We investigate nonlinear thermal transport properties of a single interacting quantum dot with two energy levels tunnel-coupled to two electrodes using nonequilibrium Green function method and Hartree-Fock decoupling approximation. In the case of asymmetric tunnel-couplings to two electrodes, for example, when the upper level of the quantum dot is open for transport, whereas the lower level is blocked, our calculations predict a strong asymmetry for the heat (energy) current, which shows that, the quantum dot system may act as a thermal rectifier in this specific situation.
We compute the spin current rectification coefficient of a non-equilibrium quantum dot subject to a spin bias and an {\it ac} charge bias with small amplitude. As a function of the position of the resonant level the spin current rectification coefficient shows a set of three peaks around the gate voltage at which the resonant or the upper level of the dot is in the vicinity of the equilibrium Fermi level in the leads. The peak heights can be related to the average number of the quantum dot electrons. We discuss the frequency dependence of the spin current rectification coefficient as well and …
We derive a formula describing the adiabatically pumped charge through an interacting quantum dot within the scattering matrix and Green's function approach. We show that when the tunneling rates between the leads and the dot are varied adiabatically in time, both in modulus and phase, the current induced in the dot consists of two terms, the pumping current and a rectification-like term. The last contribution arises from the time-derivative of the tunneling phase and can have even or odd parity with respect to the pumping phase φ. The rectification-like term is also discussed in relation to s…
Based on the multiple energy level Anderson model, this study theoretically examines the thermoelectric effects of semiconductor quantum dots (QDs) in the nonlinear response regime. The charge and heat currents in the sequential tunneling process are calculated by using the Keldysh Green's function technique. Results show that the thermal rectification effect can be observed in a multiple QD junction system, whereas the tunneling rate, size fluctuation, and location distribution of QD significantly influence the rectification efficiency.
We investigate theoretically and experimentally the statistical properties of dc current through an open quantum dot subject to ac excitation of a shape-defining gate. The symmetries of rectification current and photovoltaic current with respect to applied magnetic field are examined. Theory and experiment are found to be in good agreement throughout a broad range of frequency and ac power, ranging from adiabatic to nonadiabatic regimes.
The nonlinear thermoelectric properties of serially coupled quantum dots (SCQDs) embedded in a nanowire connected to metallic electrodes are theoretically studied in the Coulomb blockade regime. We demonstrate that the electron heat current of SCQDs exhibit a direction-dependent behavior (heat rectification) in an asymmetrical structure in which the electron Coulomb interactions are significant. The phonon thermal conductivity of the nanowire is also calculated, which is used to estimate the phonon heat current. Finally, we discuss how to reduce phonon heat current to allow observation of elec…
We report mesoscopic dc current generation in an open chaotic quantum dot with ac excitation applied to one of the shape-defining gates. For excitation frequencies large compared to the inverse dwell time of electrons in the dot (i.e., GHz), we find mesoscopic fluctuations of induced current that are fully asymmetric in the applied perpendicular magnetic field, as predicted by recent theory. Conductance, measured simultaneously, is found to be symmetric in field. In the adiabatic (i.e., MHz) regime, in contrast, the induced current is always symmetric in field, suggesting its origin is mesosco…
We investigate the rectification of heat current carried by electrons through a double quantum dot (DQD) system under a temperature bias. The DQD can be realized by molecules such as suspended carbon nanotube and be described by the Anderson-Holstein model in presence of electron-phonon interaction. Strong electron-phonon interaction can lead to formation of polaronic states in which electronic states are dressed by phonon cloud. Dressed tunneling approximation (DTA), which is nonperturbative in dealing with strong electron-phonon interaction, is employed to obtain the heat current expression.…
We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two-terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doub…
We study the time-dependent transport of charge and spin through a ring-shaped region sequentially coupled to a weakly interacting quantum dot in the presence of an Aharonov-Bohm flux and spin-orbit interaction. The time-dependent modulation of the spin-orbit interaction, or of the corresponding Aharonov-Casher flux, together with the modulation of the dot-level induces an electrically pumped spin current even in absence of a charge current. The results beyond the adiabatic regime show that an additional rectification current proportional to \cos(ϕ), being ϕthe relative phase between the time …
The transport properties of serially coupled quantum dots (SCQDs) embedded in a matrix connected to metallic electrodes are theoretically studied in the linear and nonlinear regimes. The current rectification and negative differential conductance of SCQDs under the Pauli spin blockade condition are attributed to the combination of bias-direction dependent probability weight and off-resonant energy levels yielded by the applied bias across the junctions. We observe the spin-polarization current rectification under the Zeeman effect. The maximum spin-polarization current occurs in the forward bi…
Heat engines made of quantum-dot (QD) superlattice nanowires (SLNWs) offer promising applications in energy harvesting due to the reduction of phonon thermal conductivity. In solid state electrical generators (refrigerators), one needs to generate (remove) large amount of charge current (heat current). Consequently, a high QD SLNW density is required for realistic applications. This study theoretically investigated the properties of power factor and electron heat rectification for an SLNW array under the transition from a one dimensional system to a two dimensional system. The SLNW arrays show…
The electrical conductance, thermal conductance, thermal power and figure of merit (ZT) of semiconductor quantum dots (QDs) embedded into an insulator matrix connected with metallic electrodes are theoretically investigated in the Coulomb blockade regime. The multilevel Anderson model is used to simulate the multiple QDs junction system. The charge and heat currents in the sequential tunneling process are calculated by the Keldysh Green function technique. In the linear response regime the ZT values are still very impressive in the small tunneling rates case, although the effect of electron Co…
This work explores different mechanisms that induce thermal rectification in the nanoscale. The presence of interacting energy channels combined with simple asymmetries is sufficient for promoting the desired behavior. We use simple quantum dot configurations, identifying the basic properties that enhance rectification for each case: the size of a quantum dot state space (which suggests the use of scaled up systems with many interacting channels), tunneling asymmetries due to coherent tunneling in a double quantum dot, or quantum interference in a triangular triple quantum dot. An efficient an…
We investigate the statistical fluctuations of currents in chaotic quantum dots induced by pumping and rectification at finite temperature and in the presence of dephasing. In open quantum dots, dc currents can be generated by the action of two equal-frequency ac gate voltages. The adiabatic regime occurs when the driving frequency is smaller than the electron inverse dwell time. Using numerical simulations complemented by semiclassical calculations, we consider both limits of small and large number of propagating channels in the leads when time-reversal symmetry is fully broken. We find that …
We investigate the heat flow transport properties of a parallel-coupled double quantum-dot system connected to two reservoirs with a temperature bias in the Coulomb blockade regime. We demonstrate that the effects of thermal rectification and negative differential thermal conductance (NDTC) exist in this system and analyze the influences of energy level difference and Coulomb interaction on the thermal rectification and NDTC. We find that this system can achieve a high thermal rectification ratio and NDTC when the asymmetry factor of the system is enhanced.
It is illustrated that semiconductor quantum dots (QDs) embedded into an insulating matrix connected with metallic electrodes and some vacuum space can lead to significant thermal rectification effect. A multilevel Anderson model is used to investigate the thermal rectification properties of the multiple-QD junction. The charge and heat currents in the tunneling process are calculated via the Keldysh Green's function technique. We show that pronounced thermal rectification and negative differential thermal conductance (NDTC) behaviors can be observed for the multiple-QD junction with asymmetri…
Quantum thermal transport in two-quantum-dot system with Dzyaloshinskii-Moriya interaction (DM interaction) has been studied. The sign of thermal rectification can be controlled through changing the energy splitting or the DM interaction strength. The anisotropic term in the system can also affect the sign of rectification. Compared with other proposals [Phys. Rev. B 80, 172301 (2009)], our model can offer larger rectification efficiency and show the potential application in designing the polarity-controllable thermal diode with a small size system (N=2). Moreover, quantum correlations of two-…
We analyze spin-dependent transport through a spin-diode in the presence of spin-flip and under influence of temperature bias. The current polarization and the spin accumulation are investigated in detail by means of reduced density matrix. Results show that the spin accumulation is linearly increased when the metallic electrode is warmer whereas, its behavior is more complicated when the ferromagnetic lead is warmer. Furthermore, spin-flip causes that the current polarization becomes not only a function of spin-flip rate but also a function of temperature. The current polarization is reduced …
We calculate a current rectification by molecules containing a conjugated molecular group sandwiched between two saturated (insulating) molecular groups of different length (molecular quantum dot) using an ab-initio non-equilibrium Green's function method. In particular, we study S-(CH2)m-C10H6-(CH2)n-S dithiol with Naphthalene as a conjugated central group. The rectification current ratio ~35 has been observed at m = 2 and n = 10, due to resonant tunneling through the molecular orbital (MO) closest to the electrode Fermi level (lowest unoccupied MO in the present case). The rectification is l…
Reservoir engineering is a powerful tool for the robust generation of quantum states or transport properties. Using both a weak-coupling quantum master equation and the exact solution, we show that directional transport of electrons through a double quantum dot can be achieved through an appropriately designed electronic environment. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic field, such that directionality can be reversed, as well as turned on and off dynamically. Our work introduces fermionic…
Rectification of ac displacement currents generated by periodic variation of two independent gate voltages of a quantum dot can lead to a dc voltage linear in the frequency. The presence of this rectified displacement current could account for the magnetic field symmetry observed in a recent measurement on an adiabatic quantum electron pump by Switkes et al. [Science 283, 1905 (1999)].
We theoretically investigate a quantum heat diode based on two interacting flux qubits coupled to two heat baths. Rectification of heat currents is achieved by asymmetrically coupling the qubits to the reservoirs modelled as dissipative $RLC$ resonators. We find that the coherent interaction between the qubits can be exploited to enhance the rectification factor, which otherwise would be constrained by the baths temperatures and couplings. Remarkably high values of rectification ratio up to $\mathcal R \sim 3.5$ can be obtained for realistic system parameters, with an enhancement up to $\sim 2…
The quantum dot arrays (QDAs) embedded into inhomogeneous nanowires connected to metallic electrodes show an electron heat rectification effect, which is attributed to the thermal voltage arising from a temperature bias and the QDA with a broken spatial inversion symmetry. The staircase energy levels of QDAs can be controlled to the resonant and off resonant transports for electrons in the forward and backward temperature biases, respectively. The effect of electron Coulomb interactions on the rectification efficiency of heat diode is clarified by the case of double QDs. We find that it is imp…
Rectification of microwave radiation by asymmetric, ballistic quantum dot is observed. The directed transport is studied at different frequency (1-40 GHz) temperatures (0.3K-6K)and magnetic field. Dramatic reduction of the rectification is found in magnetic fields at which the cyclotron (Larmor) radius of the electron orbits at Fermi level is smaller than the size of the quantum dot. It strongly suggests the ballistic nature of the observed nonlinear phenomena. Both symmetric and anti-symmetric with respect to the magnetic field contributions to the directed transport are presented. We have fo…
We report the observation of thermal rectification in a semiconductor quantum dot, as inferred from the asymmetric line shape of the thermopower oscillations. The asymmetry is observed at high in-plane magnetic fields and caused by the presence of a high orbital momentum state in the dot.
We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the transport coefficients are functions of the nonequilibrium screening potential that builds up in the system due to interactions. Within a mean-field approximation, we self-consistently calculate the heat rectification properties of a quantum dot attached to two terminals. We discuss nonlinear contributions to the Peltier effect and find departures from the Wiede…
Low-temperature measurements of asymmetric carbon nanotube (CNT) quantum dots are reported. The CNTs are end-contacted with one ferromagnetic and one normal-metal electrode. The measurements show a spin-dependent rectification of the current caused by the asymmetry of the device. This rectification occurs for gate voltages for which the normal-metal lead is resonant with a level of the quantum dot. At the gate voltages at which the current is at the maximum current, a significant decrease in the current shot noise is observed.
We investigate the nonlinear current-voltage characteristic of mesoscopic conductors and the current generated through rectification of an alternating external bias. To leading order in applied voltages both the nonlinear and the rectified current are quadratic. This current response can be described in terms of second order conductance coefficients and for a generic mesoscopic conductor they fluctuate randomly from sample to sample. Due to Coulomb interactions the symmetry of transport under magnetic field inversion is broken in a two-terminal setup. Therefore, we consider both the symmetric …
Transport properties of asymmetric molecular structure are studied within the kinetic equation approach, taking into consideration the electron interaction in the self-consistent manner (SCF procedure). The device is made of a molecule (modeled as a quantum dot with discrete energy levels) which is asymmetrically coupled to the two metallic electrodes through the tunnel junctions. Electrical rectification follows from the combined effect of the geometric asymmetry in the molecular structure and simultaneously in the electrostatic potential spatial profile. Primarily the influence of broadening…
We investigate the dynamics of two coupled macrospins connected to thermal baths at different temperatures. The system behaves like a diode which allows the propagation of energy and mag- netization currents in one direction only. This effect is described by a simple model of two coupled nonlinear oscillators interacting with two independent reservoirs. It is shown that the rectification phenomenon can be interpreted as a a stochastic phase synchronization of the two spin-oscillators. A brief comparison with realistic micromagnetic simulations is presented. This new effect yields promising opp…
Asymmetric current--voltage ($I(V)$) curves, known as the diode or rectification effect, in one--dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga--Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current, $I_r = [I(V)+I(-V)]/2$, measuring t…
The charge transport of a serially coupled quantum dots (SCQD) connected to the metallic electrodes is theoretically investigated in the Coulomb blockade regime. A closed-form expression for the tunneling current of SCQD in the {\color{red} weak interdot hopping} limit is obtained by solving an extended two-site Hubbard model via the Green's function method. We use this expression to investigate spin current rectification, negative differential conductance, and coherent tunneling in the nonlinear response regime. The current rectification arising from the space symmetry breaking of SCQD is sup…
We study spin correlation in a double quantum dot containing a few electrons in each dot (around 10). Clear current rectification with negative differential conductance is observed in the cotunneling regime, which is well explained by a Pauli spin blockade. The current feature is discussed in connection with exchange singlet-triplet splitting based on two simple models, one of which takes coherent interdot coupling and the other incoherent interdot coupling into account.
We demonstrate single-electron pumping in a gate-defined carbon nanotube double quantum dot. By periodic modulation of the potentials of the two quantum dots we move the system around charge triple points and transport exactly one electron or hole per cycle. We investigate the pumping as a function of the modulation frequency and amplitude and observe good current quantization up to frequencies of 18 MHz where rectification effects cause the mechanism to break down.
We describe the electronic properties of a double dot for which the lateral coupling between the two vertical dots can be controlled in-situ with a center gate voltage (Vc) and the current flows through the two dots in series. When Vc is large and positive, the two dots merge. As Vc is made less positive, two dots are formed whose coupling is reduced. We measure charging diagrams for positive and negative source-drain voltages in the weak coupling regime and observe current rectification due to the Pauli spin blockade when the hyperfine interaction between the electrons and the nuclei is suppr…
We implement silicon quantum dot devices with two layers of gate electrodes using a self-alignment technique, which allows for ultra-small gate lengths and intrinsically perfect layer-to-layer alignment. In a double quantum dot system, we investigate hole transport and observe current rectification due to Pauli spin blockade. Magnetic field measurements indicate that hole spin relaxation is dominated by spin-orbit interaction, and enable us to determine the effective hole $g$-factor $\simeq1.6$. From an avoided singlet-triplet crossing, occurring at high magnetic field, the spin-orbit coupling…
We outline the qualitatively different physics behind charging-induced current asymmetries in molecular conductors operating in the weakly interacting self-consistent field (SCF) and the strongly interacting Coulomb Blockade (CB) regimes. A conductance asymmetry arises in SCF because of the unequal mean-field potentials that shift a closed-shell conducting level differently for positive and negative bias. A very different current asymmetry arises for CB due to the unequal number of open-shell excitation channels at opposite bias voltages. The CB regime, dominated by single charge effects, typi…
We present a general formalism to study adiabatic pumping through interacting quantum dots. We derive a formula that relates the pumped charge to the local, instantaneous Green function of the dot. This formula is then applied to the infinite-U Anderson model both for weak and strong tunnel-coupling strengths.
Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well-understood. When a specific type of spin-orbit coupling known to be dominant in two dimensional semiconductor quantum dots is introduced, we show that a new interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.
We investigate adiabatic pumping via a single level quantum dot induced by periodic modulation of thermodynamic variables of reservoirs, i.e., temperatures and electrochemical potentials. We consider the impurity Anderson model and derive analytical formulas for coherent adiabatic charge pumping applicable to the strong dot-reservoir coupling within first-order perturbation with respect to Coulomb interaction. We show that charge pumping is induced by rectification effect due to delayed response of the quantum dot to time-dependent reservoir parameters. The presence of interaction is necessary…
The effect of long distance coherent tunneling (LDCT) on the charge and heat currents in serially coupled triple quantum dots (TQDs) connected to electrodes is illustrated by using a combination of the extended Hurbbard model and Anderson model. The charge and heat currents are calculated with a closed-form Landauer expression for the transmission coefficient suitable for the Coulomb blockade regime. The physical parameters including bias-dependent quantum dot energy levels, electron Coulomb interactions, and electron hopping strengths are calculated in the framework of effective mass theory f…
We study spectral and transport properties of interacting quantum dots with spin. Two particular model systems are investigated: Lateral multilevel and two parallel quantum dots. In both cases different paths through the system can give rise to interference. We demonstrate that this strengthens the multilevel Kondo effect for which a simple two-stage mechanism is proposed. In parallel dots we show under which conditions the peak of an interference-induced orbital Kondo effect can be split.
Recent breakthroughs in quantum-dot circuit-quantum-electrodynamics (circuit-QED) systems are important both from a fundamental perspective and from the point of view of quantum photonic devices. However, understanding the applications of such setups as potential thermoelectric diodes and transistors has been missing. In this paper, via the Keldysh nonequilibrium Green's function approach, we show that cavity-coupled double quantum-dots can serve as excellent quantum thermoelectric diodes and transistors. Using an enhanced perturbation approach based on polaron-transformations, we find non-mon…
We derive a complete expression for the interaction correction to the $I-V$ curve of two connected in series metallic quantum dots. For strongly asymmetric dots in a wide range of parameters this interaction correction depends logarithmically on voltage and temperature.
We observe a low-lying sharp spin mode of three interacting electrons in an array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic light scattering. The finding is enabled by a suppression of the inhomogeneous contribution to the excitation spectra obtained by reducing the number of optically-probed quantum dots. Supported by configuration-interaction calculations we argue that the observed spin mode offers a direct probe of Stoner ferromagnetism in the simplest case of three interacting spin one-half fermions.
We present a theoretical study of the detection of the decay time scales for a single-level quantum dot by means of a capacitively coupled sensor dot, which acts as an electrometer. We investigate the measurement back-action on the quantum-dot decay rates and elucidate its mechanism. We explicitly show that the setup can be used to measure the bare quantum-dot relaxation rates by choosing gate pulses that minimize the back-action. Interestingly, we find that besides the charge relaxation rate, also the rate associated to the fermion parity in the dot can be accessed with this setup.
Thermal rectification phenomenon is a manifestation of an asymmetry in the heat flux when the temperature difference between two interacting thermal reservoirs is reversed. In this letter, we present a far-field radiative thermal rectifier based on high temperature superconducting materials with a rectification ratio up to $80%$. This value is among the highest reported in literature. Two configurations are examined : a superconductor (Tl$_2$Ba$_2$CaCu$_2$O$_8$) exchanging heat with 1) a black body and 2) another superconductor, YBa$_2$Cu$_3$O$_7$ in this case. The first configuration shows a …
We analyze the charge and spin pumping in an interacting dot within the almost adiabatic limit. By using a non-equilibrium Green's function technique within the time-dependent slave boson approximation, we analyze the pumped current in terms of the dynamical constraints in the infinite-U regime. The results show the presence of parasitic pumping currents due to the additional phases of the constraints. The behavior of the pumped current through the quantum dot is illustrated in the spin-insensitive and in the spin-sensitive case relevant for spintronics applications.
We study thermoelectric effects in Kondo correlated quantum dot coupled to ferromagnetic electrodes by calculating thermopower S in the Kondo regime as function of on-dot energy level and temperature. The system is represented by the Anderson model and the results agree well with those recently measured for a quantum dot coupled to nonmagnetic leads. For magnetic electrodes one observes marked dependence of S on the degree of their polarization.
We study the noise spectra of a many-level quantum dot coupled to two electron reservoirs, when interactions are taken into account only on the dot within the Hartree-Fock approximation. The dependence of the noise spectra on the interaction strength, the coupling to the leads, and the chemical potential is derived. For zero bias and zero temperature, we find that as a function of the (external) frequency, the noise exhibits steps and dips at frequencies reflecting the internal structure of the energy levels on the dot. Modifications due to a finite bias and finite temperatures are investigate…
We analyze inelastic cotunneling through an interacting quantum dot subject to an ambient magnetic field in the weak tunneling regime under a non-adiabatic time-dependent bias-voltage. Our results clearly exhibit photon-assisted satellites and an overall suppression of differential conductance with increasing driving amplitude, which is consistent with experiments. We also predict a zero-anomaly in differential conductance under an appropriate driving frequency.
Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At ``filling factor'' near 1/2, this contribution proves to be larger than energy differences between states with different spin polarizations. After checking convergence of the method in small systems, we show results for a 12-electron quantum dot, a system which is hardly tractable by means of exact diagonalization techniques.
Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the inter quantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble using a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach maintaining local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the electron g factor on the spin…
The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size o…
