Andreas Heimes

Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor

We propose a new mechanism for topological superconductivity based on an antiferromagnetically ordered chain of magnetic atoms on the surface of a conventional superconductor. In a weak Zeeman field, a supercurrent in the substrate generates a staggered spin-current, which converts the preexisting topologically-unprotected Shiba states into Majorana fermions (MFs). The two experimental knobs can be finely tuned providing a platform with enhanced functionality for applications. Remarkably, the electronic spin-polarization of the arising edge MF wavefunctions depends solely on the parity of the number of magnetic moments, which can serve as a distinctive signature of the MFs. We introduce the basic concepts within a minimal model and make contact with experiments by a microscopic analysis based on the Shiba states.

Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface

We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin-orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration.

Tunneling and relaxation of single quasiparticles in a normal-superconductor-normal single-electron transistor

We investigate the properties of a hybrid single electron transistor, involving a small superconducting island sandwiched between normal metal leads, which is driven by dc plus ac voltages. In order to describe its properties we derive from the microscopic theory a set of coupled equations. They consist of a master equation for the probability to find excess charges on the island, with rates depending on the distribution of non-equilibrium quasiparticles. Their dynamics follows from a kinetic equation which accounts for the excitation by single-electron tunneling as well as the relaxation and eventual recombination due to the interaction with phonons. Our low-temperature results compare well with recent experimental findings obtained for ac-driven hybrid single-electron turnstiles.

Parity effect in Josephson junction arrays

We study the parity effect and transport due to quasiparticles in circuits comprised of many superconducting islands. We develop a general approach and show that it is equivalent to previous methods for describing the parity effect in their more limited regimes of validity. As an example we study transport through linear arrays of Josephson junctions in the limit of negligible Josephson energy and observe the emergence of the parity effect with decreasing number of nonequilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multijunction arrays the parity effect manifests in qualitatively different ways to the two-junction case. The role of charge disorder is also studied as this hides much of the parity physics that would otherwise be observed. Nonetheless, we see that the current through a multijunction array at low bias is limited by the formation of metastable even-parity states.

Electronic Decoherence of Two-Level Systems in a Josephson Junction

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an

Lasing and transport in a multi-level double quantum dot system coupled to a microwave oscillator

\mathrm{Al}/{\mathrm{AlO}}_{x}

Majorana fermion fingerprints in spin-polarised scanning tunnelling microscopy

/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating

Excitation of Single Quasiparticles in a Small Superconducting Al Island Connected to Normal-Metal Leads by Tunnel Junctions

{\mathrm{AlO}}_{x}

Reprint of: Majorana fermion fingerprints in spin-polarised scanning tunnelling microscopy

barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc superconducting quantum interference device driven to its resistive state. The decoherence rates were measured by observing the two-level systems quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge.

Experiments on Interaction of Quasiparticles with Two-Level-Systems in a Superconducting Phase Qubit

We study a system of two quantum dots, each with several discrete levels, which are coherently coupled to a microwave oscillator. They are attached to electronic leads and coupled to a phonon bath, both leading to inelastic processes. For a simpler system with a single level in each dot it has been shown that a population inversion can be created by electron tunneling, which in a resonance situation leads to lasing-type properties of the oscillator. In the multi-level system several resonance situations may arise, some of them relying on a sequence of tunneling processes which also involve non-resonant, inelastic transitions. The resulting photon number in the oscillator and the current-voltage characteristic are highly sensitive to these properties and accordingly can serve as a probe for microscopic details.