Spin Qubits in Multi-Electron Quantum Dots

We study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the constraint of having short pulses and small errors implies keeping accurate control, at the few percent level, of several electrode voltages. In practice, the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four.Comment: RevTex, 6 pages, 5 figures. v3: two figures added, more details provided. Accepted for publication in PR

Spin Hall effect in clean two dimensional electron gases with Rashba spin-orbit coupling

We study the spin polarization induced by a current flow in clean two dimensional electron gases with Rashba spin-orbit coupling. This geometric effect originates from special properties of the electron's scattering at the edges of the sample. In wide samples, the spin polarization has it largest value at low energies (close to the bottom of the band) and goes to zero at higher energies. In this case, the spin polarization is dominated by the presence of evanescent modes which have an explicit spin component outside the plane. In quantum wires, on the other hand, the spin polarization is dominated by interference effects induced by multiple scattering at the edges. Here, the spin polarization is quite sensitive to the value of the Fermi energy, especially close to the point where a new channel opens up. We analyzed different geometries and found that the spin polarization can be strongly enhanced.Comment: 10 pages, 13 figures, high quality figures available upon reques

Edge channel mixing induced by potential steps in an integer quantum Hall system

We investigate the coherent mixing of co-propagating edge channels in a quantum Hall bar produced by step potentials. In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing. In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step. Charge density probability has been also calculated even for the case where the step is smoothened.Comment: final version: 7 pages, 6 figure

Imaging transverse electron focusing in semiconducting heterostructures with spin-orbit coupling

Transverse electron focusing in two-dimensional electron gases (2DEGs) with strong spin-orbit coupling is revisited. The transverse focusing is related to the transmission between two contacts at the edge of a 2DEG when a perpendicular magnetic field is applied. Scanning probe microscopy imaging techniques can be used to study the electron flow in these systems. Using numerical techniques we simulate the images that could be obtained in such experiments. We show that hybrid edge states can be imaged and that the outgoing flux can be polarized if the microscope tip probe is placed in specific positions.Comment: Contribution to the Book/Proceedings of the PITP Les Houches School on "Quantum Magnetism" held on June, 2006. Final forma

Out of equilibrium transport through an Anderson impurity: Probing scaling laws within the equation of motion approach

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing in the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G_2(T,V) to test several scaling laws. We find that G_2(T,V)/G_2(T,0) is a universal function of both eV/T_K and T/T_K, being T_K the Kondo temperature. The effect of an in plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting \Delta, the computed differential conductance peak splitting depends only on \Delta/T_K, and for large fields approaches the value of 2\Delta . Besides the traditional two leads setup, we also consider other configurations that mimics recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as \ln(eV/T_K). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.Comment: 9 pages, 7 figure

Mesoscopic Fluctuations in Quantum Dots in the Kondo Regime

Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime.Comment: 4 pages, 3 figure

Experimental approval of the extended flat bands and gapped subbands in rhombohedral multilayer graphene

Graphene layers are known to stack in two stable configurations, namely ABA or ABC stacking, with drastically distinct electronic properties. Unlike the ABA stacking, little has been done to experimentally investigate the electronic properties of ABC graphene multilayers. Here, we report the first magneto optical study of a large ABC domain in a graphene multilayers flake, with ABC sequences exceeding 17 graphene sheets. The ABC-stacked multilayers can be fingerprinted with a characteristic electronic Raman scattering response, which persists even at room temperatures. Tracing the magnetic field evolution of the inter Landau level excitations from this domain gives strong evidence to the existence of a dispersionless electronic band near the Fermi level, characteristic of such stacking. Our findings present a simple yet powerful approach to probe ABC stacking in graphene multilayer flakes, where this highly degenerated band appears as an appealing candidate to host strongly correlated states.Comment: 8 pages, 4 figure

Linear conductance in Coulomb-blockade quantum dots in the presence of interactions and spin

We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we use a rate-equations approach to describe the transitions between the corresponding many-body states. We discuss both the elastic and rapid-thermalization limits, where the rate of inelastic scattering in the dot is either small or large compared with the elastic transition rate, respectively. In the elastic limit, we find several cases where a closed solution for the conductance is possible, including the case of a constant exchange interaction. In the rapid-thermalization limit, a closed solution is possible in the general case. We show that the corresponding expressions for the linear conductance simplify for a Hamiltonian that is invariant under spin rotations.Comment: 11 pages, no figures, revtex

Recurrence of fidelity in near integrable systems

Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.Comment: 13 pages, 6 figure

On general relation between quantum ergodicity and fidelity of quantum dynamics

General relation is derived which expresses the fidelity of quantum dynamics, measuring the stability of time evolution to small static variation in the hamiltonian, in terms of ergodicity of an observable generating the perturbation as defined by its time correlation function. Fidelity for ergodic dynamics is predicted to decay exponentially on time-scale proportional to delta^(-2) where delta is the strength of perturbation, whereas faster, typically gaussian decay on shorter time scale proportional to delta^(-1) is predicted for integrable, or generally non-ergodic dynamics. This surprising result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with a tilted magnetic field where we find finite parameter-space regions of non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure