Multiterminal Quantum Dot Research Articles

Simulating quantum transport with ultracold atoms and interaction effects

Quantum transport can be simulated with ultracold atoms by employing spin superpositions of fermions interacting with spin-dependent potentials. Here we first extend this scheme to an arbitrary number of spin components so as to allow simulating transport through a multiterminal quantum dot and derive a current formula in terms of a spin rotation matrix and potential phase shifts. We then show that a Fano resonance manifests itself in measuring a linear conductance at zero temperature in the case of two spin components. We also study how a weak interparticle interaction in bulk affects quantum transport in one dimension with the bosonization and renormalization techniques. In particular, we find that the conductance vanishes for an attractive interaction due to a bulk spin gap, while it is enhanced for a repulsive interaction by a power law with lowering the temperature or the chemical potential difference.

Berry phase in superconducting multiterminal quantum dots

We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a non-trivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Berry phase takes the values $\varphi_B=0$ or $\varphi_B=\pi$. We demonstrate that this non-trivial Berry phase can be observed by tunneling spectroscopy in the Floquet spectra. Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting multiterminal quantum dots are shifted by half-a-period if $\varphi_B=\pi$. Our numerical calculations based on Keldysh Green's functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.

Engineering the Floquet spectrum of superconducting multiterminal quantum dots

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave-function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road-map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.

Generation of spin-polarized current using multiterminal quantum dot with spin-orbit interaction

We theoretically examine generation of spin-polarized current using multi-terminated quantum dot with spin-orbit interaction. First, a two-level quantum dot is analyzed as a minimal model, which is connected to $N$ ($\ge 2$) external leads via tunnel barriers. When an unpolarized current is injected to the quantum dot from a lead, a polarized current is ejected to others, similarly to the spin Hall effect. In the absence of magnetic field, the generation of spin-polarized current requires $N \ge 3$. The polarization is markedly enhanced by resonant tunneling when the level spacing in the quantum dot is smaller than the level broadening due to the tunnel coupling to the leads. In a weak magnetic field, the orbital magnetization creates a spin-polarized current even in the two-terminal geometry (N=2). The numerical study for generalized situations confirms our analytical result using the two-level model.

Full counting statistics of Kondo-type tunneling in a quantum dot: Fluctuation effects of the slave-boson field

We study the full counting statistics (FCS) of electron tunneling through a multi-terminal quantum dot in the Kondo regime within the slave-boson mean field theory. By employing the A.O. Gogolin and A. Komnik's method of calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B {\bf 73}, 195301 (2006)], we obtain the counting field $\lambda$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing perturbative expansion to the first order of $\lambda$, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current auto-correlation and a positive current cross-correlation.

Shot noise properties of electron transport through an interacting multi-terminal quantumdots system

We study the correlations of tunneling currents through an interacting quantum dots(QDs) system composed of a top single QD and a bottom qubit with purely capacitivecoupling within a quantum master approach. We find that the super-Poissonian currentnoise of the qubit near resonance, which is a signature of coherent tunneling within thetransport qubit for asymmetrical contact couplings, is strongly dependent onnon-equilibrium transport through the top QD with different coupling configurations. Forpure-dephasing coupling, such a super-Poissonian feature is asymmetrically washed out byincreasing coupling strength showing obvious qubit level position dependencewith finite bias and temperature, while for orthogonal coupling we can almostsymmetrically lower the double peak to a double minimum by increasing couplingstrength or adjusting the ratio of the top QD contact couplings in the large biaslimit, indicating the transition from coherent tunneling to sequential tunneling.

Atomic-Scale, All Epitaxial In-Plane Gated Donor Quantum Dot in Silicon

Nanoscale control of doping profiles in semiconductor devices is becoming of critical importance as channel length and pitch in metal oxide semiconductor field effect transistors (MOSFETs) continue to shrink toward a few nanometers. Scanning tunneling microscope (STM) directed self-assembly of dopants is currently the only proven method for fabricating atomically precise electronic devices in silicon. To date this technology has realized individual components of a complete device with a major obstacle being the ability to electrically gate devices. Here we demonstrate a fully functional multiterminal quantum dot device with integrated donor based in-plane gates epitaxially assembled on a single atomic plane of a silicon (001) surface. We show that such in-plane regions of highly doped silicon can be used to gate nanostructures resulting in highly stable Coulomb blockade (CB) oscillations in a donor-based quantum dot. In particular, we compare the use of these all epitaxial in-plane gates with conventional surface gates and find superior stability of the former. These results show that in the absence of the randomizing influences of interface and surface defects the electronic stability of dots in silicon can be comparable or better than that of quantum dots defined in other material systems. We anticipate our experiments will open the door for controlled scaling of silicon devices toward the single donor limit.

Magnetic-field symmetries of mesoscopic non-linear conductance

We examine contributions to the DC-current of mesoscopic samples which are non-linear in applied voltage. In the presence of a magnetic field, the current can be decomposed into components which are odd (anti-symmetric) and even (symmetric) under flux reversal. For a two-terminal chaotic cavity, these components turn out to be very sensitive to the strength of the Coulomb interaction and the asymmetry of the contact conductances. For both two- and multi-terminal quantum dots we discuss correlations of current non-linearity in voltage measured at different magnetic fields and temperatures.

Asymmetries of the conductance matrix in a three-terminal quantum ring in the Coulomb blockade regime

The conductance matrix of a three-terminal quantum ring has been measured in the Coulomb blockade regime for strong coupling to the leads. In contrast to multi-terminal quantum dots in the weak coupling regime, we find that the conductance matrix is asymmetric. This is a direct evidence of the relevance of phase coherence in transport experiments through quantum dots strongly coupled to the leads.

Mesoscopic transport through a multi-terminal quantum dot system

We investigate a multi-terminal coupled-quantum-dot system, where each of the terminals is disturbed by an external wave field with frequency ω 0. The nonequilibrium Green function technique is employed, and a Landauer-Büttiker-like formula is obtained. During the transport the electrons can tunnel to electron states at different levels in the different terminals due to the absorption and emittance of photons.