Gate-Controlled Superconducting Proximity Effect in Carbon Nanotubes

Transition from Diffusive to Superdiffusive Transport in Carbon Nanotube Networks via Nematic Order Control

The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy but also other types of behaviors are suppressed by disorder. Here, we compare the dynamics of quasiparticles under strong electric fields in aligned and random CNT networks using a combination of terahertz emission and photocurrent experiments and out-of-equilibrium numerical simulations. We find that the degree of alignment strongly influences the excited quasiparticles' dynamics, rerouting the thermalization pathways. This is, in particular, evidenced in the high-energy, high-momentum electronic population (probed through the formation of low energy excitons via exciton impact ionization) and the transport regime evolving from diffusive to superdiffusive.

Influence of Rashba spin-orbit coupling on Josephson effect in triplet superconductor/two-dimensional semiconductor/triplet superconductor junctions

We study theoretically Josephson effect in a planar ballistic junction between two triplet superconductors with p-wave orbital symmetries and separated by a two-dimensional (2D) semiconductor channel with strong Rashba spin–orbit coupling. In triplet superconductors, three types of orbital symmetries are considered. We use Bogoliubov–de Gennes formalism to describe quasiparticle propagations through the junction and the supercurrents are calculated in terms of Andreev reflection coefficients. The features of the variation of the supercurrents with the change of the strength of Rashba spin–orbit coupling are investigated in some detail. It is found that for the three types of orbital symmetries considered, both the magnitudes of supercurrent and the current-phase relations can be manipulated effectively by tuning the strength of Rashba spin–orbit coupling. The interplay of Rashba spin–orbit coupling and Zeeman magnetic field on supercurrent is also investigated in some detail.

Anomalous Fano Resonance in Double Quantum Dot System Coupled to Superconductor

We analyze the influence of a local pairing on the quantum interference in nanoscopic systems. As a model system we choose the double quantum dot coupled to one metallic and one superconducting electrode in the T-shape geometry. The analysis is particularly valuable for systems containing coupled objects with considerably different broadening of energy levels. In such systems, the scattering of itinerant electrons on a discrete (or narrow) energy level gives rise to the Fano-type interference. Systems with induced superconducting order, along well understood Fano resonances, exhibit also another features on the opposite side of the Fermi level. The lineshape of these resonances differs significantly from their reflection on the opposite side of the Fermi level, and their origin was not fully understood. Here, considering the spin-polarized tunneling model, we explain a microscopic mechanism of a formation of these resonances and discuss the nature of their uncommon lineshapes. We show that the anomalous Fano profiles originate solely from the pairing of nonscattered electrons with scattered ones. We investigate also the interplay of each type of resonances with the Kondo physics and discuss the resonant features in differential conductivity.

Josephson Effect in a Few-Hole Quantum Dot

A Ge-Si core-shell nanowire is used to realize a Josephson field-effect transistor with highly transparent contacts to superconducting leads. By changing the electric field, access to two distinct regimes, not combined before in a single device, is gained: in the accumulation mode the device is highly transparent and the supercurrent is carried by multiple subbands, while near depletion, the supercurrent is carried by single-particle levels of a strongly coupled quantum dot operating in the few-hole regime. These results establish Ge-Si nanowires as an important platform for hybrid superconductor-semiconductor physics and Majorana fermions.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} Superconductor

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Combined AFM and STM measurements of a silicene sheet grown on the Ag(111) surface

In this paper, we present the first non-contact atomic force microscopy (nc-AFM) of a silicene on a silver (Ag) surface, obtained by combining non-contact atomic force microscopy and scanning tunneling microscopy (STM). STM images over large areas of silicene grown on the Ag(111) surface show both (√13 × √13)R13.9° and (4 × 4) superstructures. For the widely observed (4 × 4) structure, the observed nc-AFM image is very similar to the one recorded by STM. The structure resolved by nc-AFM is compatible with only one out of two silicon atoms being visible. This indicates unambiguously a strong buckling of the silicene honeycomb layer.

Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device

We report on transport measurements of an InAs nanowire coupled to niobium nitride leads at high magnetic fields. We observe a zero-bias anomaly (ZBA) in the differential conductance of the nanowire for certain ranges of magnetic field and chemical potential. The ZBA can oscillate in width with either the magnetic field or chemical potential; it can even split and re-form. We discuss how our results relate to recent predictions of hybridizing Majorana fermions in semiconducting nanowires, while considering more mundane explanations.

Josephson current in carbon nanotubes with spin-orbit interaction

We demonstrate that curvature-induced spin-orbit coupling induces a 0-π transition in the Josephson current through a carbon nanotube quantum dot coupled to superconducting leads. In the noninteracting regime, the transition can be tuned by applying a parallel magnetic field near the critical field where orbital states become degenerate. Moreover, the interplay between charging and spin-orbit effects in the Coulomb blockade and cotunneling regimes leads to a rich phase diagram with well-defined (analytical) boundaries in parameter space. Finally, the 0 phase always prevails in the Kondo regime. Our calculations are relevant in view of recent experimental advances in transport through ultraclean carbon nanotubes.

Electronic double slit interferometers based on carbon nanotubes

We report the realization of an electronic double slit interferometer based on individual carbon nanotubes (SWNT). By performing transport spectroscopy on two parallel SWNTs in close proximity, we observe superposition of conductance oscillation with two different frequencies, "inverse" Coulomb blockade patterns, and Fano-like line-shapes with abrupt phase shifts. These features arise from coherent interference of electrons that traverse two conduction channels with significantly different transmission coefficients, underscoring the potential of SWNT for on-chip realization of electron optics.

Gate-tunable split Kondo effect in a carbon nanotube quantum dot

We show a detailed investigation of the split Kondo effect in a carbon nanotube quantum dot with multiple gate electrodes. Two conductance peaks, observed at finite bias in nonlinear transport measurements, are found to approach each other for increasing magnetic field, to result in a recovered zero bias Kondo resonance at finite magnetic field. Surprisingly, in the same charge state, but under different gate configurations, the splitting does not disappear for any value of the magnetic field, but we observe an avoided crossing. We think that our observations can be understood in terms of a two-impurity Kondo effect with two spins coupled antiferromagnetically. The exchange coupling between the two spins can be influenced by a local gate, and the non-recovery of the Kondo resonance for certain gate configurations is explained by the existence of a small antisymmetric contribution to the exchange interaction between the two spins.

A molecular quantized charge pump

A novel single electron pump based on individual molecules (a single wall carbon nanotube) is discussed in terms of the hybrid superconducting-normal conducting pumping principle. A concept demonstration device has been built based on a carbon nanotube contacted by Nb-Ti leads. Charge current quantization is achieved through rf modulation of the back gate voltage. The device is able to transfer a given number of electrons per pumping cycle. Single electron pumping is achieved for pumping frequencies up to 80 MHz.

Hybrid superconductor-quantum dot devices

Advances in nanofabrication techniques have made it possible to make devices in which superconducting electrodes are connected to non-superconducting nanostructures such as quantum dots. The properties of these hybrid devices result from a combination of a macroscopic quantum phenomenon involving large numbers of electrons (superconductivity) and the ability to control single electrons, offered by quantum dots. Here we review research into electron transport and other fundamental processes that have been studied in these devices. We also describe potential applications, such as a transistor in which the direction of a supercurrent can be reversed by adding just one electron to a quantum dot.

Superconducting characteristics of 4-A carbon nanotube-zeolite composite

We have fabricated nanocomposites consisting of 4-A carbon nanotubes embedded in the 0.7-nm pores of aluminophosphate-five (AFI) zeolite that display a superconducting specific heat transition at 15 K. MicroRaman spectra of the samples show strong and spatially uniform radial breathing mode (RBM) signals at 510 cm(-1) and 550 cm(-1), characteristic of the (4, 2) and (5, 0) nanotubes, respectively. The specific heat transition is suppressed at >2 T, with a temperature dependence characteristic of finite-size effects. Comparison with theory shows the behavior to be consistent with that of a type II BCS superconductor, characterized by a coherence length of 14 +/- 2 nm and a magnetic penetration length of 1.5 +/- 0.7 mum. Four probe and differential resistance measurements have also indicated a superconducting transition initiating at 15 K, but the magnetoresistance data indicate the superconducting network to be inhomogeneous, with a component being susceptible to magnetic fields below 3 T and other parts capable of withstanding a magnetic field of 5 T or beyond.

Gate-tunable dissipation and "superconductor-insulator" transition in carbon nanotube josephson junctions

Dissipation is ubiquitous in quantum systems, and its interplay with fluctuations is critical to maintaining quantum coherence. We experimentally investigate the dissipation dynamics in single-walled carbon nanotubes coupled to superconductors. The voltage-current characteristics display gate-tunable hysteresis, with sizes that perfectly correlate with the normal state resistance R_{N}, indicating the junction undergoes a periodic modulation between the underdamped and overdamped regimes. Surprisingly, when a device's Fermi level is tuned through a local conductance minimum, we observe a gate-controlled transition from superconductinglike to insulatinglike states, with a "critical" R_{N} value approximately 8-20 kOmega.

Controlled fabrication and electrical properties of long quasi-one-dimensional superconducting nanowire arrays

We report a general method for reliably fabricating quasi-one-dimensional superconducting nanowire arrays, with good control over nanowire cross section and length, and with full compatibility with device processing methods. We investigate Nb nanowires with individual nanowire cross sectional areas that range from bulklike to 10 x 11 nm, and with lengths from 1 to 100 microm. Nanowire size effects are systematically studied. In particular, a comprehensive investigation of influence of nanowire length on superconductivity is reported for the first time. All results are interpreted within the context of phase-slip models.

Corrected Article: "ac response of a carbon chain under a finite frequency bias" [J. Chem. Phys. 127, 104701 (2007)]

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atomic chain connected by two semi-infinite aluminum leads, Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level, while far away from the resonance, the large enhancement of the dynamic conductance was observed. These behaviors can be understood well under the wide-band limit. By changing the coupling distance between the carbon atom and the aluminum leads, the system could change its transport response between capacitivelike and inductivelike.

Dirac fermions and conductance oscillations in s- and d-wave superconductor-graphene junctions

We investigate quantum transport in a normal-superconductor graphene heterostructure, including the possibility of an anisotropic pairing potential in the superconducting region. We find that under certain circumstances, the conductance displays an undamped, oscillatory behavior as a function of applied bias voltage. Also, we investigate how the conductance spectra are affected by a d-wave pairing symmetry. These results combine unusual features of the electronic structure of graphene with the unconventional pairing symmetry found for instance in high-Tc superconductors.

Even-odd effect in Andreev transport through a carbon nanotube quantum dot

We have measured the current (I)-voltage (V) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance dI/dV due to the Kondo resonance is observed in the normal state, this feature around zero-bias voltage is absent in the superconducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the dI/dV subgap structure caused by Andreev reflection. The first-order Andreev peak appearing around V=Delta/e is markedly enhanced in gate-voltage regions, in which the charge state of the quantum dot is odd. This enhancement is explained by a "hidden" Kondo resonance, pinned to one contact only. A comparison with a single-impurity Anderson model, which is solved numerically in a slave-boson mean-field approach, yields good agreement with the experiment.

ac response of a carbon chain under a finite frequency bias

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atom chain connected by two semi-infinite aluminum leads Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level while far away from the resonance the giant enhancement of the dynamic conductance was also observed. These behaviors can be well understood under the wide-band limit. By changing the coupling distance between the carbon atom and aluminum leads, the system could change its transport response between capacitivelike and inductivelike.

Gate-controlled superconductivity in a diffusive multiwalled carbon nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of an Al/Ti sandwich structure. We find proximity-induced superconductivity with measured critical currents up to I(cm)=1.3 nA, tunable by the gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as R(0) proportional to I(cm){-alpha} with alpha=0.74. Using IV characteristics of junctions with phase diffusion, a good agreement is obtained with the Josephson coupling energy in the long, diffusive junction model of A. D. Zaikin and G. F. Zharkov [Sov. J. Low Temp. Phys. 7, 184 (1981)].

Interaction-induced renormalization of Andreev reflection

We analyze the charge transport between a one-dimensional weakly interacting electron gas and a superconductor within the scaling approach in the basis of scattering states. We derive the renormalization group equations, which fully account for the intrinsic energy dependence due to Andreev reflection. A strong renormalization of the corresponding reflection phase is predicted even for a perfectly transparent metal-superconductor interface. The interaction-induced suppression of the Andreev conductance is shown to be highly sensitive to the normal-state resistance, providing a possible explanation of experiments with carbon-nanotube/superconductor junctions by Morpurgo et al. [Science 286, 263 (1999)].

Specular Andreev reflection in graphene

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wavelengths at the two sides of the interface; and, most fundamentally: (3) away from normal incidence the reflection angle may be the same as the angle of incidence (retroreflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wavelength in the normal region is large compared to the superconducting coherence length.

Electron transport in single-wall carbon nanotube weak links in the Fabry-Perot regime

We fabricated reproducible high transparency superconducting contacts consisting of superconducting Ti/Al/Ti trilayers to gated single-wall carbon nanotubes. The reported semiconducting single-wall carbon nanotubes have normal state differential conductance up to 3e2/h and exhibit clear Fabry-Perot interference patterns in the bias spectroscopy plot. We observed subharmonic gap structure in the differential conductance and a distinct peak in the conductance at zero bias, which is interpreted as a manifestation of the supercurrent. The gate dependence of this supercurrent as well as the excess current are examined and compared to the coherent theory of superconducting quantum point contacts with good agreement.

Superconductivity in entirely end-bonded multiwalled carbon nanotubes

We report that entirely end-bonded multiwalled carbon nanotubes (MWNTs) can exhibit superconductivity with a transition temperature (T(c)) as high as 12 K, which is approximately 30 times greater than T(c) reported for ropes of single-walled nanotubes. We find that the emergence of this superconductivity is highly sensitive to the junction structures of the Au electrode/MWNTs. This reveals that only MWNTs with optimal numbers of electrically activated shells, which are realized by end bonding, can allow superconductivity due to intershell effects.

Quantum supercurrent transistors in carbon nanotubes

Electronic transport through nanostructures is greatly affected by the presence of superconducting leads. If the interface between the nanostructure and the superconductors is sufficiently transparent, a dissipationless current (supercurrent) can flow through the device owing to the Josephson effect. A Josephson coupling, as measured by the zero-resistance supercurrent, has been obtained using tunnel barriers, superconducting constrictions, normal metals and semiconductors. The coupling mechanisms vary from tunnelling to Andreev reflection. The latter process has hitherto been observed only in normal-type systems with a continuous density of electronic states. Here we investigate a supercurrent flowing through a discrete density of states-that is, the quantized single particle energy states of a quantum dot, or 'artificial atom', placed between superconducting electrodes. For this purpose, we exploit the quantum properties of finite-sized carbon nanotubes. By means of a gate electrode, successive discrete energy states are tuned on- and off-resonance with the Fermi energy in the superconducting leads, resulting in a periodic modulation of the critical current and a non-trivial correlation between the conductance in the normal state and the supercurrent. We find, in good agreement with existing theory, that the product of the critical current and the normal state resistance becomes an oscillating function, in contrast to being constant as in previously explored regimes.

Many-body effects in finite metallic carbon nanotubes

The nonhomogeneity of the charge distribution in a carbon nanotube leads to the formation of an excitonic resonance, in a way similar to the one observed in x-ray absorption in metals. As a result, a positive anomaly at low bias appears in the tunneling density of states. This effect depends on the screening of the electron-electron interactions by metallic gates, and it modifies the coupling of the nanotube to normal and superconducting electrodes.

Insulating, superconducting, and large-compressibility phases in nanotube ropes

The superconducting properties of carbon nanotube ropes are studied using a new computational framework that incorporates the renormalization of intratube interactions and the effect of intertube Coulomb screening. This method allows one to study both the limits of thin and thick ropes ranging from purely one-dimensional physics to the setting of 3D Cooper-pair coherence, providing good estimates of the critical temperature as a function of the rope physical parameters. We discuss the connection of our results with recent experiments.

Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction

Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature or voltage dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.

Quantum dot in the Kondo regime coupled to superconductors

The Kondo effect and superconductivity are both prime examples of many-body phenomena. Here we report transport measurements on a carbon nanotube quantum dot coupled to superconducting leads that show a delicate interplay between both effects. We demonstrate that the superconductivity of the leads does not destroy the Kondo correlations on the quantum dot when the Kondo temperature, which varies for different single-electron states, exceeds the superconducting gap energy.

Quantum entanglement in carbon nanotubes

With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states-the gapped BCS superconductor and the Luttinger liquid-can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.

ROLE OF DEFECTS IN CARBON NANOTUBE CIRCUITS

We summarize recent results on the impact of defects on the electronic properties of single-wall carbon nanotubes. We probe the influence of defects on electron transport in CNFETs by combined scanning gate microscopy (SGM) and scanning impedance microscopy (SIM). Depletion surface potential of individual defects is quantified from the SGM-imaged defect radius as a function of tip bias voltage. This provides a measure of the Fermi level at the defect with zero tip voltage. In the "off" state, transport is first dominated by barriers at depleted defects. It becomes diffusive as the CNFET is turned on, and finally is quasi-ballistic in the regime of "degenerate electrostatic doping". Metallic nanotubes with good contacts show a metal-to-insulator crossover as the gate voltage is varied. In the metallic state we see quantitative agreement with the "twiston" scattering picture.

Microscopic model of superconductivity in carbon nanotubes

We propose the model of a manifold of one-dimensional interacting electron systems to account for the superconductivity observed in ropes of nanotubes. We rely on the strong suppression of single-particle hopping between neighboring nanotubes in a disordered rope and conclude that the tunneling takes place in pairs of electrons, which are formed within each nanotube due to the existence of large superconducting correlations. Our estimate of the transition temperature is consistent with the values that have been measured experimentally in ropes with about 100 metallic nanotubes.

Quantum phase slips in superconducting nanowires

We have measured the resistance vs temperature of more than 20 superconducting nanowires with nominal widths ranging from 10 to 22 nm and lengths from 100 nm to 1 microm. With decreasing cross-sectional areas, the wires display increasingly broad resistive transitions. The data are in very good agreement with a model that includes both thermally activated phase slips close to T(c) and quantum phase slips (QPS) at low temperatures, but disagree with an earlier model based on a critical value of R(N)/R(q). Our measurements provide strong evidence for QPS in thin superconducting wires.

Consistency of superconducting correlations with one-dimensional electron interactions in carbon nanotubes

We show that a model of interacting electrons in one dimension is able to explain the order of magnitude as well as the temperature dependence of the critical supercurrents recently measured in nanotube samples placed between superconducting contacts. We use bosonization methods to deal with the long-range Coulomb interaction, ending up with a picture in which the critical current does not follow the temperature dependence of the gap in the contacts. Our results also reveal the presence of a short-range attractive interaction in the nanotubes, which accounts for a significant enhancement of the critical supercurrents.

Kondo physics in carbon nanotubes

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.