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This review article describes theoretical and experimental advances in using quantum dots as a system for studying impurity quantum phase transitions and the non-Fermi liquid behavior at the quantum critical point.
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We study the nature of excitons bound to I1 basal plane stacking faults in ensembles of ultrathin GaN nanowires by continuous-wave and time-resolved photoluminescence spectroscopy. These ultrathin nanowires, obtained by the thermal decomposition of spontaneously formed GaN nanowire ensembles, are tapered and have tip diameters down to 6 nm. With decreasing nanowire diameter, we observe a strong blue shift of the transition originating from the radiative decay of stacking fault-bound excitons. Moreover, the radiative lifetime of this transition in the ultrathin nanowires is independent of temperature up to 60 K and significantly longer than that of the corresponding transition in as-grown nanowires. These findings reveal a zero-dimensional character of the confined exciton state and thus demonstrate that I1 stacking faults in ultrathin nanowires act as genuine quantum dots.
By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase induces some nonequilibrium Kondo effects in magnetic susceptibility, spectral functions and current. In the weakly correlated limit, the AFM phase is found still stable, therefore, a magnetic-field-free internal control of spin states can be expected through the continuous FM--AFM phase transition.
We consider a quantum dot embedded in a three-dimensional nanowire with tunable aspect ratio a. A configuration interaction theory is developed to calculate the energy spectra of the finite 1D quantum dot systems charged with two electrons in the presence of magnetic fields B along the wire axis. Fruitful singlet-triplet transition behaviors are revealed and explained in terms of the competing exchange interaction, correlation interaction, and spin Zeeman energy. In the high aspect ratio regime, the singlet-triplet transitions are shown designable by tuning the parameters a and B. The transitions also manifest the highly correlated nature of long nanowire quantum dots.
Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such a system multiple transitions of the spin configuration are theoretically predicted. With a combination of spin blockade and Kondo effect we are able to detect five regions with different spin configurations. Transitions are induced with changing electron numbers.
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 Greens functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.
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