Scattering theory of current and intensity noise correlations in conductors and wave guides

Thermal Properties of the Superconductor-Quantum Hall Interface

An important route of engineering topological states and excitations is to combine superconductors (SC) with the quantum Hall (QH) effect, and over the past decade, significant progress has been made in this direction. While typical measurements of these states focus on electronic properties, little attention has been paid to the accompanying thermal responses. Here, we examine the thermal properties of the interface between type-II superconducting electrodes and graphene in the QH regime. We use the thermal noise measurement to probe the local electron temperature of the superconductor next to the biased interface. Surprisingly, the measured temperature rise indicates that the superconductor provides a significant thermal conductivity, which is linear in temperature. This suggests electronic heat transport and may be unexpected, because the number of the quasiparticles in the superconductor should be exponentially suppressed. Instead, we attribute the measured electronic heat conductivity to the overlap of the normal states in the vortex cores.

Switching dynamics in Al/InAs nanowire-based gate-controlled superconducting switch

The observation of the gate-controlled supercurrent (GCS) effect in superconducting nanostructures increased the hopes for realizing a superconducting equivalent of semiconductor field-effect transistors. However, recent works attribute this effect to various leakage-based scenarios, giving rise to a debate on its origin. A proper understanding of the microscopic process underlying the GCS effect and the relevant time scales would be beneficial to evaluate the possible applications. In this work, we observed gate-induced two-level fluctuations between the superconducting state and normal state in Al/InAs nanowires (NWs). Noise correlation measurements show a strong correlation with leakage current fluctuations. The time-domain measurements show that these fluctuations have Poissonian statistics. Our detailed analysis of the leakage current measurements reveals that it is consistent with the stress-induced leakage current (SILC), in which inelastic tunneling with phonon generation is the predominant transport mechanism. Our findings shed light on the microscopic origin of the GCS effect and give deeper insight into the switching dynamics of the superconducting NW under the influence of the strong gate voltage.

Noise intensity of a Markov chain

Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the stochastic opening and closing of ion channels and the resulting fluctuations in membrane current. When the microscopic transitions are fast, the macroscopic fluctuations are nearly uncorrelated and can be fully characterized by their mean and noise intensity. We show how, for an arbitrary Markov chain, the noise intensity can be determined from an algebraic equation, based on the transition rate matrix; these results are in agreement with earlier results from the theory of zero-frequency noise in quantum mechanical and classical systems. We demonstrate the validity of the theory using an analytically tractable two-state Markovian dichotomous noise, an eight-state model for a calcium channel subunit (De Young-Keizer model), and Markov models of the voltage-gated sodium and potassium channels as they appear in a stochastic version of the Hodgkin-Huxley model.

Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.

Two-particle time-domain interferometry in the fractional quantum Hall effect regime

Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot interferometers, but almost no quantum interference when transmitted via the propagating states of Mach-Zehnder interferometers. Here, using a novel interferometric approach, we demonstrate that anyons do keep quantum coherence while propagating. Performing two-particle time-domain interference measurements sensitive to the two-particle Hanbury Brown Twiss phase, we find 53 and 60% visibilities for anyons with charges e/5 and e/3. Our results give a positive message for the challenge of performing controlled quantum coherent braiding of anyons.

Coherent and Incoherent Tunneling into Yu-Shiba-Rusinov States Revealed by Atomic Scale Shot-Noise Spectroscopy

The pair breaking potential of individual magnetic impurities in s-wave superconductors generates localized states inside the superconducting gap commonly referred to as Yu-Shiba-Rusinov (YSR) states whose isolated nature makes them promising building blocks for artificial structures that may host Majorana fermions. One of the challenges in this endeavor is to understand their intrinsic lifetime, ℏ/Λ, which is expected to be limited by the inelastic coupling with the continuum thus leading to decoherence. Here we use shot-noise scanning tunneling microscopy to reveal that electron tunneling into superconducting 2H-NbSe_{2} mediated by YSR states is not Poissonian, but ordered as a function of time, as evidenced by a reduction of the noise. Moreover, our data show the concomitant transfer of charges e and 2e, indicating that incoherent single particle and coherent Andreev processes operate simultaneously. From the quantitative agreement between experiment and theory we obtain Λ=1  μeV≪k_{B}T demonstrating that shot noise can probe energy scales and timescales inaccessible by conventional spectroscopy whose resolution is thermally limited.

Scattering theory of non-equilibrium noise and deltaTcurrent fluctuations through a quantum dot

We consider the non-equilibrium zero frequency noise generated by a temperature gradient applied on a device composed of two normal leads separated by a quantum dot. We recall the derivation of the scattering theory for non-equilibrium noise for a general situation where both a bias voltage and a temperature gradient can coexist and put it in a historical perspective. We provide a microscopic derivation of zero frequency noise through a quantum dot based on a tight binding Hamiltonian, which constitutes a generalization of the seminal result obtained for the current in the context of the Keldysh formalism. For a single level quantum dot, the obtained transmission coefficient entering the scattering formula for the non-equilibrium noise corresponds to a Breit-Wigner resonance. We compute the delta-Tnoise as a function of the dot level position, and for a broad range of values of the dot level width, in the Breit-Wigner case, for two relevant situations which were considered recently in two separate experiments. In the regime where the two reservoir temperatures are comparable, our gradient expansion shows that the delta-Tnoise is dominated by its quadratic contribution, and is minimal close to resonance. In the opposite regime where one reservoir is much colder, the gradient expansion fails and we find the noise to be typically linear in temperature before saturating. In both situations, we conclude with a short discussion of the case where both a voltage bias and a temperature gradient are present, in order to address the potential competition with thermoelectric effects.

Thermoelectric Polarization Transport in Ferroelectric Ballistic Point Contacts

We formulate a scattering theory of polarization and heat transport through a ballistic ferroelectric point contact. We predict a polarization current under either an electric field or a temperature difference that depends strongly on the direction of the ferroelectric order and can be detected by its magnetic stray field and associated thermovoltage and Peltier effect.

Higher-Order Fabry-Pérot Interferometer from Topological Hinge States

We propose an intrinsic three-dimensional Fabry-Pérot type interferometer, coined "higher-order interferometer," that is based on the chiral hinge states of second-order topological insulators and cannot be mapped to an equivalent two-dimensional setting because of higher-order topological obstructions. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple frequencies depending on the field strength and direction in a unique fashion. Our novel interferometer thus provides feasible and robust magnetotransport signatures for hinge states of higher-order topological insulators.

Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.

Intrinsic magnetic topological insulators

Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the observed QAHE appears only at ultralow temperatures. Therefore, intrinsic magnetic topological insulators are highly desired for increasing the QAHE working temperature and for investigating topological quantum phenomena further. The realization and characterization of such systems are essential for both fundamental physics and potential technical revolutions. This review summarizes recent research progress in intrinsic magnetic topological insulators, focusing mainly on the antiferromagnetic topological insulator MnBi2Te4 and its family of materials.

Tunneling current and noise of entangled electrons in correlated double quantum dot

We developed general approach for the analysis of tunneling current and its zero frequency noise for a wide class of systems where electron transport occurs through the intermediate structure with localized electrons. Proposed approach opens the possibility to study electron transport through multi-electron correlated states and allows to reveal the influence of spatial and spin symmetry of the total system on the electron transport. This approach is based on Keldysh diagram technique in pseudo-particle representation taking into account the operator constraint on the number of pseudo-particles, which gives the possibility to exclude non-physical states. It was shown that spatial and spin symmetry of the total system can block some channels for electron transport through the correlated quantum dots. Moreover, it was demonstrated that the stationary tunneling current and zero frequency noise in correlated coupled quantum dots depend on initial state of the system. In the frame of the proposed approach it was also shown that for the parallel coupling of two correlated quantum dots to the reservoirs tunneling current and its zero frequency noise are suppressed if tunneling occurs through the entangled triplet state with zero total spin projection on the z axis or enhanced for the tunneling through the singlet state in comparison with electron transport through the uncorrelated localized single-electron state. Obtained results demonstrate that two-electron entangled states in correlated quantum dots give the possibility to tune the zero frequency noise amplitude by blocking some channels for electron transport that is very promising in the sense of two-electron entangled states application in quantum communication and logic devices. The obtained nonmonotonic behavior of Fano factor as a function of applied bias is the direct manifestation of the possibility to control the noise to signal ration in correlated quantum dots. We also provide detailed calculations of current and noise for both single type of carriers and two different types of carriers in the presence and in the absence of Coulomb interaction in Supplementary materials.

Auto- versus Cross-Correlation Noise in Periodically Driven Quantum Coherent Conductors

Expressing currents and their fluctuations at the terminals of a multi-probe conductor in terms of the wave functions of carriers injected into the Fermi sea provides new insight into the physics of electric currents. This approach helps us to identify two physically different contributions to shot noise. In the quantum coherent regime, when current is carried by non-overlapping wave packets, the product of current fluctuations in different leads, the cross-correlation noise, is determined solely by the duration of the wave packet. In contrast, the square of the current fluctuations in one lead, the autocorrelation noise, is additionally determined by the coherence of the wave packet, which is associated with the spread of the wave packet in energy. The two contributions can be addressed separately in the weak back-scattering regime, when the autocorrelation noise depends only on the coherence. Analysis of shot noise in terms of these contributions allows us, in particular, to predict that no individual traveling particles with a real wave function, such as Majorana fermions, can be created in the Fermi sea in a clean manner, that is, without accompanying electron-hole pairs.

Energy Relaxation in Edge Modes in the Quantum Hall Effect

Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one-dimensional ballistic modes was predicted, and experimentally demonstrated, to have a universal value for bosons, fermions, and fractionally charged anyons. A fraction of this value is expected in non-Abelian states; harboring counterpropagating edge modes. In such exotic states, thermal-energy relaxation along the edge is expected, and can shed light on their topological nature. Here, we introduce a novel experimental setup that enables a direct observation of thermal-energy relaxation in chiral 1D edge modes in the quantum Hall effect. Edge modes, emanating from a heated reservoir, are partitioned by a quantum point contact (QPC) constriction, which is located at some distance along their path. The resulting low frequency noise, measured downstream, allows determination of the "effective temperature" of the edge mode at the location of the QPC. An expected, prominent energy relaxation was found in hole-conjugate states. However, relaxation was also observed in particlelike states, where heat is expected to be conserved. We developed a model, consisting of distance-dependent energy loss, which agrees with the observations; however, we cannot exclude energy redistribution mechanisms, which are not accompanied with energy loss.

Magnetic-Field-Dependent Equilibration of Fractional Quantum Hall Edge Modes

Fractional conductance is measured by partitioning a ν=1 edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the ν=1 plateau, respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance e^{2}/3h arising from edge reconstruction. The results reveal a remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing magnetic field.

Transport and thermodynamics in quantum junctions: A scattering approach

We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for quantum transport and reproduces recently obtained results for the quantum thermodynamics of slowly driven systems. Using this approach, new results have been obtained. First, we derived a general explicit expression for the non-equilibrium steady-state density matrix of a system composed of multiple infinite baths coupled through a general interaction. Then, we obtained a general expression for the dissipated power for the driven non-interacting resonant level to the first order in the driving speeds, where both the dot energy level and its couplings are changing, without invoking the wide-band approximation. In addition, we also showed that the symmetric splitting of the system bath interaction, employed for the case of a system coupled to one bath to determine the effective system Hamiltonian [A. Bruch et al., Phys. Rev. B 93, 115318 (2016)], is valid for the multiple bath case as well. Finally, we demonstrated an equivalence of our method to the Landauer-Buttiker formalism and its extension to slowly driven systems developed by Bruch, Lewenkopf, and von Oppen [Phys. Rev. Lett. 120, 107701 (2018)]. To demonstrate the use of this formalism, we analyze the operation of a device in which the dot is driven cyclically between two leads under strong coupling conditions. We also generalize the previously obtained expression for entropy production in such driven processes to the many-bath case.

A One-Dimensional Effective Model for Nanotransistors in Landauer-Büttiker Formalism

In a series of publications, we developed a compact model for nanotransistors in which quantum transport in a variety of industrial nano-FETs was described quantitatively. The compact nanotransistor model allows for the extraction of important device parameters as the effective height of the source-drain barrier, device heating, and the quality of the coupling between conduction channel and the contacts. Starting from a basic description of quantum transport in a multi-terminal device in Landauer–Büttiker formalism, we give a detailed derivation of all relevant formulas necessary to construct our compact nanotransistor model. Here we make extensive use of the the R-matrix method.

Nonequilibrium System as a Demon

Maxwell demons are creatures that are imagined to be able to reduce the entropy of a system without performing any work on it. Conventionally, such a Maxwell demon's intricate action consists of measuring individual particles and subsequently performing feedback. We show that much simpler setups can still act as demons: we demonstrate that it is sufficient to exploit a nonequilibrium distribution to seemingly break the second law of thermodynamics. We propose both an electronic and an optical implementation of this phenomenon, realizable with current technology.

Negative Excess Shot Noise by Anyon Braiding

Anyonic fractional charges e^{*} have been detected by autocorrelation shot noise at a quantum point contact (QPC) between two fractional quantum Hall edges. We find that the autocorrelation noise can also show a fingerprint of Abelian anyonic fractional statistics. We predict the noise of the electrical tunneling current I at the QPC of the fractional-charge detection setup, when anyons are dilutely injected, from an additional edge biased by a voltage, to the setup in equilibrium. At large voltages, the nonequilibrium noise is reduced below the thermal equilibrium noise by the value 2e^{*}I. This negative excess noise is opposite to the positive excess noise 2e^{*}I of the conventional fractional-charge detection and also to the usual positive autocorrelation noises of electrical currents. This is a signature of Abelian fractional statistics, resulting from the effective braiding of an anyon thermally excited at the QPC around another anyon injected from the additional edge.

Quasiparticle states of on-demand coherent electron sources

We introduce a general approach to extract the wave function of quasiparticles from the scattering matrix of a quantum conductor, which offers a unified way to study the features of quasiparticles from on-demand coherent electron sources with different configurations. We first show that the quasiparticles are particle-hole pairs in the Fermi sea, which can be indexed with the flow density [Formula: see text]. Both the excitation probability and the particle/hole components of the quasiparticles can be solely decided from the polar decomposition of the scattering matrix. By using such approach, we then investigate the quasiparticles from the electron sources based on a quantum point contact and a quantum dot (QD). We find that the quasiparticles from different electron sources have different features, which can be seen from the corresponding [Formula: see text]-dependence of the excitation probability and the particle/hole components. We further show that these features can also be characterized by the full counting statistics of the quasiparticles, which can be approximated by a binomial distribution with cumulant generating function [Formula: see text]. For the quantum-point-contact-based electron sources, both [Formula: see text] and [Formula: see text] are monotonically increasing functions of the driving strength. In contrast, for the quantum-dot-based electron sources, both [Formula: see text] and [Formula: see text] can exhibit oscillations, which can be attributed to the interplay between the charge excitation and charge relaxation processes in the QD.

Impact of secondary electron emission noise in SEM

In semiconductor-device inspection using scanning electron microscopes (SEMs), the irradiation dose of the electron beam becomes lower because of increasing needs for higher throughput and lower damage to the samples. Therefore, it is necessary to form images using fewer primary electrons, making noise reduction of SEM images one of the main challenges. We have modeled the imaging process of SEMs, which consists of the generation of primary, secondary and tertiary electrons (PEs, SEs and TEs, respectively), and detection. Furthermore, a method to accurately evaluate the fluctuation in the number of SEs and TEs are proposed. We found that SEM-image noise can be minimized by directly detecting SEs generated in the sample, in which case the fluctuation in the number of SEs determines the image quality. The variance number of SEs emitted from a 500-eV PE irradiation onto a Si wafer is 1.9 times as large as the value derived assuming a Poisson process. A Monte-Carlo simulation result was used to explain the experimental results and predict that PE energy less than 1 keV suppresses the fluctuation in the number of SEs, and consequently, the SEM-image noise level. These findings provide a method for determining imaging conditions that improve the throughput of SEMs.

Magnetic Moments and Electron Transport through Chromium-Based Antiferromagnetic Nanojunctions

We report the electronic, magnetic and transport properties of a prototypical antiferromagnetic (AFM) spintronic device. We chose Cr as the active layer because it is the only room-temperature AFM elemental metal. We sandwiched Cr between two non-magnetic metals (Pt or Au) with large spin-orbit coupling. We also inserted a buffer layer of insulating MgO to mimic the structure and finite resistivity of a real device. We found that, while spin-orbit has a negligible effect on the current flowing through the device, the MgO layer plays a crucial role. Its effect is to decouple the Cr magnetic moment from Pt (or Au) and to develop an overall spin magnetization. We have also calculated the spin-polarized ballistic conductance of the device within the Büttiker⁻Landauer framework, and we have found that for small applied bias our Pt/Cr/MgO/Pt device presents a spin polarization of the current amounting to ≃25%.

Unified Thermodynamic Uncertainty Relations in Linear Response

Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here, we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including, e.g., ballistic transport and periodically driven classical and quantum systems. We find that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics, it reveals a connection between the TUR and current fluctuation theorems.

Theory of electron, phonon and spin transport in nanoscale quantum devices

At the level of fundamental science, it was recently demonstrated that molecular wires can mediate long-range phase-coherent tunnelling with remarkably low attenuation over a few nanometre even at room temperature. Furthermore, a large mean free path has been observed in graphene and other graphene-like two-dimensional materials. These create the possibility of using quantum and phonon interference to engineer electron and phonon transport through nanoscale junctions for a wide range of applications such as molecular switches, sensors, piezoelectricity, thermoelectricity and thermal management. To understand transport properties of such devices, it is crucial to calculate their electronic and phononic transmission coefficients. The aim of this tutorial article is to outline the basic theoretical concepts and review the state-of-the-art theoretical and mathematical techniques needed to treat electron, phonon and spin transport in nanoscale molecular junctions. This helps not only to explain new phenomenon observed experimentally but also provides a vital design tool to develop novel nanoscale quantum devices.

Anomalous Nonlinear Shot Noise at High Voltage Bias

Since the work of Walter Schottky, it is known that the shot-noise power for a completely uncorrelated set of electrons increases linearly with the time-averaged current. At zero temperature and in the absence of inelastic scattering, the linearity relation between noise power and average current is quite robust, in many cases even for correlated electrons. Through high-bias shot-noise measurements on single Au atom point contacts, we find that the noise power in the high-bias regime shows highly nonlinear behavior even leading to a decrease in shot noise with voltage. We explain this nonlinearity using a model based on quantum interference of electron waves with varying path difference due to scattering from randomly distributed defect sites in the leads, which makes the transmission probability for these electrons both energy and voltage dependent.

Landauer-Büttiker Approach to Strongly Coupled Quantum Thermodynamics: Inside-Outside Duality of Entropy Evolution

We develop a Landauer-Büttiker theory of entropy evolution in time-dependent, strongly coupled electron systems. The formalism naturally avoids the problem of the system-bath distinction by defining the entropy current in the attached leads. This current can then be used to infer changes of the entropy of the system which we refer to as the inside-outside duality. We carry out this program in an adiabatic expansion up to first order beyond the quasistatic limit. When combined with particle and energy currents, as well as the work required to change an external potential, our formalism provides a full thermodynamic description, applicable to arbitrary noninteracting electron systems in contact with reservoirs. This provides a clear understanding of the relation between heat and entropy currents generated by time-dependent potentials and their connection to the occurring dissipation.

Spin Current Noise of the Spin Seebeck Effect and Spin Pumping

We theoretically investigate the fluctuation of a pure spin current induced by the spin Seebeck effect and spin pumping in a normal-metal-(NM-)ferromagnet(FM) bilayer system. Starting with a simple ferromagnet-insulator-(FI-)NM interface model with both spin-conserving and non-spin-conserving processes, we derive general expressions of the spin current and the spin-current noise at the interface within second-order perturbation of the FI-NM coupling strength, and estimate them for a yttrium-iron-garnet-platinum interface. We show that the spin-current noise can be used to determine the effective spin carried by a magnon modified by the non-spin-conserving process at the interface. In addition, we show that it provides information on the effective spin of a magnon, heating at the interface under spin pumping, and spin Hall angle of the NM.

Electronic conduction during the formation stages of a single-molecule junction

Single-molecule junctions are versatile test beds for electronic transport at the atomic scale. However, not much is known about the early formation steps of such junctions. Here, we study the electronic transport properties of premature junction configurations before the realization of a single-molecule bridge based on vanadocene molecules and silver electrodes. With the aid of conductance measurements, inelastic electron spectroscopy and shot noise analysis, we identify the formation of a single-molecule junction in parallel to a single-atom junction and examine the interplay between these two conductance pathways. Furthermore, the role of this structure in the formation of single-molecule junctions is studied. Our findings reveal the conductance and structural properties of premature molecular junction configurations and uncover the different scenarios in which a single-molecule junction is formed. Future control over such processes may pave the way for directed formation of preferred junction structures.

Quantum fluctuations of entropy production for fermionic systems in the Landauer-Büttiker state

The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Büttiker nonequilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analyzed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with nonvanishing probability. In spite of this fact, we show that all odd moments (in particular, the mean value of the entropy production) of the above distribution are non-negative. This result extends the second principle of thermodynamics to the quantum fluctuations of the entropy production in the Landauer-Büttiker state. The effect of the time reversal is also discussed.

Quantum Coherent Multielectron Processes in an Atomic Scale Contact

The light emission from a scanning tunneling microscope operated on a Ag(111) surface at 6 K is analyzed from low conductances to values approaching the conductance quantum. Optical spectra recorded at sample voltages V reveal emission with photon energies hν>2eV. A model of electrons interacting coherently via a localized plasmon-polariton mode reproduces the experimental data, in particular, the kinks in the spectra at eV and 2eV as well as the scaling of the intensity at low and intermediate conductances.

Detection of Majorana Kramers Pairs Using a Quantum Point Contact

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of π across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. Such a switching of the current represents a qualitative signature where multiterminal differential conductances oscillate with alternating signs when the external magnetic field is tuned. We show that this qualitative signature is also present in current cross-correlations. Thus, the change of the backscattering current nature affects both conductance and shot noise, the measurement of which offers a significant advantage over quantitative signatures such as conductance quantization in realistic measurements.

Current Correlations from a Mesoscopic Anyon Collider

Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially. While current correlations for fermions vanish, negative correlations for anyons are a clear signature of a reduced spatial exclusion as compared to fermions.

Coexistence of perfect spin filtering for entangled electron pairs and high magnetic storage efficiency in one setup

For Entangled electron pairs superconducting spintronics, there exist two drawbacks in existing proposals of generating entangled electron pairs. One is that the two kinds of different spin entangled electron pairs mix with each other. And the other is a low efficiency of entanglement production. Herein, we report the spin entanglement state of the ferromagnetic insulator (FI)/s-wave superconductor/FI structure on a narrow quantum spin Hall insulator strip. It is shown that not only the high production of entangled electron pairs in wider energy range, but also the perfect spin filtering of entangled electron pairs in the context of no highly spin-polarized electrons, can be obtained. Moreover, the currents for the left and right leads in the antiferromagnetic alignment both can be zero, indicating 100% tunnelling magnetoresistance with highly magnetic storage efficiency. Therefore, the spin filtering for entangled electron pairs and magnetic storage with high efficiencies coexist in one setup. The results may be experimentally demonstrated by measuring the tunnelling conductance and the noise power.

Shot Noise of 1,4-Benzenedithiol Single-Molecule Junctions

We report measurements of the shot noise on single-molecule Au-1,4-benzenedithiol-Au junctions, fabricated with the mechanically controllable break junction (MCBJ) technique at 4.2 K in a wide range of conductance values from 10(-2) to 0.24 conductance quanta. We introduce a simple measurement scheme using a current amplifier and a spectrum analyzer and that does not imply special requirements regarding the electrical leads. The experimental findings provide evidence that the current is carried by a single conduction channel throughout the whole conductance range. This observation suggests that the number of channels is limited by the Au-thiol bonds and that contributions due to direct tunneling from the Au to the π-system of the aromatic ring are negligible also for high conductance. The results are supported by quantum transport calculations using density functional theory.

Charge of a quasiparticle in a superconductor

Nonlinear charge transport in superconductor-insulator-superconductor (SIS) Josephson junctions has a unique signature in the shuttled charge quantum between the two superconductors. In the zero-bias limit Cooper pairs, each with twice the electron charge, carry the Josephson current. An applied bias VSD leads to multiple Andreev reflections (MAR), which in the limit of weak tunneling probability should lead to integer multiples of the electron charge ne traversing the junction, with n integer larger than 2Δ/eVSD and Δ the superconducting order parameter. Exceptionally, just above the gap eVSD ≥ 2Δ, with Andreev reflections suppressed, one would expect the current to be carried by partitioned quasiparticles, each with energy-dependent charge, being a superposition of an electron and a hole. Using shot-noise measurements in an SIS junction induced in an InAs nanowire (with noise proportional to the partitioned charge), we first observed quantization of the partitioned charge q = e*/e = n, with n = 1-4, thus reaffirming the validity of our charge interpretation. Concentrating next on the bias region eVSD ~ 2Δ, we found a reproducible and clear dip in the extracted charge to q ~ 0.6, which, after excluding other possibilities, we attribute to the partitioned quasiparticle charge. Such dip is supported by numerical simulations of our SIS structure.

The Mesoscopic Electrochemistry of Molecular Junctions

Within the context of an electron dynamic (time-dependent) perspective and a voltage driving force acting to redistribute electrons between metallic and addressable molecular states, we define here the associated electron admittance and conductance. We specifically present a mesoscopic approach to resolving the electron transfer rate associated with the electrochemistry of a redox active film tethered to metallic leads and immersed in electrolyte. The methodology is centred on aligning the lifetime of the process of electron exchange with associated resistance and capacitance quantities. Notably, however, these are no longer those empirically known as charge transfer resistance and pseudo-capacitance, but are those derived instead from a consideration of the quantum states contained in molecular films and their accessibility through a scattering region existing between them and the metallic probe. The averaged lifetime (τr) associated with the redox site occupancy is specifically dependent on scattering associated with the quantum channels linking them to the underlying metallic continuum and associated with both a quantum resistance (Rq) and an electrochemical (redox) capacitance (Cr). These are related to electron transfer rate through k = 1/τr = (RqCr)(-1). The proposed mesoscopic approach is consistent with Marcus's (electron transfer rate) theory and experimental measurements obtained by capacitance spectroscopy.

What can we learn from noise? - Mesoscopic nonequilibrium statistical physics

Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.

Entanglement discrimination in multi-rail electron-hole currents

We propose a quantum-Hall interferometer that integrates an electron-hole entangler with an analyzer working as an entanglement witness by implementing a multi-rail encoding. The witness has the ability to discriminate (and quantify) spatial-mode and occupancy entanglement. This represents a feasible alternative to limited approaches based on the violation of Bell-like inequalities.

Shot Noise of Charge and Spin Current of a Quantum Dot Coupled to Semiconductor Electrodes

On the basis of the scattering matrix theory and nonequilibrium green function method, we have investigated the fluctuations of charge and spin current of the systems that consist of a quantum dot (QD) with a resonant level coupled to two semiconductor contacts within in alternative site (AS) and alternative bond (AB) framework, where two transverse (Bx) and longitudinal (Bz) magnetic fields are applied to the QD. It is only necessary to use the autocorrelation function to characterize the fluctuations of charge current for a twoterminal system because of the relation that is defined as Σα e Sαβ = Σβ e Sαβ = 0. Our result shows that both auto-shot noise (SLL) and cross-shot noise (SLR) are essential to characterize the fluctuations of spin current when Bx is present. Moreover, our model calculations show that the sign of the cross-shot noise of spin current is negative for all surface states of AS/QD/AS junctions, whereas it oscillates between positive and negative values for two surface states of AB/QD/AB junctions as we sweep the gate voltage.

Time-dependent exchange and tunneling: detection at the same place of two electrons emitted simultaneously from different sources

Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each side of a barrier. After impinging upon a tunneling barrier, each wave packet splits into transmitted and reflected components. When the initial two-particle anti-symmetrical state is defined as a Slater determinant of any type of (normalizable) one-particle wave packet, it is shown that the probability of detecting two (identically injected) electrons at the same side of the barrier is different from zero in very common (single or double barrier) scenarios. In some particular scenarios, the transmitted and reflected components become orthogonal and the mentioned probabilities reproduce those values associated to distinguishable particles. These unexpected non-zero probabilities are still present when non-separable Coulomb interaction or non-symmetrical potentials are considered. On the other hand, for initial wave packets close to Hamiltonian eigenstates, the usual zero two-particle probability for electrons at the same side of the barrier found in the literature is recovered. The generalization to many-particle scattering probabilities with quasi-particle wave packets for low and high phase-space density are also analyzed. The far-reaching consequences of these non-zero probabilities in the accurate evaluation of quantum noise in mesoscopic systems are briefly indicated.

Magnetoconductance of the Corbino disk in graphene: chiral tunneling and quantum interference in the bilayer case

Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, using the mode-matching method to give an effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Rycerz 2010 Phys. Rev. B 81 121404; Katsnelson 2010 Europhys. Lett. 89 17001), conductance at the Dirac point shows oscillations with the flux piercing the disk area ΦD characterized by the period Φ(0) = 2 (h/e) ln(R(o)/R(i)), where R(o)(R(i)) is the outer (inner) disk radius. The oscillation magnitude depends either on the radii ratio or on the physical disk size, with the condition for maximal oscillations being R(o)/R(i) ≃ [ Rit⊥/(2ℏvF) ](4/p) (for R(o)/R(i) ≫ 1), where t⊥ is the interlayer hopping integral, vF is the Fermi velocity in graphene, and p is an even integer. Odd-integer values of p correspond to vanishing oscillations for the normal Corbino setup, or to oscillation frequency doubling for the Andreev-Corbino setup. At higher Landau levels, magnetoconductance behaves almost identically in the monolayer and bilayer cases. A brief comparison with the Corbino disk in a two-dimensional electron gas is also provided in order to illustrate the role of chiral tunneling in graphene.

Shot noise variation within ensembles of gold atomic break junctions at room temperature

Atomic-scale junctions are a powerful tool to study quantum transport, and are frequently examined through the mechanically controllable break junction technique. The junction-to-junction variation of atomic configurations often leads to a statistical approach, with ensemble-averaged properties providing access to the relevant physics. However, the full ensemble contains considerable additional information. We report a new analysis of shot noise over entire ensembles of junction configurations using scanning tunneling microscope-style gold break junctions at room temperature in ambient conditions, and compare these data with simulations based on molecular dynamics, a sophisticated tight-binding model, and nonequilibrium Green's functions. The experimental data show a suppression in the variation of the noise near conductances dominated by fully transmitting channels, and a surprising participation of multiple channels in the nominal tunneling regime. Comparison with the simulations, which agree well with published work at low temperatures and ultrahigh vacuum conditions, suggests that these effects likely result from surface contamination and disorder in the electrodes. We propose additional experiments that can distinguish the relative contributions of these factors.

Absorption and injection models for open time-dependent quantum systems

In the time-dependent simulation of pure states dealing with transport in open quantum systems, the initial state is located outside of the active region of interest. Using the superposition principle and the analytical knowledge of the free time evolution of such a state outside the active region, together with absorbing layers and remapping, a model for a very significant reduction of the computational burden associated with the numerical simulation of open time-dependent quantum systems is presented. The model is specially suited to study (many-particle and high-frequency effects) quantum transport, but it can also be applied to any other research field where the initial time-dependent pure state is located outside of the active region. From numerical simulations of open quantum systems described by the (effective mass) Schrödinger and (atomistic) tight-binding equations, a reduction of the computational burden of about two orders of magnitude for each spatial dimension of the domain with a negligible error is presented.

Enhanced noise at high bias in atomic-scale Au break junctions

Heating in nanoscale systems driven out of equilibrium is of fundamental importance, has ramifications for technological applications, and is a challenge to characterize experimentally. Prior experiments using nanoscale junctions have largely focused on heating of ionic degrees of freedom, while heating of the electrons has been mostly neglected. We report measurements in atomic-scale Au break junctions, in which the bias-driven component of the current noise is used as a probe of the electronic distribution. At low biases (<150 mV) the noise is consistent with expectations of shot noise at a fixed electronic temperature. At higher biases, a nonlinear dependence of the noise power is observed. We consider candidate mechanisms for this increase, including flicker noise (due to ionic motion), heating of the bulk electrodes, nonequilibrium electron-phonon effects, and local heating of the electronic distribution impinging on the ballistic junction. We find that flicker noise and bulk heating are quantitatively unlikely to explain the observations. We discuss the implications of these observations for other nanoscale systems, and experimental tests to distinguish vibrational and electron interaction mechanisms for the enhanced noise.

Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature

The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a 1±cosϕ dependence on the phase difference ϕ of the superconductors from which the excitations originated (with the ± sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent.