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Parallelization of pump devices is a direct way to increase the output level of the single-electron pump, which is required for metrological purposes. We fabricated a pair of single-electron pumps in parallel on a chip level and investigated their synchronized electron pumping phenomena. In the investigation, the pumping error was estimated to see whether the error was increased after the parallelization. We found that a proper choice of rf gates must be made in accordance with the direction of the applied magnetic field. In relation with the chirality of the edge state, the rf modulating gates should be chosen not to produce rf-induced heating effects.

From both a fundamental viewpoint and the perspective of wave-function engineering of an electron pumped by single-electron sources, it is important to understand how an electron gains energy while propagating along a time-dependent region in a quantum Hall channel. In our previous work, we experimentally observed that, when the electron travels through the time-dependent region before entering the pump, the pump current becomes substantially larger than the quantized value. We here present the results of a theoretical and experimental investigation of the mechanism underlying the heating of electrons traveling through a region of time-dependent potential induced by an rf signal. Using the Floquet scattering theory, we describe the energy distribution of the heated electrons, whose effective temperature can be substantially larger than the cryostat temperature. The behavior of the measured currents when the barrier height and the radio-frequency power are varied is in good qualitative agreement with the theoretical predictions., This research was supported by Research on “Redefinition of SI Base Units” (KRISS-2021-GP2021-0001), funded by the Korea Research Institute of Standards and Science. S.R. acknowledges partial support from the María de Maeztu Program for units of Excellence in R&D (MDM-2017-0711). M.B. was partially supported by the National Research Foundation of Korea (Grant No. NRF-2021R1A2C3012612). H.S. and M.B. were supported by the National Research Foundation of Korea (Grant No. SRC2016R1A5A1008184). The author at KIST acknowledges support from an IITP grant funded by the Korean government (MSIT) (Grant No. 20190004340011001).

We review recent precision measurements on semiconductor tunable-barrier electron pumps operating in a ratchet mode. Seven studies on five different designs of pumps have reported measurements of the pump current with relative total uncertainties around $10^{-6}$ or less. Combined with theoretical models of electron capture by the pumps, these experimental data exhibits encouraging evidence that the pumps operate according to a universal mechanism, independent of the details of device design. Evidence for robustness of the pump current against changes in the control parameters is at a more preliminary stage, but also encouraging, with two studies reporting robustness of the pump current against three or more parameters in the range of $\sim\!5 \times 10^{-7}$ to $\sim\!2 \times 10^{-6}$. This review highlights the need for an agreed protocol for tuning the electron pump for optimal operation, as well as more rigorous evaluations of the robustness in a wide range of pump designs., Comment: 18 pages, 8 figures

Coupling of the electron orbital motion and spin, i.e., spin-orbit coupling (SOC) leads to nontrivial changes in energy-level structures, giving rise to various spectroscopies and applications. The SOC in solids generates energy-band inversion or splitting under zero or weak magnetic fields, which is required for topological phases or Majorana fermions. Here, we examined the interplay between the Zeeman splitting and SOC by performing the transport spectroscopy of Landau levels (LLs) in indium arsenide nanowires under a strong magnetic field. We observed the anomalous Zeeman splitting of LLs, which depends on the quantum number of LLs as well as the electron spin. We considered that this observation was attributed to the interplay between the Zeeman splitting and the SOC. Our findings suggest an approach of generating spin-resolved chiral electron transport in nanowires.

A single electron pump was incorporated with a quantum Hall resistance and a Josephson voltage for the current evaluation in the framework of Ohm’s law. The pump current of about 60 pA level was amplified by a stable amplifier with a gain of 103 to induce a Hall voltage of about 60 mV level across a 1 MΩ Hall resistance array, which was compared with the Josephson voltage. The gain of the current amplifier was calibrated with a cryogenic current comparator bridge. For two different drive frequencies and repeated thermal cycles, the comparisons demonstrated that the pump current averaged over the first plateau was equal to ef within the combined uncertainty level of 0.3 × 10−6 (k = 1).

We demonstrate the robust operation of a gallium arsenide tunable-barrier single-electron pump operating with 1 part-per-million accuracy at a temperature of $1.3$~K and a pumping frequency of $500$~MHz. The accuracy of current quantisation is investigated as a function of multiple control parameters, and robust plateaus are seen as a function of three control gate voltages and RF drive power. The electron capture is found to be in the decay-cascade, rather than the thermally-broadened regime. The observation of robust plateaus at an elevated temperature which does not require expensive refrigeration is an important step towards validating tunable-barrier pumps as practical current standards., 13 pages, 7 figures (4 in main text and 3 in supplementary info

We performed a precision measurement of the current from a single-parameter electron pump, where the potential-profile for a quantum dot was manipulated by multiple top-metal gates. In an optimally tuned condition, driven with a sinusoidal-waveform microwave at f = 0.95 GHz, B = 11 T, and T = 0.3 K, the relative deviation of the pump current from ef, δIp/ef ≡ (Ip − ef)/ef was measured to be (−0.92 ± 1.37) ppm. Our experiment reproduces the current quantisation accuracy of a previous measurement of a single-parameter pump, but in a device fabricated using very different geometry, thereby indicating that accurate single-parameter pumping is insensitive to device details.

We have investigated a ‘cut-off frequency’ f c beyond which the quantized charge pumping phenomena disappear in a quantum-dot (QD) pump. We have observed a shift of fc in the opposite direction to that of δ 2 parameter, the figure of merit for the current-plateau flatness, depending on the potential profiles of the QD which can be controlled by a plunger gate. In relation with f c , we discuss the level-shift rate of a QD quasibound state in a nonadiabtic pumping phase.

Measurements of the distribution of stochastic switching currents in homogeneous, ultra-narrow superconducting nanowires provide strong evidence that the low-temperature current-switching in such systems occurs through quantum phase slips—topological quantum fluctuations of the superconducting order parameter via which tunnelling occurs between current-carrying states.

Collective transverse plasma modes in Bi 2 Sr 2 CaCu 2 O 8+x intrinsic Josephson junctions (UJs) can be excited by the moving fluxon lattices. Progressive transformation of the standing-wave-like fluxon-lattice configuration from a triangular lattice to a rectangular lattice takes place as the dynamic fluxon-lattice modes are in resonance with the collective transverse plasma modes. In this paper, we review the progress in terahertz-frequency-range electromagnetic wave generation from the IJJs using the resonance between moving fluxon lattice and the collective transverse plasma modes.

Stacked intrinsic Josephson junctions form in highly anisotropic high- T c superconductors such as Bi 2 Sr 2 CaCu 2 O 8+ x . Josephson-vortex dynamics in such systems attracts much research interests, both academic and application points of view. In a dense Josephson-vortex state (in the range of 4–5 T external magnetic field applied in parallel with the junction planes) of Bi 2 Sr 2 CaCu 2 O 8+ x stacked intrinsic Josephson junctions vortex-flow motion is in resonance with the collective plasma oscillation modes. With increasing magnetic fields beyond ∼2 T hysteretic quasiparticle branches keep shrinking, while the collective Josephson-vortex-flow branches start appearing and become clearer. The Josephson-vortex-flow branches split into multiple sub-branches corresponding to the number of coupled junctions in the stack. The low-bias characteristics of the Josephson-vortex-flow sub-branches fit well to the inductive-capacitive hybrid coupling model.

Detailed tunneling characteristics of a stack of intrinsic Josephson junctions in a Bi 2 Sr 2 CaCu 2 O 8+x single crystal were obtained both in spin-degenerate and spin-polarized bias configurations. Injection of the spin-polarized quasiparticles effectively weakened the in-plane superconducting strength and the interlayer Jospehson coupling. The superconducting gap and the Josephson critical current of the stack were, in general, further suppressed by an external field applied in parallel with the c-axis direction. Study of the spin-dependent tunneling characteristics may provide valuable information on clarifying the mechanism of high-Tc superconductivity as well as the interlayer phase fluctuation induced by the "pancake vortices" on CuO 2 layers.

We observed subbranch splitting in the low-bias vortex-flow branch of a dense-Josephson-vortex state in current-voltage characteristics of Bi 2 Sr 2 CaCu 2 O 8+x intrinsic Josephson junctions in the long-junction limit. We suggest that each subbranch corresponds to a plasma mode in serially coupled Josephson junctions, manifested in the Josephson vortex-flow current-voltage characteristics resonating with the plasma modes.

The dynamic characteristics of Josephson fluxons in naturally stacked intrinsic Josephson junctions in Bi2Sr2CaCu2O8+δ single crystals were studied experimentally. The Josephson fluxons were generated either by irradiating microwaves or by applying dc magnetic fields in parallel with the junction planes. In the presence of a finite tunneling bias current the fluxons are driven along the junctions in resonance with the excitation modes of Josephson plasma and thus exhibit a variety of dynamic characteristics. Thus in the flux-flow state of fluxons in both cases above, for a relatively low vortex density, sub-branch splitting of the ‘supercurrent’ branch in the current–voltage (I–V) characteristics was observed, which corresponded to different plasma excitation modes. For a higher vortex density, on the other hand, all the quasiparticle branches merged into a single non-hysteretic I–V curve which exhibited step-like kink features, very similar to the recently predicted ones corresponding to different moving fluxon patterns. The detailed agreement with the theoretical prediction, however, is yet to be confirmed.

We studied the motion of fluxons in a stack of intrinsic Josephson junctions (IJJs) of Bi2Sr2CaCu2O8+δ single crystals in a long junction limit. Driven by the tunnelling bias, current Josephson fluxons excite plasma oscillations and move in resonance with the plasma propagation modes. We examined two types of samples in this study; mesa structure (UD1) and a stack of junctions sandwiched between normal-metallic electrodes (DSC1). In a high magnetic field, the hysteresis in the I–V characteristics of both-types of samples vanished. The resulting single I–V curve exhibited a cusp structure at characteristic bias voltages which were believed to be boundaries of different moving fluxon configurations. We studied the sample-geometry dependence of the cusp characteristics by comparing the results from the two types of samples.

Our quantum-dot (QD) electron pump has uniqueness in design in that the QD potential shape can be manipulated, especially its potential depth can be controlled by a plunger gate. We find that there exist strong correlations between the potential depth of the QD and the upper frequency limit, fm, when the modulating microwave power is fixed. As the depth of the QD potential is deepened, fm shows decreasing characteristics while the flatness of the 1st current plateau is increased. We have semi-quantitatively analyzed these correlations by using the notion of so-called “non-adiabatic Coulomb blockade gap energy,” ΔELU. We find that ΔELU parameter being under control by a plunger gate is proportional to the pumping frequency f.

We present an experimental investigation on the spectral characteristics of an artificial atom "transmon qubit" constituting a three-level cascade system ({\Xi}-system) in the presence of a pair of external driving fields. We observe two different types of Autler-Townes (AT) splitting: type I, where the phenomenon of two-photon resonance tends to diminish as the coupling field strength increases, and type II, where this phenomenon mostly stays constant. We find that the types are determined by the cooperative effect of the decay rates and the field strengths. Theoretically analyzing the density-matrix elements in the weak-field limit where the AT effect is suppressed, we single out events of pure two-photon coherence occurring owing to constructive quantum interference., Comment: accepted for publication in PRA

We report nonequilibrium transport measurements of gate-tunable Andreev bound states in a carbon nanotube quantum dot coupled to two superconducting leads. In particular, we observe clear features of two types of Kondo ridges, which can be understood in terms of the interplay between the Kondo effect and superconductivity. In the first type (type I), the coupling is strong and the Kondo effect is dominant. Levels of the Andreev bound states display anticrossing in the middle of the ridge. On the other hand, crossing of the two Andreev bound states is shown in the second type (type II) together with the 0-π transition of the Josephson junction. Our scenario is well understood in terms of only a single dimensionless parameter, kBTKminâ¡ /Δ, where TKminâ¡ and Δ are the minimum Kondo temperature of a ridge and the superconducting order parameter, respectively. Our observation is consistent with measurements of the critical current, and is supported by numerical renormalization group calculations. © 2013 American Physical Society., This work was supported by the National Research Foundation of Korea (NRF) (Grants No. 2009-0084606, No. 2012R1A1A2003957, No. 2010-0025880, No. 2011-0012494, and No. 2011-0015895), and by the Korea Research Institute of Standards and Science. R. L and J. S. L were supported by MINECO Grants No. FIS2008-00781, No. FIS2011-23526, and No. CSD2007-00042 (CPAN).

We demonstrate a reliable technique for counting atomic planes (n) of few-layer graphene (FLG) on SiO2/Si substrates by Raman spectroscopy. Our approach is based on measuring the ratio of the integrated intensity of the G graphene peak and the optical phonon peak of Si, I(G)/I(Si), and is particularly useful in the range n>4 where few methods exist. We compare our results with atomic force microscopy (AFM) measurements and Fresnel equation calculations. Lastly, we apply our method to unambiguously identify n of FLG devices and find that the mobility (~2000 cm2 V-1 s-1) is independent of layer thickness for n>4., Comment: 18 pages, 5 figures The manuscipt was withdrawn to avoid complications for publication elsewhere

We directly image hot spot formation in functioning mono- and bilayer graphene field effect transistors (GFETs) using infrared thermal microscopy. Correlating with an electrical-thermal transport model provides insight into carrier distributions, fields, and GFET power dissipation. The hot spot corresponds to the location of minimum charge density along the GFET; by changing the applied bias this can be shifted between electrodes or held in the middle of the channel in ambipolar transport. Interestingly, the hot spot shape bears the imprint of the density of states in mono- vs. bilayer graphene. More broadly, we find that thermal imaging combined with self-consistent simulation provides a non-invasive approach for more deeply examining transport and energy dissipation in nanoscale devices.

We report measurements of magnetoresistance in single-layer graphene as a function of gate voltage (carrier density) at 250 mK. By examining signatures of weak localization (WL) and universal conductance fluctuations (UCF), we find a consistent picture of phase coherence loss due to electron-electron interactions. The gate-dependence of the elastic scattering terms suggests that the effect of trigonal warping, i.e., the non-linearity of the dispersion curves, may be strong at high carrier densities, while intra-valley scattering may dominate close to the Dirac point. In addition, a decrease in UCF amplitude with decreasing carrier density can be explained by a corresponding loss of phase coherence.

We report measurements of switching current distribution (SWCD) from a phase-diffusion branch (PDB) to a quasiparticle-tunneling branch (QTB) as a function of temperature in a cuprate-based intrinsic Josephson junction. Contrary to the thermal-activation model, the width of the SWCD increases and the corresponding switching rate shows a nonlinear behavior with a negative curvature in a semilogarithmic scale with decreasing temperature down to 1.5 K. Based on the multiple-retrapping model, we quantitatively demonstrate that the frequency-dependent junction quality factor, representing the energy dissipation in a phase-diffusion regime, determines the observed temperature dependence of the SWCD and the switching rate. We also show that a retrapping process from the QTB to the PDB is related to the low-frequency limit damping.

Microwave response of S-shaped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ (BI-2212) micron-scale samples, in which the supercurrent was forced to flow perpendicular to the crystal layers, was investigated. A treatment with a focused ion beam allowed us to reduce the plasma frequency down to ${f}_{p}\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ at $T=0.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in naturally stacked Josephson junctions in a crystal. We observed Shapiro steps at frequencies as low as $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. Well-developed zero-crossing Shapiro steps were observed at frequencies as low as $\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. They appeared as constant-voltage plateaus with a nonzero voltage occurring at zero bias current. We confirmed that zero-crossing Shapiro steps in the Bi-2212 stacked junctions can be observed when the irradiated frequency is sufficiently larger than ${f}_{p}$. The observed high-order fractional steps in the microwave responses indicate that the interlayer-coupled Bi-2212 Josephson junctions have nonsinusoidal current-phase relation. Based on the temperature dependence of the steps, we also showed that the finite slope of the steps is due to the enhancement of the phase-diffusion effect.

We report on heating-compensated interlayer tunneling spectroscopy (ITS) performed on stacks of overdoped ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+x}$ intrinsic junctions, where most of the bias-induced heating in the ITS was eliminated. The onset temperature of a pseudogap (PG), which was revealed in the hump structure of the electronic excitation spectra, nearly reached room temperature for our overdoped intrinsic junctions, which represented the genuine PG onset. At a temperature below but close to ${T}_{c}$, both the superconducting coherence peak and the pseudogap hump coexisted, implying that the two gaps are of separate origins. The hump voltage increased below ${T}_{c}$, following the superconducting gap voltage, which led to the conclusion that the hump structure below ${T}_{c}$ in our ITS arose from the combined contributions of the quasiparticle spectral weights of two different characters: one of the superconducting state and another of the PG state near the antinodal region.

We report the experimental confirmation of the collective transverse plasma modes excited by the Josephson vortex lattice in stacks of intrinsic Josephson junctions in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ single crystals. The excitation was confirmed by analyzing the temperature $(T)$ and magnetic-field $(H)$ dependencies of the multiple sub-branches in the Josephson vortex-flow region of the current-voltage characteristics of the system. In the near-static Josephson vortex state for a low tunneling bias current, pronounced magnetoresistance oscillations were observed, which represented a triangular-lattice vortex configuration along the $c$ axis. In the dynamic vortex state in a sufficiently high magnetic field and for a high-bias current, splitting of a single Josephson vortex-flow branch into multiple sub-branches was observed. Detailed examination of the sub-branches for varying $H$ field reveals that sub-branches represent the different modes of the Josephson vortex lattice along the $c$ axis, with varied configuration from a triangular to a rectangular lattice. These multiple sub-branches merge to a single curve at a characteristic temperature, above which no dynamical structural transitions of the Josephson vortex lattice is expected.

We report on the successful terahertz emission (0.6--1 THz) that is continuous and tunable in its frequency and power, by driving Josephson vortices in resonance with the collective standing Josephson plasma modes excited in stacked ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ intrinsic Josephson junctions. Shapiro-step detection was employed to confirm the terahertz-wave emission. Our results provide a strong feasibility of developing long-sought solid-state terahertz-wave emission devices.

We confirmed the existence of the collective transverse plasma modes excited by the motion of the Josephson vortex lattice in stacked intrinsic Josephson junctions of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by observing the multiple subbranches in the Josephson-vortex-flow current-voltage characteristics. We also observed the symptom of the microwave emission from the resonance between the Josephson vortex lattice and the collective transverse plasma modes, which provides the possibility of developing Josephson-vortex-flow electromagnetic oscillators., 4 pages, 3 figures

Collective transverse plasma modes in a stack of Bi2Sr2CaCu2O8+x intrinsic Josephson junctions (IJJs) can be examined by observing the resonating Josephson vortex motion in the stack. In this study, we observed distinct multiple branches in the Josephson vortex‐flow current‐voltage characteristics, which suggested a transformation of Josephson vortex configuration among different collective plasma modes. For a dc bias on one of the multiple branches, we also obtained an evidence for the microwave emission from the transverse Josephson vortex motion in a stacked IJJs. The emission was examined by observing the changes in the quasiparticle branches of another stack of IJJs placed in proximity to the stack under study.

We observed splitting of the low-bias vortex-flow branch in a dense-Josephson-vortex state into multiple subbranches in current-voltage characteristics of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ intrinsic Josephson junctions in the long-junction limit. Each subbranch corresponds to a plasma mode in serially coupled Josephson junctions. Splitting into low-bias linear subbranches with a spread in the slopes and the intersubbranch mode-switching character are in good quantitative agreement with the prediction of the weak but finite interjunction capacitive-coupling model incorporated with the inductive coupling.

We report the observation of the collective transverse plasma (CTP) modes induced by the Josephson vortex lattice motion and the excitation of corresponding electromagnetic waves in a stack of intrinsic Josephson junctions (IJJs) in Bi 2 Sr 2 CaCu 2 O 8+ x . The existence of the CTP modes was confirmed by observing the sub-branches in the tunneling current–voltage curves of staked junctions in the Josephson vortex-flow region. For a proper bias in the sub-branches, the emission of the electromagnetic waves by the collective vortex resonance motion in a stack of IJJs (the oscillator stack) was examined using another on-chip stack of IJJs (the detector stack). The microwave emission from the oscillator stack and the resulting irradiation onto the detector stack was evidenced by the increase of Josephson vortex-flow voltages in the detector stack.

We observed periodic oscillations in the differential resistance vs. voltage curves of Au/Bi2Sr2CaCu2O8 + x (Au/Bi2212) junctions near the bulk superconducting transition temperature Tc of the Bi2212 single crystals. The oscillations can be explained in terms of the McMillan–Rowell coherent states resulting from the Andreev-reflected quasiparticles in the normal-metallic layer. This is the first observation of the McMillan–Rowell oscillations in the c-axis transport of the Bi2212 material.

We studied the collective motion of Josephson vortices generated by microwave irradiation and by an external dc magnetic field applied in parallel with the planes of intrinsic junctions of Bi 2 Sr 2 CaCu 2 O 8+ δ single crystals. In both cases, for a low vortex density and driving current, splitting of the ‘supercurrent’ branch corresponding to different plasma excitation modes was observed in the current–voltage characteristics (IVC). For a high vortex density in fields beyond 3–4 T, the IVC merged into a single non-hysteretic curve with kinks, similar to those arising from the theoretically proposed structural transformation of moving vortex patterns.

We study current-voltage (V-I) characteristics of short supercon- ducting nanowires of length 100nm exposed to microwave (MW) radiation of frequencies between 2 and 15GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V-I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol- Beasley-Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.

Josephson vortices in naturally stacked Bi-2212 tunneling junctions display rich dynamic behavior that derives from the coexistence of three basic states: static Josephson vortex lattice, coherently moving lattice, and incoherent quasiparticle tunneling state. Rich structure of hysteretic branches observed in the current-voltage characteristics can be understood as combinatorial combinations of these three states which are realized in different junctions and evolve separately with magnetic field and bias current. In particular, the multiple Josephson-vortex-flow branches at low bias currents arise from the individual depinning of Josephson vortex rows in each junction.