Research

My interests

I enjoy thinking about problems that require combining analytical insight with equations only a computer can solve. Mesoscopic systems often benefit from this approach: they are small enough to behave quantum mechanically, and yet large enough to require several degrees of freedom to describe them.

🔨 Mesoscopic superconductivity

Two-dimensional devices offer the possibility of combining different materials such that different properties combine and give rise to tailored phenomena.

For example, placing a superconductor in close proximity to a semiconductor turns the latter into a superconductor via the proximity effect, and allows to design Josephson junctions with highly tunable properties.

My colleagues and I found that superconducting trijunctions can host chiral protected transport of Andreev bound states.

📄 Paper 💻 GitHub Repository

🪢 Topological phases of matter

Protected transport also naturally arises in topological phases of matter, where conduction channels are robust while the bulk remains insulating and symmetry-protected. A Chern insulator, for example, hosts two counter-propagating edge states that may not disappear unless the bulk undergoes a delocalization transition. A powerful tool to characterize these phases are scattering invariants, which rely on a transport setup to probe the topological properties of a system.

Johanna, Anton, and I recently generalized these invariants to phases protected by spatial symmetries, which may or may not host conducting protected modes.

📄 Paper 💻 GitHub Repository

💻 Open-source software

Complex quantum mechanical systems with too many degrees of freedom are often impossible to solve analytically, and sometimes even numerically. Constructing an effective model that captures the essential physics of the system is then the key to making progress. A common approach is to use the Schrieffer–Wolff transformation to block-diagonalize the Hamiltonian perturbatively, separating the low-energy subspace from the rest. This is, however, standard and yet tedious. Even worse, Schrieffer–Wolff transformations scale poorly with the perturbative order of the Hamiltonian, and they are limited to two subspaces.

My colleagues and I developed an efficient algorithm and a Python package 📦 that automates this process. Pymablock works with any number of subspaces, any number of perturbative orders, and it can handle both symbolic and numerical inputs ✨.

📖 Documentation 💻 GitHub Repository 📄 Paper

Publications

Talks