## Contact

Department of Physics
University of Basel
Klingelbergstrasse 82
CH-4056 Basel, Switzerland
 office: 4.8 email: view address tel: ++41 (0)61 267 37 47

## Short CV

 Since September 2013 PhD student in the Condensed Matter Theory & Quantum Computing group at the University of Basel, under the supervision of Prof. Daniel Loss 2012 Masters Thesis at the Boston University Physics Department, Boston under the supervision of Prof. Claudio Chamon and Prof. Manfred Sigrist 2008 - 2013 Undergraduate studies at ETH Zurich, Faculty of Physics

## Publications

Show all abstracts.

 1. Detecting Topological Superconductivity with $\varphi_{0}$ Josephson Junctions Constantin Schrade, Silas Hoffman, and Daniel Loss. arXiv:1607.07794 The interplay of superconductivity, magnetic fields, and spin-orbit interaction lies at the heart of topological superconductivity. Remarkably, the recent experimental discovery of $\varphi_{0}$ Josephson junctions by Szombati et al., Nat. Phys. 12, 568 (2016), characterized by a finite phase offset in the supercurrent, require the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we theoretically show that a quantum dot φ0 Josephson junction can serve as a new qualitative indicator for topological superconductivity: Microscopically, we find that the phase shift in a junction of s−wave superconductors is due to the spin-orbit induced mixing of singly occupied states on the qantum dot, while for a topological superconductor junction it is due to singlet-triplet mixing. Because of this important difference, when the spin-orbit vector of the quantum dot and the external Zeeman field are orthogonal, the s-wave superconductors form a $\pi$ Josephson junction while the topological superconductors have a finite offset $\varphi_{0}$ by which topological superconductivity can be distinguished from conventional superconductivity. Our prediction can be immediately tested in nanowire systems currently used for Majorana fermion experiments and thus offers a new and realistic approach for detecting topological bound states. 2. Universal Quantum Computation with Hybrid Spin-Majorana Qubits Silas Hoffman, Constantin Schrade, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 94, 045316 (2016) We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot tunnel-coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid CNOT gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a CNOT gate is implemented that acts on neighboring Majorana qubits, and eliminates the necessity of inter-qubit braiding. In both setups the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a SWAP or hybrid SWAP gate which is sufficient for universal quantum computation without projective measurements. 3. Proximity-Induced $\pi$ Josephson Junctions in Topological Insulators and Kramers Pairs of Majorana Fermions Constantin Schrade, Alexander Zyuzin, Jelena Klinovaja, and Daniel Loss. Phys. Rev. Lett. 115, 237001 (2015) We study two microscopic models of topological insulators in contact with an s-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of randomly distributed scalar and of randomly oriented spin impurities. Here, we demonstrate that spin-flip tunneling dominates over the spin-conserving one. In the second model the tunnel coupling is realized by a spatially nonuniform array of single-level quantum dots with randomly oriented spins. We find that the tunnel region forms a $\pi$ junction where the effective order parameter changes sign. Because of the random spin orientation, effectively both models exhibit time-reversal symmetry. The proposed $\pi$ junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates.