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

Supercurrent-enabled Andreev reflection in a chiral quantum Hall edge state

Funding: ABM and TLS acknowledge support from the National Research Fund, Luxembourg under the grant ATTRACT, Grant No. A14/MS/7556175/MoMeSys. ABM and BB acknowledge support from St. Leonard’s European Inter-University Doctoral Scholarship of the University of St. Andrews. PR acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the framework of Germany’s Excellence Strategy-EXC-2123 QuantumFrontiers-390837967.A chiral quantum Hall (QH) edge state placed in proximity to an s-wave superconductor experiences induced superconducting correlations. Recent experiments have observed the effect of proximity coupling in QH edge states through signatures of the mediating process of Andreev reflection. We present the microscopic theory behind this effect by modeling the system with a many-body Hamiltonian, consisting of an s-wave superconductor, subject to spin-orbit coupling and a magnetic field, which is coupled by electron tunneling to an integer QH edge state. By integrating out the superconductor we obtain an effective pairing Hamiltonian in the QH edge state. We clarify the qualitative appearance of nonlocal superconducting correlations in a chiral edge state and analytically predict the suppression of electron-hole conversion at low energies (Pauli blocking) and negative resistance as experimental signatures of Andreev reflection in this setup. In particular, we show how two surface phenomena of the superconductor, namely, Rashba spin-orbit coupling and a supercurrent due to the Meissner effect, are essential for the Andreev reflection. Our work provides a promising pathway to the realization of Majorana zero modes and their parafermionic generalizations.Publisher PDFPeer reviewe

Supercurrent-enabled Andreev reflection in a chiral quantum Hall edge state

A chiral quantum Hall (QH) edge state placed in proximity to an s-wave superconductor experiences induced superconducting correlations. Recent experiments have observed the effect of proximity-coupling in QH edge states through signatures of the mediating process of Andreev reflection. We present the microscopic theory behind this effect by modeling the system with a many-body Hamiltonian, consisting of an s-wave superconductor, subject to spin-orbit coupling and a magnetic field, which is coupled by electron tunneling to a QH edge state. By integrating out the superconductor we obtain an effective pairing Hamiltonian in the QH edge state. We clarify the qualitative appearance of nonlocal superconducting correlations in a chiral edge state and analytically predict the suppression of electron-hole conversion at low energies (Pauli blocking) and negative resistance as experimental signatures of Andreev reflection in this setup. In particular, we show how two surface phenomena of the superconductor, namely Rashba spin-orbit coupling and a supercurrent due to the Meissner effect, are essential for the Andreev reflection. Our work provides a promising pathway to the realization of Majorana zero-modes and their parafermionic generalizations.Comment: 15 pages, 7 figure

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