Fingerprints of Majorana fermions in current-correlations measurements from a superconducting tunnel microscope

We compute various current correlation functions of electrons flowing from a topological nanowire to the tip of a superconducting scanning tunnel microscope and identify fingerprints of a Majorana bound state. In particular, the spin resolved cross-correlations are shown to display a clear distinction between the presence of a such an exotic state (negative correlations) and an Andreev bound state (positive correlations). Similarity and differences with measurements with a normal tunnel microscope are also discussed, like the robustness to finite temperature for instance.Comment: 7 pages, 2 figure

Transport signatures of topological phases in double nanowires probed by spin-polarized STM

We study a double-nanowire setup proximity coupled to an $s$-wave superconductor and search for the bulk signatures of the topological phase transition that can be observed experimentally, for example, with an STM tip. Three bulk quantities, namely, the charge, the spin polarization, and the pairing amplitude of intrawire superconductivity are studied in this work. The spin polarization and the pairing amplitude flip sign as the system undergoes a phase transition from the trivial to the topological phase. In order to identify promising ways to observe bulk signatures of the phase transition in transport experiments, we compute the spin current flowing between a local spin-polarized probe, such as an STM tip, and the double-nanowire system in the Keldysh formalism. We find that the spin current contains information about the sign flip of the bulk spin polarization and can be used to determine the topological phase transition point.Comment: 12 pages, 7 figure

Spin and Charge Signatures of Topological Superconductivity in Rashba Nanowires

We consider a Rashba nanowire with proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological superconductivity that can be accessed experimentally. We find a similar behaviour for the charge of the bulk quasiparticle states, also exhibiting a sign reversal at the transition. We show that these signatures are robust against random static disorder

Spin-dependent coupling between quantum dots and topological quantum wires

Considering Rashba quantum wires with a proximity-induced superconducting gap as physical realizations of Majorana fermions and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spin-dependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana fermion. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Majorana fermions. The direction of the induced magnetic field on the dot depends on the occupation of the nonlocal fermion formed from the two Majorana end states which can be used as a readout for such a Majorana qubit.Comment: 18 pages, 11 figure

Detection of finite frequency photo-assisted shot noise with a resonant circuit

Photo-assisted transport through a mesoscopic conductor occurs when an oscillatory (AC) voltage is superposed to the constant (DC) bias which is imposed on this conductor. Of particular interest is the photo assisted shot noise, which has been investigated theoretically and experimentally for several types of samples. For DC biased conductors, a detection scheme for finite frequency noise using a dissipative resonant circuit, which is inductively coupled to the mesoscopic device, was developped recently. We argue that the detection of the finite frequency photo-assisted shot noise can be achieved with the same setup, despite the fact that time translational invariance is absent here. We show that a measure of the photo-assisted shot noise can be obtained through the charge correlator associated with the resonant circuit, where the latter is averaged over the AC drive frequency. We test our predictions for a point contact placed in the fractional quantum Hall effect regime, for the case of weak backscattering. The Keldysh elements of the photo-assisted noise correlator are computed. For simple Laughlin fractions, the measured photo-assisted shot noise displays peaks at the frequency corresponding to the DC bias voltage, as well as satellite peaks separated by the AC drive frequency

Poissonian tunneling through an extended impurity in the quantum Hall effect

We consider transport in the Poissonian regime between edge states in the quantum Hall effect. The backscattering potential is assumed to be arbitrary, as it allows for multiple tunneling paths. We show that the Schottky relation between the backscattering current and noise can be established in full generality: the Fano factor corresponds to the electron charge (the quasiparticle charge) in the integer (fractional) quantum Hall effect, as in the case of purely local tunneling. We derive an analytical expression for the backscattering current, which can be written as that of a local tunneling current, albeit with a renormalized tunneling amplitude which depends on the voltage bias. We apply our results to a separable tunneling amplitude which can represent an extended point contact in the integer or in the fractional quantum Hall effect. We show that the differential conductance of an extended quantum point contact is suppressed by the interference between tunneling paths, and it has an anomalous dependence with respect to the bias voltage

Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires

We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, we conclude that this behavior is unrelated to topological superconductivity. To support our analytical model, we also perform a numerical simulation of a hybrid system while explicitly incorporating a thin superconducting layer, showing that all qualitative features of our analytical model are also present in the numerical results.Comment: Accepted for publication in Phys. Rev.

Topological Phase Detection in Rashba Nanowires with a Quantum Dot

We study theoretically the detection of the topological phase transition occurring in Rashba nanowires with proximity-induced superconductivity using a quantum dot. The bulk states lowest in energy of such a nanowire have a spin polarization parallel or antiparallel to the applied magnetic field in the topological or trivial phase, respectively. We show that this property can be probed by the quantum dot created at the end of the nanowire by external gates. By tuning one of the two spin-split levels of the quantum dot to be in resonance with nanowire bulk states, one can detect the spin polarization of the lowest band via transport measurement. This allows one to determine the topological phase of the Rashba nanowire independently of the presence of Majorana bound states

Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momenta, which is an important fingerprint of long range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with non zero momentum is exponential. The distribution of the quasi-condensate is however quasi Gaussian. Experimental relevance of our findings for recent cold atoms experiments are discussed.Comment: 10 pages, 4 figure

On the Gender Bazaar

Denis Chevallier, curator of the exhibition “At the Bazaar of Gender, Feminine-Masculine in the Mediterranean” and Director of Research and Education at Marseille’s Museum of European and Mediterranean Civilizations (MuCEM), spoke with Leora Auslander and Michelle Zancarini-Fournel on 8 December 2013, after taking them on a tour of the exhibition. The exhibition, which closed on 6 January 2014, resulted in two publications, a volume co-authored by Denis Chevallier, Michel Bozon, Michelle Per..