Evolution of the Kondo effect in a quantum dot probed by shot noise

Shot-noise measurements of single-atom junctions using a scanning tunneling microscope

Current fluctuations related to the discreteness of charge passing through small constrictions are termed shot noise. This unavoidable noise provides both advantages-being a direct measurement of the transmitted particles' charge-and disadvantages-a main noise source in nanoscale devices operating at low temperature. While better understanding of shot noise is desired, the technical difficulties in measuring it result in relatively few experimental works, especially in single-atom structures. Here, we describe a local shot-noise measurement apparatus and demonstrate successful noise measurements through single-atom junctions. Our apparatus, based on a scanning tunneling microscope, operates at liquid helium temperatures. It includes a broadband commercial amplifier mounted in close proximity to the tunnel junction, thus reducing both the thermal noise and input capacitance that limit traditional noise measurements. The full capabilities of the microscope are maintained in the modified system, and a quick transition between different measurement modes is possible.

Homemade-HEMT-based transimpedance amplifier for high-resolution shot-noise measurements

We report a cryogenic transimpedance amplifier (TA) suitable for cross-correlation current-noise measurements. The TA comprises homemade high-electron-mobility transistors with high transconductance and low noise characteristics, fabricated in an AlGaAs/GaAs heterostructure. The low input-referred noise and wide frequency band of the TA lead to a high resolution in current-noise measurements. The TA's low input impedance suppresses unwanted crosstalk between two distinct currents from a sample, justifying the advantage of the TA for cross-correlation measurements. We demonstrate the high resolution of a TA-based experimental setup by measuring the shot noise generated at a quantum point contact in a quantum Hall system.

Three-body correlations in nonlinear response of correlated quantum liquid

Behavior of quantum liquids is a fascinating topic in physics. Even in a strongly correlated case, the linear response of a given system to an external field is described by the fluctuation-dissipation relations based on the two-body correlations in the equilibrium. However, to explore nonlinear non-equilibrium behaviors of the system beyond this well-established regime, the role of higher order correlations starting from the three-body correlations must be revealed. In this work, we experimentally investigate a controllable quantum liquid realized in a Kondo-correlated quantum dot and prove the relevance of the three-body correlations in the nonlinear conductance at finite magnetic field, which validates the recent Fermi liquid theory extended to the non-equilibrium regime.

Recent theory has shown that the non-equilibrium response of a Kondo model can be described by the Fermi liquid theory with three-body correlations. Here, the authors experimentally measure such correlations in the nonlinear conductance of a Kondo-correlated quantum dot.

Cryogenic GaAs high-electron-mobility-transistor amplifier for current noise measurements

We show that a cryogenic amplifier composed of a homemade GaAs high-electron-mobility transistor (HEMT) is suitable for current-noise measurements in a mesoscopic device at dilution-refrigerator temperatures. The lower noise characteristics of our homemade HEMT lead to a lower noise floor in the experimental setup and enable more efficient current-noise measurement than is available with a commercial HEMT. We present the dc transport properties of the HEMT and the gain and noise characteristics of the amplifier. With the amplifier employed for current-noise measurements in a quantum point contact, we demonstrate the high resolution of the measurement setup by comparing it with that of the conventional one using a commercial HEMT.

Fermi Liquid Theory for Nonlinear Transport through a Multilevel Anderson Impurity

We present a microscopic Fermi liquid view on the low-energy transport through an Anderson impurity with N discrete levels, at arbitrary electron filling N_{d}. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to N=6, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range 1≲N_{d}≲N-1. It significantly affects the current noise for N>2 and the behavior of noise in magnetic fields.

Enhanced Shot Noise of Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot in SU(2) and SU(4) Kondo regimes

The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. Our result suggests that the Kondo effect is responsible for this strong enhancement.

Atomic scale shot-noise using cryogenic MHz circuitry

By implementing dedicated cryogenic circuitry operating in the MHz regime, we have developed a scanning tunneling microscope (STM) capable of conventional, low frequency (<10 kHz), microscopy as well spectroscopy and shot-noise detection at 1 MHz. After calibrating our AC circuit on a gold surface, we illustrate our capability to detect shot-noise at the atomic scale and at low currents (<1 nA) by simultaneously measuring the atomically resolved differential conductance and shot-noise on the high temperature superconductor Bi₂Sr₂CaCu₂O_8+x . We further show our direct sensitivity to the temperature of the tunneling electrons at low voltages. Our MHz circuitry opens up the possibility to study charge and correlation effects at the atomic scale in all materials accessible to STM.

Charge Fractionalization in the Two-Channel Kondo Effect

The phenomenon of charge fractionalization describes the emergence of novel excitations with fractional quantum numbers, as predicted in strongly correlated systems such as spin liquids. We elucidate that precisely such an unusual effect may occur in the simplest possible non-Fermi liquid, the two-channel Kondo effect. To bring this concept down to experimental test, we study nonequilibrium transport through a device realizing the charge two-channel Kondo critical point in a recent experiment by Iftikhar et al. [Nature (London) 526, 233 (2015)NATUAS0028-083610.1038/nature15384]. The shot noise at low voltages is predicted to result in a universal Fano factor e^{*}/e=1/2. This allows us to experimentally identify elementary transport processes of emergent fermions carrying half-integer charge.

Noise of a Chargeless Fermi Liquid

We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot-normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in the case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudocharge. In contrast to other correlated Fermi liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, e^{*}=2e. In addition, we find a strong suppression of noise when the linear conductance is unitary, even for its nonlinear part.

Noise of a superconducting magnetic flux sensor based on a proximity Josephson junction

We demonstrate simultaneous measurements of DC transport properties and flux noise of a hybrid superconducting magnetometer based on the proximity effect (superconducting quantum interference proximity transistor, SQUIPT). The noise is probed by a cryogenic amplifier operating in the frequency range of a few MHz. In our non-optimized device, we achieve minimum flux noise ~4 μΦ₀/Hz^1/2, set by the shot noise of the probe tunnel junction. The flux noise performance can be improved by further optimization of the SQUIPT parameters, primarily minimization of the proximity junction length and cross section. Furthermore, the experiment demonstrates that the setup can be used to investigate shot noise in other nonlinear devices with high impedance. This technique opens the opportunity to measure sensitive magnetometers including SQUIPT devices with very low dissipation.

Corrected Kondo temperature beyond the conventional Kondo scaling limit

In the Kondo systems such as the magnetic impurity screened by the conduction electrons in a metal host, as well as the quantum dots connected by the leads, the low energy behaviors have universal dependence on the [Formula: see text] or [Formula: see text], where [Formula: see text] is the conventional Kondo temperature. However, it was shown that this scaling behavior is only valid at low-energy; this is called the Kondo scaling limit. Here we explore the extention of the scaling parameter range by introducing the corrected Kondo temperature T _K, which may depend on the temperature and bias, as well as the other external parameters. We define the corrected Kondo temperature by scaling the local density of states near the Fermi level, obtained by accurate hierarchy of equations of motion approach at finite temperature and finite bias, and thus obtain a phenomenological expression of the corrected Kondo temperature. By using the corrected Kondo temperature as a characteristic energy scale, the conductance of the quantum dot can be well scaled in a wide parameter range, even two orders beyond the conventional scaling parameter range. Our work indicates that the Kondo scaling, although dominated by the conventional Kondo temperature in the low-energy of the Kondo system, could be extended to a higher energy regime, which is useful for analyzing the physics of the Kondo transport in non-equilibrium or high temperature cases.

Lévy flights in an infinite potential well as a hypersingular Fredholm problem

We study Lévy flights with arbitrary index 0<μ≤2 inside a potential well of infinite depth. Such a problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schrödinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain D, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numerically with some analytical results regarding the structure of the spectrum.

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.

Non-Markovian full counting statistics in quantum dot molecules

Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.

Anisotropic charge Kondo effect in a triple quantum dot

We predict that an anisotropic charge Kondo effect appears in a triple quantum dot, when the system has twofold degenerate ground states of (1,1,0) and (0,0,1) charge configurations. Using bosonization and refermionization methods, we find that at low temperature the system has the two different phases of massive charge fluctuations between the two charge configurations and vanishing fluctuations, which are equivalent with the Kondo-screened and ferromagnetic phases of the anisotropic Kondo model, respectively. The phase transition is identifiable by electron conductance measurement, offering the possibility of experimentally exploring the anisotropic Kondo model. Our charge Kondo effect has a similar origin to that in a negative-U Anderson impurity.

Controlling shot noise in double-barrier magnetic tunnel junctions

We demonstrate that shot noise in Fe/MgO/Fe/MgO/Fe double-barrier magnetic tunnel junctions is determined by the relative magnetic configuration of the junction and also by the asymmetry of the barriers. The proposed theoretical model, based on sequential tunneling through the system and including spin relaxation, successfully accounts for the experimental observations for bias voltages below 0.5 V, where the influence of quantum well states is negligible. A weak enhancement of conductance and shot noise, observed at some voltages (especially above 0.5 V), indicates the formation of quantum well states in the middle magnetic layer. The observed results open up new perspectives for a reliable magnetic control of the most fundamental noise in spintronic structures.

Full counting statistics for orbital-degenerate impurity Anderson model with Hund's rule exchange coupling

We study nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling, and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value F(b)=(9M+6)/(5M+4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M=2, using the numerical renormalization group approach.

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.

Measurement of quantum noise in a carbon nanotube quantum dot in the Kondo regime

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies ν of the order or higher than the frequency associated with the Kondo effect k(B)T (K)/h, with TK the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for hν ≈ k(B)T(K) a Kondo effect related singularity at a voltage bias eV ≈ hν, and a strong reduction of this singularity for hν ≈ 3k(B)T(K), in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the nonequilibrium dynamics of many-body phenomena in nanoscale devices.

Nonequilibrium conductance of a nanodevice for small bias voltage

Using nonequilibrium renormalized perturbation theory, we calculate the retarded and lesser self-energies, the spectral density ρ(ω) near the Fermi energy, and the conductance G through a quantum dot as a function of a small bias voltage V, in the general case of electron-hole asymmetry and intermediate valence. The linear terms in ω and V are given exactly in terms of thermodynamic quantities. When the energies necessary to add the first electron (Ed) and the second one (Ed + U) to the quantum dot are not symmetrically placed around the Fermi level, G has a term linear in V if, in addition, either the voltage drop or the coupling to the leads is not symmetric. The effects of temperature are discussed. The results simplify for a symmetric voltage drop, a situation usual in experiment.