Katharina Laubscher
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Short CV
2018  present:  PhD student in the Condensed Matter Theory & Quantum Computing Group at the University of Basel, supervised by Prof. Dr. Jelena Klinovaja and Prof. Dr. Daniel Loss (QCQT Fellowship) 
2014  2017:  Master of Science in Physics, University of Basel 
Master's thesis: Universal quantum computation using a hybrid quantum double model, supervised by Dr. James Wootton and Prof. Dr. Daniel Loss  
2011  2014:  Bachelor of Science in Physics, University of Basel 
Research interests
Majorana fermions and parafermions in condensed matter systems, topological quantum computationPublications
Show all abstracts.1.  Fractional secondorder topological insulator from a threedimensional coupledwires construction 
Katharina Laubscher, Pim Keizer, and Jelena Klinovaja. arXiv:2207.04026
We construct a threedimensional secondorder topological insulator with
gapless helical hinge states from an array of weakly tunnelcoupled Rashba
nanowires. For suitably chosen interwire tunnelings, we demonstrate that the
system has a fully gapped bulk as well as fully gapped surfaces, but hosts a
Kramers pair of gapless helical hinge states propagating along a path of hinges
that is determined by the hierarchy of interwire tunnelings and the boundary
termination of the system. Furthermore, the coupledwires approach allows us to
incorporate electronelectron interactions into our description. At suitable
filling factors of the individual wires, we show that sufficiently strong
electronelectron interactions can drive the system into a fractional
secondorder topological insulator phase with hinge states carrying only a
fraction $e/p$ of the electronic charge $e$ for an odd integer $p$.
 
2.  RKKY interaction at helical edges of topological superconductors 
Katharina Laubscher, Dmitry Miserev, Vardan Kaladzhyan, Daniel Loss, and Jelena Klinovaja. arXiv:2203.08137
We study spin configurations of magnetic impurities placed close to the edge of a twodimensional topological superconductor both analytically and numerically. First, we demonstrate that the spin of a single magnetic impurity close to the edge of a topological superconductor tends to align along the edge. The strong easyaxis spin anisotropy behind this effect originates from the interaction between the impurity and the gapless helical Majorana edge states. We then compute the RudermanKittelKasuyaYosida (RKKY) interaction between two magnetic impurities placed close to the edge. We show that, in the limit of large interimpurity distances, the RKKY interaction between the two impurities is mainly mediated by the Majorana edge states and leads to a ferromagnetic alignment of both spins along the edge. This effect can be used to detect helical Majorana edge states.
 
3.  Majorana bound states in semiconducting nanostructures 
Katharina Laubscher and Jelena Klinovaja. Journal of Applied Physics 130, 081101 (2021); arXiv:2104.14459.
In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the wellknown Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spinorbit interaction (SOI) placed in a magnetic field and proximitized by a conventional swave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of twodimensional (2D) topological insulators. We introduce the JackiwRebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D secondorder topological superconductors. This Tutorial is mainly aimed at graduate students  both theorists and experimentalists  seeking to familiarize themselves with some of the basic concepts in the field.
 
4.  Fractional boundary charges with quantized slopes in interacting one and twodimensional systems 
Katharina Laubscher, Clara S. Weber, Dante M. Kennes, Mikhail Pletyukhov, Herbert Schoeller, Daniel Loss, and Jelena Klinovaja. Phys. Rev. B 104, 035432 (2021); arXiv:2101.10301.
We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors ν=1/(2l+1), where l is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has 2l+1 different branches that cannot be connected adiabatically, reflecting the (2l+1)fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.
 
5.  Kramers pairs of Majorana corner states in a topological insulator bilayer 
Katharina Laubscher, Danial Chughtai, Daniel Loss, and Jelena Klinovaja. Phys. Rev. B 102, 195401 (2020); arXiv:2007.13579.
We consider a system consisting of two tunnelcoupled twodimensional topological insulators proximitized by a top and bottom superconductor with a phase difference of π between them. We show that this system exhibits a timereversal invariant secondorder topological superconducting phase characterized by the presence of a Kramers pair of Majorana corner states at all four corners of a rectangular sample. We furthermore investigate the effect of a weak timereversal symmetry breaking perturbation and show that an inplane Zeeman field leads to an even richer phase diagram exhibiting two nonequivalent phases with two Majorana corner states per corner as well as an intermediate phase with only one Majorana corner state per corner. We derive our results analytically from continuum models describing our system. In addition, we also provide independent numerical confirmation of the resulting phases using discretized lattice representations of the models, which allows us to demonstrate the robustness of the topological phases and the Majorana corner states against parameter variations and potential disorder.
 
6.  Majorana zero modes and their bosonization 
Victor Chua, Katharina Laubscher, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 102, 155416 (2020); arXiv:2006.03344.
The simplest continuum model of a onedimensional noninteracting superconducting fermionic symmetryprotected topological (SPT) phase is analyzed in great detail using analytic methods. A full exact diagonalization of the meanfield Bogoliubovde Gennes Hamiltonian is carried out with open boundaries and finite lengths. Majorana zero modes are derived and studied in great detail. Thereafter exact operator bosonization in both open and closed geometries is carried out. The complementary viewpoints provided by fermionic and bosonic formulations of the superconducting SPT phase are then reconciled. In particular, we provide a complete and exact account of how the topological Majorana zero modes manifest in a bosonized description of an SPT phase.
 
7.  Majorana and parafermion corner states from two coupled sheets of bilayer graphene 
Katharina Laubscher, Daniel Loss, and Jelena Klinovaja. Phys. Rev. Research 2, 013330 (2020); arXiv:1912.10931.
We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spinorbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable interwire couplings the system supports a topological insulator phase exhibiting Kramers partners of gapless helical edge states, while the additional presence of a small inplane magnetic field and weak proximityinduced superconductivity leads to the emergence of zeroenergy Majorana corner states at all four corners of a rectangular sample, indicating the transition to a secondorder topological superconducting phase. The presence of strong electronelectron interactions is shown to promote the above phases to their exotic fractional counterparts. In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional secondorder topological superconducting phase exhibiting zeroenergy Z_{2m} parafermion corner states, where m is an odd integer determined by the position of the chemical potential.
 
8.  Fractional topological superconductivity and parafermion corner states 
Katharina Laubscher, Daniel Loss, and Jelena Klinovaja. Phys. Rev. Research 1, 032017(R) (2019); arXiv:1905.00885.
We consider a system of weakly coupled Rashba nanowires in the strong spinorbit interaction (SOI) regime. The nanowires are arranged into two tunnelcoupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. We show that in such a system strong electronelectron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of ℤ2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak inplane magnetic field, the system is driven into a secondorder topological superconducting phase hosting zeroenergy ℤ2m parafermion bound states localized at two opposite corners of a rectangular sample. As a special case, zeroenergy Majorana corner states emerge in the noninteracting limit m=1, where the chemical potential is tuned to the SOI energy of the single nanowires.
 
9.  Universal quantum computation in the surface code using nonAbelian islands 
Katharina Laubscher, Daniel Loss, and James R. Wootton. Phys. Rev. A 100, 012338 (2019); arxiv:1811.06738.
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to faulttolerantly apply nonClifford gates. Additional techniques are therefore required to achieve universal quantum computation. Here we propose a new method, using small islands of a qudit variant of the surface code. This allows the nontrivial action of the nonAbelian anyons in the latter to process information stored in the former. Specifically, we show that a nonstabilizer state can be prepared, which allows universality to be achieved.
 
10.  Poking holes and cutting corners to achieve Clifford gates with the surface code 
Benjamin J. Brown, Katharina Laubscher, Markus S. Kesselring, and James R. Wootton. Phys. Rev. X 7, 021029 (2017); arXiv:1609.04673.
The surface code is currently the leading proposal to achieve faulttolerant quantum computation. Among its strengths are the plethora of known ways in which faulttolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes and even by braiding engineered Majorana modes using twist defects. Here we present a unified framework to describe these methods, which can be used to better compare different schemes, and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform singlequbit Clifford gates by exchanging the corners of the planar code via code deformation. We analyse ways in which different schemes can be combined, and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code without loss of distance using code deformations, thus offering an attractive alternative to ancillamediated schemes to complete the Clifford group with lattice surgery.
