Dario Ferraro

Wigner function approach to single electron coherence in quantum Hall edge channels

Recent electron quantum optics experiments performed with on-demand single electron sources call for a mixed time/frequency approach to electronic quantum coherence. Here, we present a Wigner function representation of first-order electronic coherence and show that it provides a natural visualization of the excitations emitted by recently demonstrated single electron sources. It also gives a unified perspective on single particle and two particle interferometry experiments. In particular, we introduce a non-classicality criterion for single electron coherence and discuss it in the context of Mach-Zehnder interferometry. Finally, the electronic Hanbury Brown and Twiss and the Hong-Ou-Mandel experiments are interpreted in terms of overlap of Wigner function, thus connecting them to signal processing.

Electron quantum optics in ballistic chiral conductors

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics-like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on-demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury-Brown and Twiss geometry where two-particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.

Electrical switching and interferometry of massive Dirac particles in topological insulator constrictions

We investigate the electrical switching of charge and spin transport in a topological insulator nanoconstriction in a four terminal device. The switch of the edge channels is caused by the coupling between edge states which overlap in the constriction and by the tunneling effects at the contacts and therefore can be manipulated by tuning the applied voltages on the split-gate or by geometrical etching. The switching mechanism can be conveniently studied by electron interferometry involving the measurements of the current in different configurations of the side gates, while the applied bias from the external leads can be tuned to obtain pure charge or pure spin currents (charge- and spin- bias configurations). Relevant signatures of quantum confinement effects, quantum size effects and energy gap are evident in the Fabry-Perot physics of the device allowing for a full characterization of the charge and spin currents. The proposed electrical switching behavior offers an efficient tool to manipulate topological edge state transport in a controllable way.

Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

Non-Abelian BF theory for 2 + 1 dimensional topological states of matter

We present a field theoretical analysis of the 2+1 dimensional BF model with boundary in the Abelian and the non-Abelian case based on Symanziks separability condition. Our aim is to characterize the low-energy properties of time reversal invariant topological insulators. In both cases, on the edges, we obtain Kaalgebras with opposite chiralities reflecting the time reversal invariance of the theory. While the Abelian case presents an apparent arbitrariness in the value of the central charge, the physics on the boundary of the non-Abelian theory is completely determined by time reversal and gauge symmetry. The discussion of the non-Abelian BF model shows that time reversal symmetry on the boundary implies the existence of counter- propagating chiral currents.

Anomalous charge tunneling in fractional quantum Hall edge states at a filling factor ν=5/2.

We explain effective charge anomalies recently observed for fractional quantum Hall edge states at ν=5/2 [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys. Rev. B 81, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly taking into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic 1/f noise. We demonstrate that a peculiar agglomerate excitation with charge e/2, double the expected e/4 charge, dominates the transport properties at low energies.

Relevance of multiple quasiparticle tunneling between edge states at nu=p/(2np+1).

We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series nu=p/(2np+1), for extremely weak backscattering and low temperatures [Y. C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003)10.1103/PhysRevLett.91.216804]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticle tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach p times the single-quasiparticle charge. In this Letter, we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.

Tunneling between helical edge states through extended contacts

INFN, Via Dodecaneso 33, 16146, Genova, Italy.(Dated: June 8, 2012)We consider a quantum spin Hall system in a two-terminal setup, with an extended tunneling contactconnecting upper and lower edges. We analyze the effects of this geometry on the backscatteringcurrent as a function of voltage, temperature, and strength of the electron interactions. We find thatthis configuration may be useful to confirm the helical nature of the edge states and to extract theirpropagation velocity. By comparing with the usual quantum point contact geometry, we observethat the power-law behaviors predicted for the backscattering current and the linear conductanceare recovered for low enough energies, while different power-laws also emerge at higher energies.

Minimal excitation states for heat transport in driven quantum Hall systems

We investigate minimal excitation states for heat transport into a fractional quantum Hall system driven out of equilibrium by means of time-periodic voltage pulses. A quantum point contact allows for tunneling of fractional quasiparticles between opposite edge states, thus acting as a beam splitter in the framework of the electron quantum optics. Excitations are then studied through heat and mixed noise generated by the random partitioning at the barrier. It is shown that levitons, the single-particle excitations of a filled Fermi sea recently observed in experiments, represent the cleanest states for heat transport since excess heat and mixed shot noise both vanish only when Lorentzian voltage pulses carrying integer electric charge are applied to the conductor. This happens in the integer quantum Hall regime and for Laughlin fractional states as well, with no influence of fractional physics on the conditions for clean energy pulses. In addition, we demonstrate the robustness of such excitations to the overlap of Lorentzian wave packets. Even though mixed and heat noise have nonlinear dependence on the voltage bias, and despite the noninteger power-law behavior arising from the fractional quantum Hall physics, an arbitrary superposition of levitons always generates minimal excitation states.

Spin current pumping in helical Luttinger liquids

We study the DC spin current induced into an unbiased quantum spin Hall system through a two-point contacts setup with time dependent electron tunneling amplitudes. By means of two external gates, it is possible to drive a current with spin-preserving and spin-flipping contributions showing peculiar oscillations as a function of pumping frequency, electron-electron interaction and temperature. From its interference patterns as a function of the Fabry-Perot and Aharonov-Bohm phases, it is possible to extract information about the helical nature of the edge states and the intensity of the electron-electron interaction.