Majorana and Andreev States in Hybrid Circuits combining Spin-active and Superconducting Materials – MASH

To investigate this variety of hybrid structures, tools that have been developed by several of the partners will be implemented:
- Theoretically, the traditional tool to investigate superconductivity in mesoscopic juctions is the Green function's method in Nambu space and the resolution of Bogoliubov de Gennes equations. Further difficulties arise when the Coulomb interaction starts to play a role, in the quantum dot geometry typical of carbon nanotube devices, and possibly in quantum wires also. More advanced numerical techniques (Numerical Renormalization Group, Quantum Monte Carlo) will be used here or further developed in order to address specific questions related to the present proposal (such as the interplay of charging energy, Kondo effect and superconductivity).
-The simple observation of a supercurrent constitutes by itself a proof of the propagation of superconducting correlations throughout the system. This measurement will therefore be the first step for all new hybrid systems.
-Equilibrium properties of Andreev Bound States can be accessed either
By tunneling spectroscopy
The coherent conductor is connected to a superconducting fork forming a loop and a superconducting probe is weakly connected to its central part. The measurement of the differential conductance at low temperatures by this tunnel probe gives access to the local density of states.
By measurements of the current-phase relation and of its derivative.
The hybrid junction is placed in parallel with a conventional Josephson junction having a much larger critical current. The current is proportional to the derivative of the ABS energy with respect to the phase.
-The dynamics of hybrid structures is probed by means of high frequency signals. A general method is to place the hybrid junction in parallel with an inductance (either a real one, or a Josephson junction) in which an ac current leads to an ac modulation of the phase difference across the weak link.

Find below a list of the topics treated during this period. The results are detailed in the corresponding publications (see references in the scientific production part)

Andreev states spectroscopy in atomic contacts

Tunnel spectroscopy of a carbon nanotube quantum dot coupled to a superconductor

Phase-dependent Andreev spectrum in a diffusive SNS junction: Static and dynamic current response

Current-phase relation in carbon nanotubes

AC Josephson effect in topological Josephson junctions,

Dynamics of Majorana States in a Topological Josephson Junction
Nonlocal spin correlations mediated by a superconductor

Superharmonic long-range triplet current in a diffusive Josephson junction

Band structure of magnetic excitations in the vortex phase of a ferromagnetic,superconductor

Stimulation of a Singlet Superconductivity in SFS Weak Links by Spin-Exchange Scattering of Cooper Pairs

On the theory of the proximity effect in atomic scale superconducting/normal metal multilayered structures

From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

Continue to develop the project objectives such as we have planned.

List of Pubicaltions of the Consortium:
Exciting Andreev pairs in a superconducting atomic contact, L. Bretheau, Ç. Ö. Girit, H.,Pothier, D. Esteve, and C. Urbina, Nature 499, 312-315, (2013).
Tunneling spectroscopy of a single quantum dot coupled to a superconductor: From Kondo ridge to Andreev bound states, Pillet J-D, Joyez P, Žitko R, et Goffman M. F., Phys. Rev. B 88, 045101 (2013).
Dissipation and Supercurrent Fluctuations in a Diffusive Normal-Metal–Superconductor Ring B.Dassonneville, M. Ferrier, S. Guéron, and H. Bouchiat Phys. Rev. Lett. 110, 217001 (2013).
Phase-dependent Andreev spectrum in a diffusive SNS junction: Static and dynamic current response M. Ferrier, B. Dassonneville, S. Guéron, and H. Bouchiat Phys. Rev. B 88, 174505 (2013).
Ac Josephson effect in topological Josephson junctions, D. M. Badiane, L. I. Glazman M. Houzet, J. S. Meyer, envoyé à C.R. Physique.
Dynamics of Majorana States in a Topological Josephson Junction, M. Houzet, J. S. Meyer, D. M. Badiane, L. I. Glazman, Phys. Rev. Lett. 111, 046401 (2013).
Nonlocal spin correlations mediated by a superconductor, Taewan Noh, M. Houzet, J. S. Meyer, V. Chandrasekhar, Phys. Rev. B 87, 220502(R) (2013).
Superharmonic long-range triplet current in a diffusive Josephson junction, C. Richard, M. Houzet, J. S. Meyer, Phys. Rev. Lett. 110, 217004 (2013).
Band structure of magnetic excitations in the vortex phase of a ferromagnetic superconductor, Bespalov, A.A. and Buzdin A. I, Phys. Rev. B 87, 094509 (2013).
On the theory of the proximity effect in atomic scale superconducting/normal metal multilayered structures, Montiel X. and Buzdin A. I., Supercond. Sci. Thechnol. 26 085011 (2013).
From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model, D. Sticlet, L. Seabra, F. Pollmann, and J. Cayssol, submitted to Phys. Rev. B.

The supercurrent established between two superconductors connected through a mesoscopic link is mainly carried by localized quasiparticle states, the “Andreev bound states” (ABS).
The first axis of the project is to explore novel fundamental phenomena recently predicted to occur when the spin degree of freedom plays a major role in ABS. These phenomena open a whole avenue of research midway between the fields of spintronics and superconducting devices. For instance we will investigate weak links made of semiconducting nanowires with strong spin-orbit interaction (such as InAs) under an axial magnetic field. Such systems are stirring intense activity worldwide both theoretically and experimentally because it was recently predicted that peculiar ABS could form which behave like Majorana fermions, a type of “elementary particle” that remains elusive in high-energy physics. Besides the quest for Majorana fermions, the project will also consider other properties of spin-active superconducting systems. We will investigate weak links made of half-metallic magnet and non-collinear ferromagnetic heterostructures which are believed to display a highly unusual type of superconductivity with pairs of total spin S=1 instead of S=0. Finally, we will explore the ABS spectrum in quantum dots where the Kondo coupling and superconductivity compete.
The second axis of the project addresses the dynamics of ABS in general, an area that remains relatively unexplored despite several proposals to use ABS as a basis for a new class of qubits. In particular, we aim to explain the recent unexpected observation of low frequency dissipation in diffusive weak links and to assess the energy and phase relaxation times of ABS in atomic contacts. Finally Josephson systems with coexisting Zeeman and spin-orbit effects are also predicted to have very interesting dynamical response which couples the magnetization and the superconductivity degrees of freedom.
Two large experimental groups experts in mesoscopic physics and superconductivity, and two groups of theorists with complementary skills, get strongly involved (465 person.month) in this ambitious project.