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Register a new userGround State and Excitations of Quantum Dots with Magnetic Impurities
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We consider an impurity with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the clean Kondo box model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles.
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We present a new method for calculating ground state properties of quantum dots in high magnetic fields. It takes into account the equilibrium positions of electrons in a Wigner cluster to minimize the interaction energy in the high field limit. Assuming perfect spin alignment the many-body trial function is a single Slater determinant of overlapping oscillator functions from the lowest Landau level centered at and near the classical equilibrium positions. We obtain an analytic expression for the ground state energy and present numerical results for up to N=40.
We analyze the electronic transport through a quantum dot that contains a magnetic impurity. The coherent transport of electrons is governed by the quantum confinement inside the dot, but is also influenced by the exchange interaction with the impurity. The interplay between the two gives raise to the singlet-triplet splitting of the energy levels available for the tunneling electron. In this paper, we focus on the charge fluctuations and, more precisely, the height of the conductance peaks. We show that the conductance peaks corresponding to the triplet levels are three times higher than those corresponding to singlet levels, if electronic correlations are neglected (for non-interacting dots, when an exact solution can be obtained). Next, we consider the Coulomb repulsion and the many-body correlations. In this case, the singlet/triplet peak height ratio has a complex behavior. Usually the highest peak corresponds to the state that is lowest in energy (ground state), regardless if it is singlet or triplet. In the end, we get an insight on the Kondo regime for such a system, and show the formation of three Kondo peaks. We use the equation of motion method with appropriate decoupling.
Using different techniques, and Fermi-liquid relationships, we calculate the variation with applied magnetic field (up to second order) of the zero-temperature equilibrium conductance through a quantum dot described by the impurity Anderson model. We focus on the strong-coupling limit $U gg Delta$ where $U$ is the Coulomb repulsion and $Delta$ is half the resonant-level width, and consider several values of the dot level energy $E_d$, ranging from the Kondo regime $epsilon_F-E_d gg Delta$ to the intermediate-valence regime $epsilon_F-E_d sim Delta$, where $epsilon_F$ is the Fermi energy. We have mainly used density-matrix renormalization group (DMRG) and numerical renormalization group (NRG) combined with renormalized perturbation theory (RPT). Results for the dot occupancy and magnetic susceptibility from DMRG and NRG+RPT are compared with the corresponding Bethe ansatz results for $U rightarrow infty$, showing an excellent agreement once $E_d$ is renormalized by a constant Haldane shift. For $U < 3 Delta$ a simple perturbative approach in $U$ agrees very well with the other methods. The conductance decreases with applied magnetic field for dot occupancies $n_d sim 1$ and increases for $n_d sim 0.5$ or $n_d sim 1.5$ regardless of the value of $U$. We also relate the energy scale for the magnetic-field dependence of the conductance with the width of low energy peak in the spectral density of the dot.
Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the inter-electron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron hopping throughout the system. For stronger periodic confinement potentials, however, the system makes a crossover to a Mott-type strongly correlated ground state where the electrons are completely localized at the individual dots with little inter-dot tunneling. In between these two phases, the system is essentially a strongly correlated electron liquid with inter-site electron hopping constrained by strong Coulomb interaction. We characterize this Wigner-Mott-liquid quantum crossover with detailed numerical finite-size diagonalization calculations of the coupled interacting qubit system, showing that these phases can be smoothly connected by tuning the system parameters. Experimental feasibility of observing such a hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor quantum dot qubits is discussed. In particular, we connect our theoretical results to recent quantum-dot-based quantum emulation experiments where collective Coulomb blockade was demonstrated. One conclusion of our theory is that currently available realistic quantum dot arrays are unable to explore the low-density Wigner phase with only the Mott-liquid crossover being accessible experimentally.
We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain proportional to level spacing. With increasing interaction strength, the even-odd alternation of addition energies disappears, and the probability of non-minimal spin increases, but never exceeds 50%. Within a two-orbital model, we show that the off-diagonal Coulomb matrix elements help stabilize a ground state of minimal spin.
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