During the last years there has been an increasing excitement in nanomotors and particularly in current-driven nanomotors. Despite the broad variety of stimulating results found, the regime of strong Coulomb interactions has not been fully explored for this application. Here we consider nanoelectromechanical devices composed by a set of coupled quantum dots interacting with mechanical degrees of freedom taken in the adiabatic limit and weakly coupled to electronic reservoirs. We use a real-time diagrammatic approach to derive general expressions for the current-induced forces, friction coefficients, and zero-frequency force noise in the Coulomb blockade regime of transport. We prove our expressions accomplish with Onsager's reciprocity relations and the fluctuation-dissipation theorem for the energy dissipation of the mechanical modes. The obtained results are illustrated in a nanomotor consisting of a double quantum dot capacitively coupled to some rotating charges. We analyze the dynamics and performance of the motor as function of the applied voltage and loading force for trajectories encircling different triple points in the charge stability diagram.
We study the relation between quantum pumping of charge and the work exchanged with the driving potentials in a strongly interacting ac-driven quantum dot. We work in the large-interaction limit and in the adiabatic pumping regime, and we develop a treatment that combines the time-dependent slave-boson approximation with linear response in the rate of change of the ac-potentials. We find that the time evolution of the system can be described in terms of equilibrium solutions at every time. We analyze the effect of the electronic interactions on the performance of the dot when operating as a qu…
We investigate gain in microwave photonic cavities coupled to voltage-biased double quantum dot systems with an arbitrary strong dot-lead coupling and with a Holstein-like light-matter interaction, by adapting the diagrammatic Keldysh nonequilibrium Green's function approach. We compute out-of-equilibrium properties of the cavity : its transmission, phase response, mean photon number, power spectrum, and spectral function. We show that by the careful engineering of these hybrid light-matter systems, one can achieve a significant amplification of the optical signal with the voltage-biased elect…
We investigate the second-order von Neumann approach from a diagrammatic point-of-view and demonstrate its equivalence with the resonant tunneling approximation. Investigation of higher-order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough co…
The time evolution of a quantum dot exciton in Coulomb interaction with wetting layer carriers is treated using an approach similar to the independent boson model. The role of the polaronic unitary transform is played by the scattering matrix, for which a diagrammatic, linked cluster expansion is available. Similarities and differences to the independent boson model are discussed. A numerical example is presented.
A large-N diagrammatic approach is used to study coupled quantum dots in a parallel geometry. We show that the Friedel sum rule (FSR) holds at lowest order in a 1/N expansion for this system, thereby suggesting that the ground state is a Fermi liquid. Using the FSR together with the dot occupancy, we compute the dot system's conductance. Our finding that the 1/N expansion indicates the system is a Fermi liquid is in agreement with both prior results based on the Bethe ansatz and slave boson mean field theory.
We propose schemes for generating spin currents into a semiconductor by adiabatic or non-adiabatic pumping of electrons through interacting quantum dots. The appeal of such schemes lies in the possibility to tune the pumping characteristics via gate voltages that control the properties of the quantum dot. The calculations are based on a systematic perturbation expansion in the tunnel-coupling strength and the pumping frequency, expressed within a diagrammatic real-time technique. Special focus is put on the possibility of pure spin pumping, i.e., of pumping spin currents without charge current…
We study adiabatic pumping through a two-level quantum dot with spin-orbit coupling. Using a diagrammatic real-time approach, we calculate both the pumped charge and spin for a periodic variation of the dot's energy levels in the limit of weak tunnel coupling. Thereby, we compare the two limits of vanishing and infinitely large charging energy on the quantum dot. We discuss the dependence of the pumped charge and pumped spin on gate voltages, the symmetry in the tunnel-matrix elements and spin-orbit coupling strength. We identify the possibility to generate pure spin currents in the absence of…
We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics (FCS). Using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data the formalism is shown to capture the basic properties of the st…
Weak localization correction to the density of transmission eigenvalues in the presence of magnetic field and spin-orbit coupling for a chaotic quantum dot
The transient response of a quantum dot with strong Coulomb interaction to a fast change in the gate potential, as well as the stationary ac-response to a slow harmonic variation of the gate potential are computed by means of a real-time diagrammatic expansion in the tunnel-coupling strength. We find that after a fast switching, the relaxation of charge and spin are governed by a single time constant each, which differ from each other due to Coulomb repulsion. We compare the response to a step potential with the $RC$ time extracted from the ac response.
We investigate the linear ac-conductance for tunneling through an arbitrary interacting quantum dot in the presence of a finite dc-bias. In analogy to the well-known Meir-Wingreen formula for the dc case, we are able to derive a general formula for the ac-conductance. It can be expressed entirely in terms of local correlations on the quantum dot, in the form of a Keldysh block diagram with four external legs. We illustrate the use of this formula as a starting point for diagrammatic calculations by considering the ac-conductance of the noninteracting resonant level model and deriving the resul…
We calculate the nonequilibrium local density of states on a vibrational quantum dot coupled to two electrodes at T=0 using a numerically exact diagrammatic Monte Carlo method. Our focus is on the interplay between the electron-phonon interaction strength and the bias voltage. We find that the spectral density exhibits a significant voltage dependence if the voltage window includes one or more phonon sidebands. A comparison with well-established approximate approaches indicates that this effect could be attributed to the nonequilibrium distribution of the phonons. Moreover, we discuss the long…
We consider a three-terminal system consisting of a quantum dot strongly coupled to two superconducting reservoirs in the infinite gap limit and weakly coupled to a normal metal. Using a real-time diagrammatic approach, we calculate the dynamics of the proximity-induced pair amplitude on the quantum dot. We find that after a quench the pair amplitude shows pronounced oscillations with a frequency determined by the coupling to the superconductors. In addition, it decays exponentially on a time scale set by the coupling to the normal metal. Strong oscillations of the pair amplitude occur also wh…
Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductance, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative…
We analyze tunneling-induced quantum fluctuations in a single-level quantum dot with arbitrarily strong onsite Coulomb interaction, generating cotunneling processes and renormalizing system parameters. For a perturbative analysis of these quantum fluctuations, we remove off-shell parts of the Hamiltonian via a canonical transformation. We find that the tunnel couplings for the transitions connecting empty and single occupation and connecting single and double occupation of the dot renormalize with the same magnitude but with opposite signs. This has an important impact on the shape of the reno…
The Andreev transport through a quantum dot coupled to two external ferromagnetic leads and one superconducting lead is studied theoretically by means of the real-time diagrammatic technique in the sequential and cotunneling regimes. We show that the tunnel magnetoresistance (TMR) of the Andreev current displays a nontrivial dependence on the bias voltage and the level detuning, and can be described by analytical formulas in the zero temperature limit. The cotunneling processes lead to a strong modification of the TMR, which is most visible in the Coulomb blockade regime. We find a zero-bias a…
We study adiabatic pumping of electrons through quantum dots attached to ferromagnetic leads. Hereby we make use of a real-time diagrammatic technique in the adiabatic limit that takes into account strong Coulomb interaction in the dot. We analyze the degree of spin polarization of electrons pumped from a ferromagnet through the dot to a nonmagnetic lead (N-dot-F) as well as the dependence of the pumped charge on the relative leads' magnetization orientations for a spin-valve (F-dot-F) structure. For the former case, we find that, depending on the relative coupling strength to the leads, spin …
We consider a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. We employ a diagrammatic real-time approach to calculate the finite-frequency current noise for subgap transport. The noise spectrum gives direct access to the internal dynamics of the dot. In particular the noise spectrum shows sharp dips at the frequency of the coherent oscillations of Cooper pairs between dot and superconductor. This feature is most pronounced when the superconducting correlation is maximal. Furthermore, in the quantum-noise regime, $ω> k_\text{B}T,μ_\text{N}$, the noise spectr…
We study the spin-polarized transport through a triple quantum dot molecule weakly coupled to ferromagnetic leads. The analysis is performed by means of the real-time diagrammatic technique including up to the second order of perturbation expansion with respect to the tunnel coupling. The emphasis is put on the impact of dark states on spin-resolved transport characteristics. It is shown that the interplay of coherent population trapping and cotunneling processes results in a highly nontrivial behavior of the tunnel magnetoresistance, which can take negative values. Moreover, a super-Poissonia…
We calculate adiabatic charge and spin pumping through a serial double quantum dot with strong Coulomb interaction, coupled to normal metal or ferromagnetic contacts. We use a real-time diagrammatic approach in the regime of weak coupling to the reservoirs. In the case of weak interdot tunnel coupling we investigate the influence of tunnel-induced renormalization effects due to charge fluctuations on the pumped charge and spin. We show that tunneling through thermally excited states can play an important role in the strong interdot coupling regime. In particular, for ferromagnetic contacts, bo…
We calculate the time dependent nonequilibrium current through a single level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real time dynamics caused by an instantaneous coupling of the leads to the quantum dot is discussed using an approximate method. The approach, which is specially designed for the strong polaronic regime, is based on the so-called polaron tunneling approximation. Considering different initial dot occupations, we show that a common steady state is reached after times much larger than the typical electron tunneling times due to a polaron blocking eff…
We investigate two schemes for pumping spin adiabatically from a ferromagnet through an interacting quantum dot into a normal lead, which exploit the possibility to vary in time the ferromagnet's magnetization, either its amplitude or its direction. For this purpose, we extend a diagrammatic real-time technique for pumping to situations in which the leads' properties are time dependent. In the first scheme, the time-dependent magnetization amplitude is combined with a time-dependent level position of the quantum dot to establish both a charge and a spin current. The second scheme uses a unifor…
We investigate Andreev transport through a quantum dot attached to two external ferromagnetic leads and one superconducting electrode. The transport properties of the system are studied by means of the real-time diagrammatic technique in the sequential tunneling regime. To distinguish various contributions to Andreev current we calculate the current cross-correlations, i.e. correlations between currents flowing through two junctions with normal leads. We analyze dependence of current cross-correlations on various parameters of the considered model, both in linear and nonlinear transport regime…
Diagrammatic Analysis of the Unitary Group for Double Barrier Ballistic Cavities: Equivalence with Circuit Theory
我们推导了一组耦合的非线性代数方程组的泊松核分布的渐近描述的统计特性的两端双障碍的混沌台球（或弹道量子点）。这些方程是根据Brouwer和Beenakker [J.Math.Phys.37，4904（1996）]提出的在酉群上进行平均的图解技术计算的。我们给出了强有力的分析证据，证明这些方程等价于一个更简单的多项式方程，该方程是根据Nazarov电路理论的最近扩展计算的[A. M. S. Macedo，Phys.Rev.B66，033306（2002）]。这些结果提供了有趣的前景，在该领域的进一步发展，通过直接转换的一种方法到其他。
Since the realization of high-quality microwave cavities coupled to quantum dots, one can envisage the possibility to investigate the coherent interaction of light and matter in semiconductor quantum devices. Here we study a parallel double quantum dot device operating as single-electron splitter interferometer, with each dot coupled to a local photon cavity. We explore how quantum correlation and entanglement between the two separated cavities are generated by the coherent transport of a single electron passing simultaneously through the two different dots. We calculate the covariance of the …
We investigate the AC Josephson current through a quantum dot with strong Coulomb interaction attached to two superconducting and one normal lead. To this end, we perform a perturbation expansion in the tunneling couplings within a diagrammatic real-time technique. The AC Josephson current is connected to the reduced density matrix elements that describe superconducting correlations induced on the quantum dot via proximity effect. We analyze the dependence of the AC signal on the level position of the quantum dot, the charging energy, and the applied bias voltages.
Interactions, superconducting $T_c$, and fluctuation magnetization for two coupled dots in the crossover between the Gaussian Orthogonal and Unitary ensembles
We investigate the current cross-correlations in a double quantum dot based Cooper pair splitter coupled to one superconducting and two ferromagnetic electrodes. The analysis is performed by assuming a weak coupling between the double dot and ferromagnetic leads, while the coupling to the superconductor is arbitrary. Employing the perturbative real-time diagrammatic technique, we study the Andreev transport properties of the device, focusing on the Andreev current cross-correlations, for various parameters of the model, both in the linear and nonlinear response regimes. Depending on parameters…
Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared to what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. S…
We analyze numerically the spin-dependent transport through coherent chains of three coupled quantum dots weakly connected to external magnetic leads. In particular, using the diagrammatic technique on the Keldysh contour, we calculate the conductance, shot noise and tunnel magnetoresistance (TMR) in the sequential and cotunneling regimes. We show that transport characteristics greatly depend on the strength of the interdot Coulomb correlations, which determines the spacial distribution of electron wave function in the chain. When the correlations are relatively strong, depending on the transp…
We consider a quantum dot weakly tunnel coupled to superconducting reservoirs. A finite superconducting pair amplitude can be induced on the dot via the proximity effect. We investigate the dynamics of the induced pair amplitude after a quench and under periodic driving of the system by means of a real-time diagrammatic approach. We find that the quench dynamics is dominated by an exponential decay towards equilibrium In contrast, the periodically driven system can sustain coherent oscillations of both the amplitude and the phase of the induced pair amplitude in analogy to Higgs and Nambu-Gold…
We analyze heat and charge transport through a single-level quantum dot coupled to two BCS superconductors at different temperatures to first order in the tunnel coupling. In order to describe the system theoretically, we extend a real-time diagrammatic technique that allows us to capture the interplay between superconducting correlations, strong Coulomb interactions, and nonequilibrium physics. We find that a thermoelectric effect can arise due to the superconducting proximity effect on the dot. In the nonlinear regime, the thermoelectric current can also flow at the particle-hole symmetric p…
We analyze the real-time dynamics of a quantum two-state system in the presence of nonequilibrium quantum fluctuations. The latter are generated by a coupling of the two-state system to a single electronic level of a quantum dot which carries a nonequilibrium tunneling current. We restrict to the sequential tunneling regime and calculate the dynamics of the two-state system, of the dot population, and of the nonequilibrium charge current on the basis of a diagrammatic perturbative method valid for a weak tunneling coupling. We find a nontrivial dependence of the relaxation and dephasing rates …
We derive the symmetrized current-noise spectrum of a quantum dot, which is weakly tunnel-coupled to an electron reservoir and driven by a slow time-dependent gate voltage. This setup can be operated as an on-demand emitter of single electrons into a mesoscopic conductor. By extending a real-time diagrammatic technique which is perturbative in the tunnel coupling, we obtain the time-resolved finite-frequency noise as well as its decomposition into noise harmonics in the presence of both strong Coulomb interaction and slow time-dependent driving. We investigate the noise over a large range of f…
We investigate current-current correlations of adiabatic charge pumping through interacting quantum dots weakly coupled to reservoirs. To calculate the zero-frequency noise for a time-dependently driven system, possibly in the presence of an additional dc bias, we perform within a real-time diagrammatic approach a perturbative expansion in the tunnel coupling to the reservoirs in leading and next-to-leading order. We apply this formalism to study the adiabatic correction to the zero-frequency noise, i.e., the pumping noise, in the case of a single-level quantum dot charge pump. If no stationar…
We study the effects of spin accumulation (inside reservoirs) on electronic transport with tunneling and reflections at the gates of a quantum dot. Within the stub model, the calculation focus on the current-current correlation function for the flux of electrons injected into the quantum dot. The linear response theory used allows to obtain the noise power in the regime of thermal crossover as a function of parameters that reveal the spin polarization at the reservoirs. The calculation is performed employing diagrammatic integration within the universal groups (ensembles of Dyson) for a non-id…
We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical res…
We revisit the transport of spin-degrees of freedom across an electrically and thermally biased tunnel junction between two ferromagnets with non-collinear magnetizations. Besides the well-known charge and spin currents we show that a non-zero spin-quadrupole current flows between the ferromagnets. This tensor-valued current describes the non-equilibrium transport of spin-anisotropy relating to both local and non-local multi-particle spin correlations of the circuit. This quadratic spin-anisotropy, quantified in terms of the spin-quadrupole moment, is fundamentally a two-electron quantity. In …
We investigate the Andreev transport through double-quantum-dot Cooper pair splitters with ferromagnetic leads. The analysis is performed with the aid of the real-time diagrammatic technique in the sequential tunneling regime. We study the dependence of the Andreev current, the differential conductance, and the tunnel magnetoresistance on various parameters of the model in both the linear and nonlinear response regimes. In particular, we analyze the spin-resolved transport in the crossed Andreev reflection regime, where a blockade of the current occurs due to enhanced occupation of the triplet…
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all Feynman diagrams, obtained in a controlled and accurate way with the tensor cross interpolation algorithm. It yields the full time evolution of physical quantities in the presence of any arbitrary time dependent interaction. Our benchmarks on the Anderson quantum impurity problem, within the real time non-equilibrium Schwinger-Keldysh formalism, demonstrate that …
We investigate the pumped charge and spin at zero-bias by adiabatic modulation of two control parameters using the full counting statistics with quantum master equation approach. First we study higher order effects of the pumping frequency in general Markov systems and show the equivalence between our approach and the real-time diagrammatic approach. An adiabatic modulation of the control parameters induces the Berry-Sinitsyn-Nemenman (BSN) phase. We show that the origin of the BSN phase is a non-adiabatic effect. The adiabatically pumped charge (spin) is given by a summation of (i) a time int…
High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as $1/N$ in sample number $N$; parametrically faster than $1/\sqrt{N}$ in Monte Carlo. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.
We calculate conductance through a quantum dot weakly coupled to metallic contacts by means of Keldysh out of equilibrium formalism. We model the quantum dot with the SU(2) Anderson model and consider the limit of infinite Coulomb repulsion. We solve the interacting system with the numerical diagrammatic Non-Crossing Approximation (NCA). We calculate the conductance as a function of temperature and gate voltage, from differential conductance (dI/dV) curves. We discuss these results in comparison with those from the linear response approach which can be performed directly in equilibrium conditi…
Current precision in interacting hybrid Normal-Superconducting systems
The Abdus Salam International Center for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore（纳米科学研究所-意大利国家研究委员会及比萨高等师范学院）；Dipartimento di Fisica, Università di Napoli “Federico II”（那不勒斯费德里科二世大学物理系）；School of Chemical and Physical Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington（惠灵顿维多利亚大学化学与物理科学学院及麦克迪尔米德先进材料与纳米技术研究所）
