Dot-lead Coupling Research Articles

Tunable photonic cavity coupled to a voltage-biased double quantum dot system: Diagrammatic nonequilibrium Green's function approach

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 electronic system serving as a gain medium. We also study the steady state current across the device, identifying elastic and inelastic tunnelling processes which involve the cavity mode. Our results show how recent advances in quantum electronics can be exploited to build hybrid light-matter systems that behave as single-atom amplifiers and photon source devices. The diagrammatic Keldysh approach is primarily discussed for a cavity-coupled double quantum dot architecture, but it is generalizable to other hybrid light-matter systems.

Reappearance of the Kondo effect in serially coupled symmetric triple quantum dots

We investigate the spectral properties of a serially coupled triple quantum dot (STQD) system by means of the hierarchical equations of motion (HEOM) approach. We find that with the increase of the interdot coupling t, the first Kondo screening is followed by another Kondo effect reappearing due to the transition from the respective Kondo singlet state of individual QD to the coherence bonding state generated among the three QDs. The reappearance of the Kondo effect results in the three-peak structure of the spectral functions of peripheral QD-1(3). By investigating the susceptibility χ, we find that the local susceptibility of intermediate QD-2 is a positive value at weak interdot coupling, while it changes into a negative value at strong interdot coupling, at which the STQD system gives rise to the reappearance of the Kondo effect. We also find that the slopes of will deviate from a straight line behaviour at low temperature in the reappearing Kondo regime. In addition, the influence of temperature and dot-lead coupling strength on the reappearing Kondo effect as well as the Kondo-correlated transport properties are afterwards exploited in detail.

Majorana zero modes choose Euler numbers as revealed by full counting statistics

We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly, the full counting statistics is qualitatively different in the presence of the Majorana coupling.

Phase diagram and low temperature scenario for a triangular triple dot system

We present a triangular triple quantum dot (TTQD) system with two dots connected parallelly to one conduction lead, and investigate the phase diagram, the electric transport, and the temperature-dependent magnetic moment at half filling. When the hopping between two connected dots t12 = 0, and those between the connected dots and the side dot are symmetric t13 = t23, two connected dots form a spin triplet due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated by the dot-lead coupling and/or the hopping t13 (t23). For t13 = 0, the triplet is partially screened by the conduction leads at low temperature. Both the connected dots and the side dot contribute to the magnetic moment of the system. For any definite t13, the triplet is totally screened by the conduction leads and the side dot, and the two-stage Kondo effect occurs. When t12 increases beyond a critical t12c, two connected dots form a spin singlet and decouple from the side dot. In this case, the Kondo peak is strongly suppressed, indicating zero conductance, and only the localized side dot contribute to the magnetic moment at low temperature. When t13 ≠ t23, we find a crossover as t12 increases, contrast to the first order transition of the symmetric case. Numerical renormalization group technique and physical arguments are used to obtain a detailed understanding of these problems.

RKKY interaction and local density of states for a triangular triple quantum dot system

By means of the numerical renormalization group technique, we study the local density of states (LDOS) for a triangular triple quantum dot system, with two dots connected in parallel to the conduction leads. We find the location of the Ruderman–Kittel–Kasuya–Yosida (RKKY) peak identified in the LDOS could be illustrated as JRKKY=aΓ2/U+bt22/U, with U being the on-site Coulomb repulsion, Γ the dot-lead coupling, and t2 the hopping between the connected dots and the side dot. When the hopping between two connected dots t1 turns on, the spectrum weight of the RKKY peaks decreases due to the competition between the direct and the RKKY interactions. As t1 increases beyond a critical point t1c, two connected dots form a spin singlet, and decouple from both the side dot and the conduction leads, thus the Kondo and RKKY peaks could not be found. For t1<t1c, the conductance reaches to the unitary limit, while for t1≥t1c, it drops to zero.

Influence of Majorana doublet on transport through a quantum dot system with ferromagnetic leads

We investigate the electron transport through a quantum dot connected with two ferromagnetic leads, by coupling one Majorana doublet laterally to the quantum dot. It is found that Majorana doublet keeps the value of zero-bias conductance to be independent of the shift of structural parameters, including dot level, relative lead-magnetization direction, and magnetic field on the dot. Even in the cases of asymmetric dot-lead couplings, the zero-bias conductance is weakly dependent on the relative lead-magnetization direction. On the other hand, when Majorana doublet is replaced by Majorana singlet, the zero-bias conductance value becomes sensitive to the structural parameters. Via analyzing the respective particle motion processes, the different influences of Majorana doublet and singlet are explained. We believe that this work can be helpful for understanding the peculiar properties of Majorana doublet.

Spin-Polarized Transport Through a Quantum Dot Coupled to Leads with Spin-Dependent Electron Temperature

We study the effect of a spin-dependent electron temperature detected in a recent experiment on the electronic transport through a quantum dot connected to external leads. At low temperatures, the electron occupation number on the dot and the current become fully spin-polarized even in the presence of a weak temperature difference between spin-up and spin-down electrons. With rising temperature, the spin information will be overwhelmed by the electrons’ thermal motion. Under an applied magnetic field, the resonances in the spin-up and spin-down currents are separated and then a 100 % spin-polarized current emerges. Now the device operates as a spin filter. It is also found that the magnitude of the current’s spin polarization can be obviously enhanced by properly adjusting the left–right asymmetry of the dot–lead coupling strengths.

Heat generation by spin-polarized current in a quantum-dot spin battery

Abstract We study the heat generation by spin-polarized current due to the electron–phonon coupling in a single-level quantum-dot, which is connected to an external either symmetric or asymmetric dipolar spin battery. We find that the heat generation depends sensitively on the configuration of the spin battery's chemical potentials. In the case of the dot coupled to symmetric spin battery, there is remarkable negative differential of the heat generation, which disappears if the spin battery is asymmetric. We also find that the magnitude of the heat generation in asymmetric spin battery is much larger than that in symmetric one despite of the reduced intensity of the electric current. Moreover, the heat generation is insensitive to the system's temperature, and develops peaks when the dot-lead coupling strength or the intradot Coulomb interaction approaches the phonon's energy quanta.

Electron transport through a graphene quantum dot: the role of line defect

We investigate the electron transport through a graphene quantum dot with one line defect, by coupling the dot to two normal metallic leads. It is found that in the cases of the leads coupling to the same-type edges of the dot, the presence of line defect enhances the conductance at the Dirac point by inducing a new conductance peak or strengthening the original conductance peak. Such results are irrelevant to the graphene dot size. On the other hand, if the leads couple to the different-type edges of the dot, the line defect will induce two new conductance peaks near the Dirac point. The conductance enhancement is considered to originate from the fact that one bound state at the Dirac point induced by the line defect couples to the leads, which provides an additional channel for electron motion. Nevertheless, different dot–lead coupling manners change the contribution of the new channel to the electron motion, leading to the complicated transport results. These results show that the line-defect-existed graphene quantum dot will be beneficial to the realization of electron transport manipulation.

Trajectory phases of a quantum dot model

We present a thermodynamic formalism to study the trajectories of charge transport through a quantum dot coupled to two leads in the resonant-level model. We show that a close analogue of equilibrium phase transitions exists for the statistics of transferred charge; by tuning an appropriate ‘counting field’, crossovers to different trajectory phases are possible. Our description reveals a mapping between the statistics of a given device and current measurements over a range of devices with different dot–lead coupling strengths. Furthermore insight into features of the trajectory phases are found by studying the occupation of the dot conditioned on the transported charge between the leads; this is calculated from first principles using a trajectory biased two-point projective measurement scheme.

Current noise cross correlation mediated by Majorana bound states

We study the transport properties of a quantum dot-Majorana hybrid system, in which each of paired Majorana bound states is connected to one quantum dot. With the help of non-equilibrium Green's function method, we obtain an exact solution of the Green's functions and calculate the currents through the quantum dots and nonlocal noise cross correlation between the currents. As a function of dot energy levels $\epsilon_{1}$ and $\epsilon_{2}$, we find that for the symmetric level configuration $\epsilon_{1}=\epsilon_{2}$, the noise cross correlation is negative in the low lead voltage regime, while it becomes positive with the increase of the lead voltages. Due to the particle-hole symmetry, the cross correlation is always positive in the anti-symmetric case $\epsilon_{1}=-\epsilon_{2}$. In contrast, the cross correlation of non-Majorana setups is always positive. For comparison, we also perform the diagonalized master equation calculation to check its applicability. It is found that the diagonalized master equations work well in most regimes of system parameters. Nevertheless, it shows an obvious deviation from the exact solution by the non-equilibrium Green's function method when all eigenenergies of the dot-Majorana hybrid system and simultaneously the energy intervals are comparable to the dot-lead coupling strength.

Weak measurement of cotunneling time

Quantum mechanics allows the existence of "virtual states" that have no classical analogue. Such virtual states defy direct observation through strong measurement, which would destroy the volatile virtual state. Here we show how a virtual state of an interacting many-body system can be detected employing a weak measurement protocol with postselection. We employ this protocol for the measurement of the time it takes an electron to tunnel through a virtual state of a quantum dot (cotunneling). Contrary to classical intuition, this cotunneling time is independent of the strength of the dot-lead coupling and may deviate from that predicted by time-energy uncertainty relation. Our approach, amenable to experimental verification, may elucidate an important facet of quantum mechanics which hitherto was not accessible by direct measurements.

Properties of Heat Generation in a Double Quantum Dot

We investigate the electronic-current-induced heat generation in a double quantum dot connected by two normal leads. The dots are coupled in series with a coupling strength td. It is found that, at zero temperature and weak dot-lead coupling, td affects the heating and current heavily. In particular, the effects on the heat generation and on the current are quite different. For example, at a heating valley the current can exhibit a deep valley, a plateau, or a high peak depending on td. As a result, we can find an ideal working condition, large current while small heating, for the double dots system by tuning the interdot coupling strength.

Thermoelectric effects in molecular quantum dots with contacts

We consider the steady-state thermoelectric transport through a vibrating molecular quantum dot that is contacted to macroscopic leads. For moderate electron-phonon interaction strength and comparable electronic and phononic timescales, we investigate the impact of the formation of a local polaron on the thermoelectric properties of the junction. We apply a variational Lang-Firsov transformation and solve the equations of motion in the Kadanoff-Baym formalism up to second order in the dot-lead coupling parameter. We calculate the thermoelectric current and voltage for finite temperature differences in the resonant and inelastic tunneling regimes. For a near resonant dot level, the formation of a local polaron can boost the thermoelectric effect because of the Franck-Condon blockade. The line shape of the thermoelectric voltage signal becomes asymmetrical due to the varying polaronic character of the dot state and in the nonlinear transport regime, vibrational signatures arise.

Electron transport through a triple-quantum-dot ring in various kinds of dot-lead coupling configurations

Electron transport through a triple-quantum-dot ring in various kinds of dot-lead coupling configurations has been investigated using the nonequilibrium Green’s function technique. The conductance is numerically calculated as a function of the dots’ levels. The appearance of Fano resonance and the formation of bound state in the continuum strongly depend on the configuration of dot-lead coupling strengths. Moreover, a striking conductance dip is found and the conductance spectrum can be interchanged by tuning extra magnetic flux.

Bipolaronic blockade effect in quantum dots with negative charging energy

We investigate single-electron transport through quantum dots with negative charging energy induced by a polaronic energy shift. For weak dot-lead tunnel couplings, we demonstrate a bipolaronic blockade effect at low biases which suppresses the oscillating linear conductance, while the conductance resonances under large biases are enhanced. A novel conductance plateau develops when the coupling asymmetry is introduced, with its height and width tuned by the coupling strength and external magnetic field. It is further shown that the amplitude ratio of the magnetic-split conductance peaks changes from 3 to 1 for increasing coupling asymmetry. Though we demonstrate all these transport phenomena in the low-order single-electron tunneling regime, they are already strikingly different from the usual Coulomb blockade physics and are easy to observe experimentally.

Pure spin polarized transport based on Rashba spin—orbit interaction through the Aharonov—Bohm interferometer embodied four-quantum-dot ring

rThe spin-polarized linear conductance spectrum and current—voltage characteristics in a four-quantum-dot ring embodied into Aharonov—Bohm (AB) interferometer are investigated theoretically by considering a local Rashba spin—orbit interaction. It shows that the spin-polarized linear conductance and the corresponding spin polarization are each a function of magnetic flux phase at zero bias voltage with a period of 2π, and that Hubbard U cannot influence the electron transport properties in this case. When adjusting appropriately the structural parameter of inter-dot coupling and dot-lead coupling strength, the electronic spin polarization can reach a maximum value. Furthermore, by adjusting the bias voltages applied to the leads, the spin-up and spin-down currents move in opposite directions and pure spin current exists in the configuration space in appropriate situations. Based on the numerical results, such a model can be applied to the design of a spin filter device.

Evaluating dot–lead coupling in a non-parabolic quantum dot connected to two conducting leads

A manifestly novel approach is developed by considering excitons in a semiconductor non-parabolic quantum dot as hydrogen-atom-like quasi-particles confined in a spherical quantum box, the dot being connected to two conducting leads. In fact, the maximal dot–lead coupling energy is calculated in terms of maximum Fermi velocity within a new perspective.

Fano antiresonance in electron transport through a parallel-coupled quantum-dot structure

The Fano effect in electron transport through a parallel-coupled multi-quantum-dot system is theoretically studied by adjusting the asymmetries of dot-lead couplings. As a result, we find that three kinds of Fano lineshapes emerge in the linear conductance spectra. Namely, when the dot-lead couplings are up-down asymmetric, two kinds of Fano effects occur with the tuning of local magnetic fluxes. The other Fano effect is observed in the case of left-right asymmetry of the dot-lead couplings, which is tightly dependent on the dot number. We then transform the Hamiltonian into molecular orbital representation and discuss the three kinds of Fano interference mechanisms in detail. It is observed that the coupling manners between the leads and molecular states are the key factors to induce the Fano antiresonance. Since the abundant Fano effects, we consider such a structure to be a candidate of a thermoelectric device. We believe that the numerical results help to understand the Fano effect of the parallel-coupled multi-quantum-dot structure.

Phonon-affected steady-state transport through molecular quantum dots

We consider the transport through a vibrating molecular quantum dot contacted to macroscopic leads acting as charge reservoirs. In the equilibrium and nonequilibrium regimes, we study the formation of a polaron-like transient state at the quantum dot for all the ratios of the dot–lead coupling to the energy of the local phonon mode. We show that the polaronic renormalization of the dot–lead coupling is a possible mechanism for negative differential conductance. Moreover, the effective dot level follows one of the lead chemical potentials to enhance resonant transport, causing novel features in the inelastic tunneling signal. In the linear response regime, we investigate the impact of the electron–phonon interaction on the thermoelectrical properties of the quantum dot device.