A superconducting sandwich offers hope for Majorana qubits

In solids, the Fermi surface is the boundary (in momentum space) between occupied and unoccupied electron levels, just as the shoreline of the ocean is the boundary between water and dry land. And, just like a shoreline, every Fermi surface should form a single unbroken loop. That is, unless your material is a Weyl semimetal like platinum-bismuth-two (PtBi2).

Thanks to its unusual topology, PtBi2 has some electrons confined to special channels on its surface known as ‘Fermi arcs’. Rather than forming closed loops by themselves, each Fermi arc on the top surface of the material forms half of a loop completed by an arc on the bottom surface. Fermi arcs have been seen before, usually buried deep within the electronic ‘sea’. But in PtBi2 they lie almost exactly at the Fermi surface.

Excitingly, the Fermi arcs on the top and bottom surfaces of PtBi2 are in fact superconducting. This means that the electrons interact and team up, allowing them to move without any resistance. This is the first time that superconductivity has been seen to emerge in Fermi arcs, made possible by their unusual proximity to the Fermi surface. Because the arcs arise thanks to the inherent topology of the electronic structure, this finding opens up a plethora of possibilities to manipulate topological and superconducting phases in a single material.

Theory and experiment come together
A lot of research is invested in accurately determining the electronic structure of materials so that we can better predict and understand their properties. At the IFW Dresden, there is close collaboration between the Institute for Theoretical Solid State Physics, led by Prof. Jeroen van den Brink, and the experiments-oriented Institute for Solid State Research, led by Prof. Bernd Büchner. “Detailed theoretical calculations by the group of van den Brink predicted the existence of the Fermi surface arcs in this material, so we went to look for them experimentally,” explains Borisenko.

Borisenko is an expert in angle-resolved photoemission spectroscopy (ARPES). These experiments involve shining extreme ultraviolet light on a material. This light has enough energy to kick out electrons from the sample. A detector measures both the energy and the angle with which electrons leave the material, from which researchers can reconstruct the electronic structure within the crystal.

In line with the theoretical predictions, Borisenko’s team found the arcs almost exactly at the Fermi level, very localised in momentum and energy. “These arcs are the most robust objects in photoemission I've ever seen. It is a dream for every ARPES practitioner to see such bright peaks in the spectrum. The electron count was sometimes so high, we had to be careful not to burn our detector!” laughs Borisenko.

Two superconductors for the price of one
Also visible in the ARPES measurements is the opening of a superconducting energy gap within the Fermi arcs. Only the Fermi arcs showed signs of a gap, meaning that the superconductivity is entirely confined to the top and bottom surfaces of the material. This means a single crystal of PtBi2 naturally makes a superconductor-metal-superconductor sandwich. Since the top and bottom surfaces of PtBi2 have distinct Fermi arcs, the two surfaces become superconducting separately, with different transition temperatures.

By varying the thickness of a single crystal, one can tune the thickness of the non-superconducting sandwich filling. This makes the material a tunable, intrinsic Josephson junction. Josephson junctions have important applications including sensitive magnetometers, superconducting qubits and digital signal processors.

A future for Majorana qubits
Another tantalising possibility is that PtBi2 offers a new way to produce long-sought-after quasiparticles called Majorana zero modes, which are predicted to arise from topological superconductivity. If they are confirmed to exist, they could be used as extremely stable, fault-tolerant qubits for the next generation of quantum computers. Unfortunately, it is not easy to prove the existence of a Majorana particle. Experimental efforts in other systems have so far not led to conclusive, generally accepted results.

In PtBi2, the Majorana modes could appear when the superconducting gaps open in the Fermi arcs. They would then reside on the edges around the superconducting surfaces, right at the Fermi energy. “In our experiments we measure a weak angle-independent signal right at the Fermi level, which gets more pronounced when we look at terraced regions of the material surface (where there are more edges present). This hints at the existence of Majorana particles, but this still needs to be confirmed by a more detailed analysis of the electronic structure,” concludes Borisenko.

A. Kuibarov, O. Suvorov, R. Vocaturo, A. Fedorov, R. Lou, L. Merkwitz, V. Voroshnin, J. I. Facio, K. Koepernik, A. Yaresko, G. Shipunov, S. Aswartham, J. van den Brink, B. Büchner, S. Borisenko,
Evidence of superconducting Fermi arcs.
Nature 626, 294–299 (2024) (arXiv)