips on the dependences dV/dI - Vat dc voltage corresponding to some multiples of Δ/e. Presentedresults show that coherent phenomena governed by Andreevreflection are not self-averaging and are maintained over amacroscopic scale.

Two-dimensional array of diffusive SNS junctions with high-transparent interfaces

We report the first comparative study of the properties of two-dimensional arrays and single superconducting film - normal wire - superconducting film (SNS) junctions. The NS interfaces of our SNS junctions are really high transparent, for superconducting and normal metal parts are made from the same material (superconducting polycrystalline PtSi film). We have found that the two-dimensional arrays reveal some novel features: (i) the significant narrowing of the zero bias anomaly (ZBA) in comparison with single SNS junctions, (ii) the appearance of subharmonic energy gap structure (SGS), with up to n=16 (eV=\pm 2\Delta/n), with some numbers being lost, (iii) the transition from 2D logarithmic weak localization behavior to metallic one. Our experiments show that coherent phenomena governed by the Andreev reflection are not only maintained over the macroscopic scale but manifest novel pronounced effects as well. The behavior of the ZBA and SGS in 2D array of SNS junctions strongly suggests that the development of a novel theoretical approach is needed which would self-consistently take into account the distribution of the currents, the potentials, and the superconducting order parameter.