Electron transport in multiterminal networks of Majorana bound states

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics (FCS). In particular, we apply our general results to T-shaped junctions of two Majorana nanowires. When the wires are in the topologically nontrivial regime, three MBS are localized near the outer ends of the wires, while one MBS is localized near the crossing point, and when the lengths of the wires are finite adjacent MBS can overlap. We propose a combination of current and cross-correlation measurements to reveal the predicted coupling of four Majoranas in a topological T~junction. Interestingly, we show that the elementary transport processes at the central lead are different compared to the outer leads, giving rise to characteristic non-local signatures in electronic transport. We find quantitative agreement between our analytical model and numerical simulations of a tight-binding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the cross-correlation functions.Comment: 9 pages, 3 figure

Mott transitions of exciton-polaritons and indirect excitons in a periodic potential

We derive an effective Bose-Hubbard model that predicts a phase transition from Bose-Einstein condensate to Mott insulator in two different systems subject to applied periodic potentials: microcavity exciton-polaritons and indirect excitons. Starting from a microscopic Hamiltonian of electrons and holes, we derive an effective Bose-Hubbard model for both systems and evaluate the on-site Coulomb interaction U and hopping transition amplitudes t. Experimental parameters required for observing a phase transition between a Bose-Einstein condensate and a Mott insulator are discussed. Our results suggest that strong periodic potentials and polaritons with a very large excitonic component are required for observing the phase transition. The form of the indirect exciton interaction is derived including direct and exchange components of the Coulomb interaction. For indirect excitons, the system crosses over from a Bose-Hubbard model into a double layer Fermi-Hubbard model as a function of increasing bilayer separation. The Fermi-Hubbard model parameters are calculated, and the criteria for the location of this crossover are derived. We conjecture that a crossover between a Bose Mott insulator to a Fermi Mott insulator should occur with increasing bilayer separation.Comment: 30 pages, 8 figure

Dynamical Coulomb blockade and spin-entangled electrons

We consider the production of mobile and nonlocal pairwise spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal Fermi liquid leads. The necessary mechanism to separate the two electrons coming from the same Cooper pair (spin-singlet) is achieved by coupling the SC to leads with a finite resistance. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two spin-entangled electrons into the same lead compared to the process where the pair splits and each electron tunnels into a different lead. On the other hand in the pair-split process, the spatial correlation of a Cooper pair leads to a current suppression as a function of distance between the two tunnel junctions which is weaker for effectively lower dimensional SCs.Comment: 5 pages, 2 figure

A Mesoscopic Resonating Valence Bond system on a triple dot

We introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly-occupied dot (spin qubit). Two other strongly capacitively islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1); this embodies the weight of the pendulum. The triple dot is placed between two superconducting leads as shown in Fig. 1. Under well-defined conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent. Consequences in a SQUID-geometry are carefully investigated.Comment: final version to appear in PR

Paramagnetic-diamagnetic interplay in quantum dots for non-zero temperatures

In the usual Fock-and Darwin-formalism with parabolic potential characterized by the confining energy \eps_o := \hbar\omega_o= 3.37 meV, but including explicitly also the Zeeman coupling between spin and magnetic field, we study the combined orbital and spin magnetic properties of quantum dots in a two-dimensional electron gas with parameters for GaAs, for N =1 and N >> 1 electrons on the dot. For N=1 the magnetization M(T,B) consists of a paramagnetic spin contribution and a diamagnetic orbital contribution, which dominate in a non-trivial way at low temperature and fields rsp. high temperature and fields. For N >> 1, where orbital and spin effects are intrinsically coupled in a subtle way and cannot be separated, we find in a simplified Hartree approximation that at N=m^2, i.e. at a half-filled last shell, M(T,B,N) is parallel (antiparallel) to the magnetic field, if temperatures and fields are low enough (high enough), whereas for N\ne m^2 the magnetization oscillates with B and N as a T-dependent periodic function of the variable x:=\sqrt{N}eB/(2m^*c\omega_o), with T-independent period \Delta x =1 (where m^* := 0.067 m_o is the small effective mass of GaAs, while m_o is the electron mass). Correspondingly, by an adiabatic demagnetization process, which should only be fast enough with respect to the slow transient time of the magnetic properties of the dot, the temperature of the dot diminishes rsp. increases with decreasing magnetic field, and in some cases we obtain quite pronounced effects.Comment: LaTeX, 28 pages; including three .eps-figures; final version accepted by J. Phys. CM, with minimal changes w.r.to v

Quantum control on entangled bipartite qubits

Ising interaction between qubits could produce distortion in entangled pairs generated for engineering purposes (as in quantum computation) in presence of parasite magnetic fields, destroying or altering the expected behavior of process in which is projected to be used. Quantum control could be used to correct that situation in several ways. Sometimes the user should be make some measurement upon the system to decide which is the best control scheme; other posibility is try to reconstruct the system using similar procedures without perturbate it. In the complete pictures both schemes are present. We will work first with pure systems studying advantages of different procedures. After, we will extend these operations when time of distortion is uncertain, generating a mixed state, which needs to be corrected by suposing the most probably time of distortion.Comment: 10 pages, 5 figure

Narcolepsy: autoimmunity, effector T cell activation due to infection, or T cell independent, major histocompatibility complex class II induced neuronal loss?

Human narcolepsy with cataplexy is a neurological disorder, which develops due to a deficiency in hypocretin producing neurons in the hypothalamus. There is a strong association with human leucocyte antigens HLA-DR2 and HLA-DQB1*0602. The disease typically starts in adolescence. Recent developments in narcolepsy research support the hypothesis of narcolepsy being an immune-mediated disease. Narcolepsy is associated with polymorphisms of the genes encoding T cell receptor alpha chain, tumour necrosis factor alpha and tumour necrosis factor receptor II. Moreover the rate of streptococcal infection is increased at onset of narcolepsy. The hallmarks of anti-self reactions in the tissue—namely upregulation of major histocompatibility antigens and lymphocyte infiltrates—are missing in the hypothalamus. These findings are questionable because they were obtained by analyses performed many years after onset of disease. In some patients with narcolepsy autoantibodies to Tribbles homolog 2, which is expressed by hypocretin neurons, have been detected recently. Immune-mediated destruction of hypocretin producing neurons may be mediated by microglia/macrophages that become activated either by autoantigen specific CD4+ T cells or superantigen stimulated CD8+ T cells, or independent of T cells by activation of DQB1*0602 signalling. Activation of microglia and macrophages may lead to the release of neurotoxic molecules such as quinolinic acid, which has been shown to cause selective destruction of hypocretin neurons in the hypothalamu

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.Comment: 15 pages, 2 figure

Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler

We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport is dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at the same energy [P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001)]. We seek to revisit the transport of those nonlocal Cooper pairs as well as the efficiency of such an Andreev entangler when including the quantum noise (decoherence).Comment: 15 pages and 6 figures; final version to appear in Physical Review

Aharonov-Bohm effect and broken valley-degeneracy in graphene rings

We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modelled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.Comment: 7 pages, 7 figures, replaced with considerably extended new versio