Research

Trivial and Topological States in Low-dimensional Devices

One theme of our theoretical work is distinguishing topological from trivial states. Trivial states due to disorder physics can produce strikingly similar experimental signatures to topological states such as Majorana bound states. For instance, we recently investigated the nature of so-called “poor man’s Majoranas” (PMMs), which are highly tunable Majorana-like states in short chains of coupled quantum dots. Our analysis revealed a subtlety: some (“false PMMs”) evolve into trivial states as the chain is made longer and some evolve into topological states (“true PMMs” ). However, in minimal systems with just a few quantum dots, both true and false PMMs have almost identical experimental signatures. Notably, we have also shown that even more advanced experimental protocols can be mimicked by trivial physics. For instance, our theoretical work demonstrated how a band of trivial Andreev bound states can produce an apparent closing and reopening of the bulk energy gap in nonlocal conductance—a signature claimed to be a hallmark of a topological phase transition and integral, for instance, to Microsoft Quantum’s topological gap protocol. Beyond identifying these pitfalls, our work also explores different platforms, for instance with a proposed, planar Josephson junctions in Germanium, that can be driven into a topological phase using only superconducting phase control, avoiding the large magnetic fields that often complicate other experimental setups.

Key References

1. Legg, H. F., Loss, D., & Klinovaja, J. Majorana bound states in topological insulators without a vortex. Physical Review B, 104, 165405 (2021).
2. Luethi, M., Legg, H. F., Loss, D., & Klinovaja, J. Fate of poor man’s Majoranas in the long Kitaev chain limit. Physical Review B 111, 115419 (2025).
3. Hess, R., Legg, H. F., Loss, D., & Klinovaja, J. Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires. Physical Review Letters 130, 207001 (2023).
4. Hess, R., Legg, H. F., Loss, D., & Klinovaja, J. Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors. Physical Review B 106, 104503 (2022).
5. Luethi, M., Legg, H. F., Laubscher, K., Loss, D., & Klinovaja, J. Majorana bound states in germanium Josephson junctions via phase control. Physical Review B 108, 195406 (2023).

Nonlinear Transport Phenomena and the Superconducting Diode Effect

Another key thread of our work explores nonlinear and non-reciprocal transport phenomena in quantum materials. Whilst conventional electronics are governed by Ohm’s law, where resistance is constant, breaking fundamental symmetries in a material or device can lead to new effects beyond Ohm’s law. One such phenomenon is magnetochiral anisotropy (MCA), where a material’s resistance depends on both the direction of current flow and an applied magnetic field. Our work has shown that topological materials can host exceptionally large non-reciprocal effects. In topological insulator nanowires (see below for further details), for instance, we predicted and experimentally confirmed a giant MCA by using a gate to artificially break inversion symmetry. A similarly gigantic effect was also discovered in the topological semimetal ZrTe₅, which we attribute to its unique torus-shaped Fermi surface near a topological quantum phase transition. These normal-state phenomena have a direct analogue in the superconducting state, known as the Superconducting Diode Effect (SDE), where the critical current itself becomes directional. Our theoretical work has explored the SDE in various topological platforms. In TI nano-SQUIDs, for example, we showed that the device naturally functions as a highly tunable Josephson diode, where the effect is controlled by both magnetic flux and gate voltage. More fundamentally, we have established that the SDE can serve as a powerful probe of the underlying physics. Theoretical analysis shows that a change in the diode effect can signal the onset of a topological phase transition, providing a new experimental signature for these elusive states. This has also led to proposals for novel devices like a Josephson transistor, where the diode effect is switched by moving magnetic textures such as skyrmions.

Key References

1. Legg, H. F., Rößler, M., Münning, F., et al. Giant magnetochiral anisotropy from quantum-confined surface states of topological insulator nanowires. Nature Nanotechnology 17, 696 (2022).
2. Wang, Y., Legg, H. F., Bömerich, T., et al. Gigantic Magnetochiral Anisotropy in the Topological Semimetal ZrTe₅. Physical Review Letters 128, 176602 (2022).
3. Legg, H. F., Loss, D., & Klinovaja, J. Superconducting diode effect due to magnetochiral anisotropy in topological insulators and Rashba nanowires. Physical Review B 106, 104501 (2022).
4. Nikodem, E., Schluck, J., Geier, M., Papaj, M., Legg, H. F., et al. Tunable superconducting diode effect in a topological nano-SQUID. Science Advances 11, eadw4898 (2025).
5. Legg, H. F., Laubscher, K., Loss, D., & Klinovaja, J. Parity-protected superconducting diode effect in topological Josephson junctions. Physical Review B 108, 214520 (2023).
6. Hess, R., Legg, H. F., Loss, D., & Klinovaja, J. Josephson transistor from the superconducting diode effect in domain wall and skyrmion magnetic racetracks. Physical Review B 108, 174516 (2023).

Novel Effects in Topological Insulator Devices