Out-of-equilibrium Kondo effect in a mesoscopic device

Quantum Monte Carlo Method in the Steady State

We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.

Feedback lock-in: A versatile multi-terminal measurement system for electrical transport devices

We present the design and implementation of a measurement system that enables parallel drive and detection of small currents and voltages at numerous electrical contacts to a multi-terminal electrical device. This system, which we term a feedback lock-in, combines digital control-loop feedback with software-defined lock-in measurements to dynamically source currents and measure small, pre-amplified potentials. The effective input impedance of each current/voltage probe can be set via software, permitting any given contact to behave as an open-circuit voltage lead or as a virtually grounded current source/sink. This enables programmatic switching of measurement configurations and permits measurement of currents at multiple drain contacts without the use of current preamplifiers. Our 32-channel implementation relies on commercially available digital input/output boards, home-built voltage preamplifiers, and custom open-source software. With our feedback lock-in, we demonstrate differential measurement sensitivity comparable to a widely used commercially available lock-in amplifier and perform efficient multi-terminal electrical transport measurements on twisted bilayer graphene and SrTiO₃ quantum point contacts. The feedback lock-in also enables a new style of measurement using multiple current probes, which we demonstrate on a ballistic graphene device.

Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach

A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical transformation that completely decouples the impurity and bath degrees of freedom. Combining it with Gaussian states, we present a family of many-body states to efficiently encode nontrivial impurity-bath correlations. We demonstrate its successful application to the anisotropic and two-lead Kondo models by studying their spatiotemporal dynamics and universal behavior in the correlations, relaxation times, and the differential conductance. We compare them to previous analytical and numerical results. In particular, we apply our method to study new types of nonequilibrium phenomena that have not been studied by other methods, such as long-time crossover in the ferromagnetic easy-plane Kondo model. The present approach will be applicable to a variety of unsolved problems in solid-state and ultracold-atomic systems.

Voltage Quench Dynamics of a Kondo System

We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. The time-dependent current saturation temperature connects the equilibrium Kondo temperature to a substantially increased value at voltages outside of the linear response. These signatures are directly observable by experiments in the time domain.

Fast probe of local electronic states in nanostructures utilizing a single-lead quantum dot

Transport measurements are powerful tools to probe electronic properties of solid-state materials. To access properties of local electronic states in nanostructures, such as local density of states, electronic distribution and so on, micro-probes utilizing artificial nanostructures have been invented to perform measurements in addition to those with conventional macroscopic electronic reservoirs. Here we demonstrate a new kind of micro-probe: a fast single-lead quantum dot probe, which utilizes a quantum dot coupled only to the target structure through a tunneling barrier and fast charge readout by RF reflectometry. The probe can directly access the local electronic states with wide bandwidth. The probe can also access more electronic states, not just those around the Fermi level, and the operations are robust against bias voltages and temperatures.

Green's functions from real-time bold-line Monte Carlo calculations: spectral properties of the nonequilibrium Anderson impurity model

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

Novel spectral features of nanoelectromechanical systems

Electron transport through a quantum dot or single molecule coupled to a quantum oscillator is studied by the Keldysh nonequilibrium Green's function formalism to obtain insight into the quantum dynamics of the electronic and oscillator degrees of freedom. We tune the electronic level of the quantum dot by a gate voltage, where the leads are kept at zero temperature. Due to the nonequilibrium distribution of the electrons in the quantum dot, the spectral function becomes a function of the gate voltage. Novel spectral features are identified for the ground and excited states of nanomechanical oscillators that can be used to enhance the measurement sensitivity.

Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(1+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.

Relaxation in driven integer quantum Hall edge states

A highly nonthermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al., Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.

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.

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

We measure the current and shot noise in a quantum dot in the Kondo regime to address the nonequilibrium properties of the Kondo effect. By systematically tuning the temperature and gate voltages to define the level positions in the quantum dot, we observe an enhancement of the shot noise as temperature decreases below the Kondo temperature, which indicates that the two-particle scattering process grows as the Kondo state evolves. Below the Kondo temperature, the Fano factor defined at finite temperature is found to exceed the expected value of unity from the noninteracting model, reaching 1.8±0.2.

Out of equilibrium transport through an Anderson impurity: probing scaling laws within the equation of motion approach

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing on the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G(2)(T, V) in order to test several scaling laws. We find that G(2)(T, V)/G(2)(T, 0) is a universal function of both eV/T(K) and T/T(K), T(K) being the Kondo temperature. The effect of an in-plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting Δ, the computed differential conductance peak splitting depends only on Δ/T(K), and for large fields approaches the value of 2Δ. Besides studying the traditional two leads setup, we also consider other configurations that mimic recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as ln(eV/T(K)). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.

Kondo effect in a semiconductor quantum dot with a spin-accumulated lead

We study the Kondo effect in a semiconductor quantum dot in contact with a spin-accumulated lead. The spin accmulation in a nonmagnetic semiconductor is realized by spin injection from a spin-polarized quantum point contact in combination with magnetic focusing, thus creating spin-unbalanced chemical potentials. We demonstrate that the spin splitting of the Kondo densities of states (DOS) for spin-up and spin-down electrons can be controlled by selectively shifting only the spin-up DOS using spin accumulation. We also show the possibility to recover the Kondo effect in a high magnetic field, by compensating for Zeeman splitting by spin accumulation.

Nonequilibrium dephasing in Coulomb blockaded quantum dots

We present a theory of zero-bias anomalies and dephasing rates for a Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage biased source and drain leads. We interpret our results in terms of the statistics of voltage fluctuations in the system.

Universal scaling in nonequilibrium transport through a single channel Kondo dot

Scaling laws and universality play an important role in our understanding of critical phenomena and the Kondo effect. We present measurements of nonequilibrium transport through a single-channel Kondo quantum dot at low temperature and bias. We find that the low-energy Kondo conductance is consistent with universality between temperature and bias and is characterized by a quadratic scaling exponent, as expected for the spin-1/2 Kondo effect. We show that the nonequilibrium Kondo transport measurements are well described by a universal scaling function with two scaling parameters.

Tuning the Kondo effect with a mechanically controllable break junction

We study electron transport through C(60) molecules in the Kondo regime using a mechanically controllable break junction. By varying the electrode spacing, we are able to change both the width and the height of the Kondo resonance, indicating modification of the Kondo temperature and the relative strength of coupling to the two electrodes. The linear conductance as a function of T/T(K) agrees with the scaling function expected for the spin-1/2 Kondo problem. We are also able to tune finite-bias Kondo features which appear at the energy of the first C(60) intracage vibrational mode.

Hanbury Brown-Twiss correlations and noise in the charge transfer statistics through a multiterminal Kondo dot

We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown-Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data.

Multipeak Kondo effect in one- and two-electron quantum dots

We have fabricated a few-electron quantum dot that can be tuned down to zero electrons while maintaining strong coupling to the leads. Using a nearby quantum point contact as a charge sensor, we can determine the absolute number of electrons in the quantum dot. We find several sharp peaks in the differential conductance, occurring at both zero and finite source-drain bias, for the one- and two-electron quantum dot. We attribute the peaks at finite bias to a Kondo effect through excited states of the quantum dot and investigate the magnetic field dependence of these Kondo resonances.

Probing the Kondo density of states in a three-terminal quantum ring

We have measured the Kondo effect in a quantum ring connected to three terminals. In this configuration nonlinear transport measurements allow us to check which lead contributes to the Kondo density of states (DOS) and which does not. The ring geometry allows a fine-tuning of the coupling to each lead through the Aharonov-Bohm effect via application of a magnetic field. When the ring is connected to two strongly and one weakly coupled leads, conductance through the weakly coupled lead provides a direct measurement of the DOS in the Kondo regime. By applying a bias between the two strongly coupled leads, we demonstrate directly the splitting of the out-of-equilibrium Kondo DOS.

Fermi-edge resonance and tunneling in nonequilibrium electron gas

Fermi-edge singularity changes in a nonequilibrium system, acquiring features that reflect the structure of energy distribution. In particular, it splits into several components if the energy distribution exhibits multiple steps. While conventional approaches, such as bosonization, fail to describe the nonequilibrium problem, an exact solution for a generic energy distribution can be obtained with the help of the method of functional determinants. In the case of a split Fermi distribution, the "open loop" part of the Greens function possesses power law singularities. At the same time, the resulting tunneling density of states exhibits broadened peaks centered at Fermi sublevels.

Detection of local-moment formation using the resonant interaction between coupled quantum wires

We study the influence of many-body interactions on the transport characteristics of a pair of quantum wires that are coupled to each other by means of a quantum dot. Under conditions where a local magnetic moment is formed in one of the wires, tunnel coupling to the other gives rise to an associated peak in its density of states, which can be detected directly in a conductance measurement. Our theory is therefore able to account for the key observations in the recent study of T. Morimoto et al. [Appl. Phys. Lett., ()]], and demonstrates that coupled quantum wires may be used as a system for the detection of local magnetic-moment formation.