Entanglement of an impurity and conduction spins in the Kondo model

Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length $\xi_K$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly same to that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.Comment: 5 pages, 2 figures, accepted for publication in Physical Review

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure

Tunable few electron quantum dots in InAs nanowires

Quantum dots realized in InAs are versatile systems to study the effect of spin-orbit interaction on the spin coherence, as well as the possibility to manipulate single spins using an electric field. We present transport measurements on quantum dots realized in InAs nanowires. Lithographically defined top-gates are used to locally deplete the nanowire and to form tunneling barriers. By using three gates, we can form either single quantum dots, or two quantum dots in series along the nanowire. Measurements of the stability diagrams for both cases show that this method is suitable for producing high quality quantum dots in InAs.Comment: 8 pages, 4 figure

Universality of the Kondo effect in quantum dots with ferromagnetic leads

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. In most odd Coulomb valleys the Kondo resonance exhibits a pronounced splitting, which depends on the tunnel coupling to the leads and an external magnetic field $B$, and only weakly on gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on $g \mu_B (B-B_c) / k_B T_K$, where $T_K$ is the Kondo temperature and $B_c$ the external field compensating the splitting.Comment: 4 pages, 4 figure

Electron transport through multilevel quantum dot

Quantum transport properties through some multilevel quantum dots sandwiched between two metallic contacts are investigated by the use of Green's function technique. Here we do parametric calculations, based on the tight-binding model, to study the transport properties through such bridge systems. The electron transport properties are significantly influenced by (a) number of quantized energy levels in the dots, (b) dot-to-electrode coupling strength, (c) location of the equilibrium Fermi energy $E_F$ and (d) surface disorder. In the limit of weak-coupling, the conductance ($g$) shows sharp resonant peaks associated with the quantized energy levels in the dots, while, they get substantial broadening in the strong-coupling limit. The behavior of the electron transfer through these systems becomes much more clearly visible from our study of current-voltage ($I$-$V$) characteristics. In this context we also describe the noise power of current fluctuations ($S$) and determine the Fano factor ($F$) which provides an important information about the electron correlation among the charge carriers. Finally, we explore a novel transport phenomenon by studying the surface disorder effect in which the current amplitude increases with the increase of the surface disorder strength in the strong disorder regime, while, the amplitude decreases in the limit of weak disorder. Such an anomalous behavior is completely opposite to that of bulk disordered system where the current amplitude always decreases with the disorder strength. It is also observed that the current amplitude strongly depends on the system size which reveals the finite quantum size effect.Comment: 12 pages, 7 figure

Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the one-band Hubbard model, reconfirming the numerical renormalization group results.Comment: 4 pages, 4 figure

Measurements of higher order noise correlations in a quantum dot with a finite bandwidth detector

We present measurements of the fourth and fifth cumulants of the distribution of transmitted charge in a tunable quantum dot. We investigate how the measured statistics is influenced by the finite bandwidth of the detector and by the finite measurement time. By including the detector when modeling the system, we use the theory of full counting statistics to calculate the noise levels for the combined system. The predictions of the finite-bandwidth model are in good agreement with measured data

Coulomb oscillations in three-layer graphene nanostructures

We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Three lateral graphene gates are used to electrostatically tune the device. An individual three-layer graphene constriction has been investigated separately showing a transport gap near the charge neutrality point. The graphene tunneling barriers show a strongly nonmonotonic coupling as function of gate voltage indicating the presence of localized states in the constrictions. We show Coulomb oscillations and Coulomb diamond measurements proving the functionality of the graphene SET. A charging energy of $\approx 0.6$ meV is extracted.Comment: 10 pages, 6 figure

A nearly closed ballistic billiard with random boundary transmission

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $\sigma$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur

Universal phase shift and non-exponential decay of driven single-spin oscillations

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear spin bath. Due to the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of ~pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.Comment: Main text: 4 pages, 3 figures, Supplementary material: 2 pages, 3 figure