Full counting statistics of Majorana interferometers

in Physica E: Low-Dimensional Systems and Nanostructures (2015), 74

We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained ... [more ▼]

We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained from the 4×4 scattering matrix S that relates the outgoing Dirac fermions to the incoming Dirac fermions. After presenting explicit expressions for the higher-order current correlations for a modified Hanbury Brown–Twiss interferometer, we note that the cumulant-generating function can be interpreted such that unit-charge transfer processes correspond to two independent half-charge transfer processes, or alternatively, to two independent electron-hole conversion processes. By a combination of analytical and numerical approaches, we verify that this factorization property holds for a general SO(4) scattering matrix, i.e. for a general interferometer geometry. [less ▲]

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Scientific Conference (2015, July)

Parafermions in time-reversal invariant topological insulators

Presentation (2015, June)

Z4 parafermions in time-reversal invariant topological insulators

Presentation (2015, June)

Spin texture of generic helical edge states

in Physical Review. B (2015), 91

We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin symmetry. By considering honeycomb and square-lattice realizations ... [more ▼]

We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin symmetry. By considering honeycomb and square-lattice realizations of topological insulators, we show that in all cases the generic behavior of a momentum-dependent rotation of the spin quantization axis is realized. Here we establish this mechanism also for disk geometries with continuous rotational symmetry. Finally, we demonstrate that the rotation of spin-quantization axis remains intact for arbitrary geometries, i.e., in the absence of any continuous symmetry. We also calculate the dependence of this rotation on the model and material parameters. Finally, we propose a spectroscopy measurement which should directly reveal the rotation of the spin-quantization axis of the helical edge states. [less ▲]

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Scientific Conference (2015, March)

Non-Abelian parafermions in time-reversal invariant interacting helical systems

in Physical Review. B (2015), 91

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical ... [more ▼]

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\pi$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems. [less ▲]

Electron transport in multiterminal networks of Majorana bound states

in Physical Review. B (2014), 90

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to T-shaped ... [more ▼]

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. 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 nonlocal 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. [less ▲]

Detecting an exciton crystal by statistical means

in Physica B. Condensed Matter (2014), 441

We investigate an ensemble of excitons in a coupled quantum well excited via an applied laser field. Using an effective disordered quantum Ising model, we perform a numerical simulation of the ... [more ▼]

We investigate an ensemble of excitons in a coupled quantum well excited via an applied laser field. Using an effective disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function P(M) to create M excitons as well as their correlation function. It shows clear evidence of the existence of two phases corresponding to a liquid and a crystal phase. We demonstrate that not only the correlation function but also the distribution P(M) is very well suited to monitor this transition. [less ▲]

Transport properties of double quantum dots with electron-phonon coupling

in Physical Review. B (2013), 88

We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the ... [more ▼]

We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the interplay between strong electron-phonon coupling and interdot tunneling can lead to a negative differential conductance at bias voltages exceeding the phonon frequency. Various transport properties are discussed, and we explain the physics of the occurrence of negative differential conductance in this system. [less ▲]