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Journal of sciences, Islamic Republic of Iran

Bistability in the Electric Current through a Quantum-Dot Capacitively Coupled to a Charge-Qubit

S. Mojtaba Tabatabaei

Published Jan 30, 2018• 0 citations
Publisher

Abstract

We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of interaction between the quantum-dot and the charge-qubit by employing the Majorana fermion representation for isospin operators of the qubit. Our results show that in the particle-hole symmetric situation, the electric current of the QD exhibits a unitary linear conductance at low bias voltage and at the higher bias voltage it has a nonlinear dependence on the bias voltage. Moreover, we find that at some appropriate parameter regimes, the current through the QD as a function of gate voltage, at a fixed bias voltage shows bistability.

DOI
10.22059/jsciences.2018.64796

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We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of interaction between the quantum-dot and the charge-qubit by employing the Majorana fermion representation for isospin operators of the qubit. Our results show that in the particle-hole symmetric situation, the electric current of the QD exhibits a unitary linear conductance at low bias voltage and at the higher bias voltage it has a nonlinear dependence on the bias voltage. Moreover, we find that at some appropriate parameter regimes, the current through the QD as a function of gate voltage, at a fixed bias voltage shows bistability.
We consider the capacitive interaction between a charge qubit and a sensor quantum dot (SQD) perturbatively to the second order of their coupling constant at zero temperature by utilizing the method of nonequilibrium Green's functions together with infinite-UUU Lacroix approximation and employing Majorana fermion representation for qubit isospin operators. The effect of back-actions on dynamics of the system is taken into account by calculating the self-energies and the Green's functions in a self-consistent manner. To demonstrate the applicability of the method, we investigate relevant physical quantities of the system at zero and finite bias voltages. In the regime of weak SQD-qubit coupling, we find a linear relation between the stationary-state expectation values of the third component of the qubit isospin vector, $\ensuremath{\langle}{\ensuremath{\tau}}_{3}\ensuremath{\rangle}$, and the differential conductance of the SQD. Furthermore, our numerical results predict that the effect of SQD-qubit coupling on differential conductance of the SQD should be maximized at zero bias voltage. Moreover, we obtain an analytical expression to describe the behavior of the differential conductance of the SQD with respect to the qubit parameters. Our results at zero bias voltage are consistent with the results of numerical renormalization group method.
We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.
We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of nonequilibrium cluster perturbation theory and the nonequilibrium variational cluster approach, respectively. Results for the steady-state current are benchmarked against data from accurate matrix product state based time evolution. We show that for low to medium interaction strength, nonequilibrium cluster perturbation theory already yields good results, while for higher interaction strength the self-consistent feedback of the nonequilibrium variational cluster approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the nonequilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle-hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [A. V. Kretinin et al., Phys. Rev. B 84, 245316 (2011)].
Scattering states fulfill the correct boundary conditions of a current carrying open quantum system. Discretizing the energy continuum of these states allows for employing Wilson's numerical renormalization group approach without violating the boundary conditions by using a finite size system. We evolve the analytically known steady-state density operator for a non-interacting quantum-system at finite bias to the full interacting problem by the time-dependent numerical renormalization group after switching on the local charging energy. Using a newly developed algorithm for steady-state nonequilibrium Green functions, we can calculate the current I as function of bias voltage V for arbitrary temperature and magnetic field. A comparison with second-order and GW Kadanoff-Baym-Keldysh results shows excellent agreement for weak interaction strength U .
Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for RRR depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.
Abstract. We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zerobias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.