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At the core of a quantum computer is a qubit, which is used to make high-speed calculations. The qubits currently used are very sensitive to noise and interference from the computer’s surroundings, which introduces errors into the calculations. A new type of qubit, called a topological qubit, could solve this issue, and 1D Majorana zero energy modes may be the key to making them.

– A topological quantum computer is based on topological qubits, which are supposed to be much more noise tolerant than other qubits. However, topological qubits have not been produced in the lab yet, explains Professor Peter Liljeroth, the lead researcher on the project.

MZMs are groups of electrons bound together in a specific way so they behave like a particle called a Majorana fermion, a semi-mythical particle first proposed by Ettore Majorana in the 1930s. If Majorana’s theoretical particles could be bound together, they would work as a topological qubit. One catch: no evidence for their existence has ever been seen, either in the lab or in astronomy. Instead of attempting to make a particle that no one has ever seen anywhere in the universe, researchers instead try to make regular electrons behave like them.

To make MZMs, researchers need incredibly small materials, an area in which Professor Liljeroth’s group at Aalto University specialises. MZMs are formed by giving a group of electrons a very specific amount of energy, and then trapping them together so they can’t escape. To achieve this, the materials need to be 2-dimensional, and as thin as physically possible. To create 1D MZMs, the team needed to make an entirely new type of 2D material: a topological superconductor.

1D Majorana Zero energy form at the edge of a 2D topological superconductor. Image: Alex Tokarev, Ella Maru Studio.

Topological superconductivity is the property that occurs at the boundary of a magnetic electrical insulator and a superconductor. To create 1D MZMs, Professor Liljeroth’s team needed to be able to trap electrons together in a topological superconductor, however it’s not as simple as sticking any magnet to any superconductor.

– If you put most magnets on top of a superconductor, you stop it from being a superconductor. The interactions between the materials disrupt their properties, but to make MZMs, you need the materials to interact just a little bit. The trick is to use 2D materials: they interact with each other just enough to make the properties you need for MZMs, but not so much that they disrupt each other, explains Dr. Shawulienu Kezilebieke, the first author of the study.

The property in question is the spin. In a magnetic material, the spin is aligned all in the same direction, whereas in a superconductor the spin is anti-aligned with alternating directions. Bringing a magnet and a superconductor together usually destroys the alignment and anti-alignment of the spins. However, in 2D layered materials the interactions between the materials are just enough to “tilt” the spins of the atoms enough that they create the specific spin state, called Rashba spin-orbit coupling, needed to make the MZMs.

CSC’s computing resources utilized

The topological superconductor in this study is made of a layer of chromium bromide, a material which is still magnetic when only one-atom-thick. Professor Liljeroth’s team grew one-atom-thick islands of chromium bromide on top of a superconducting crystal of niobium diselenide, and measured their electrical properties using a scanning tunneling microscope. At this point, they turned to the computer modelling expertise of Professor Adam Foster at Aalto University and Professor Teemu Ojanen at Tampere University to understand what they had made. The simulations were computed with CSC’s Puhti supercomputer.

– There was a lot of simulation work needed to prove that the signal we’re seeing was caused by MZMs, and not other effects. We needed to show that all the pieces fitted together to prove that we had produced MZMs, says Professor Foster.

– The Density Functional Theory (DFT) methodology permits us to understand how the electrons behave in a chemical environment such as the heterostructure in this study. In this heterostructure, a two dimensional ferromagnetic layer is brought together to a superconductor and through the DFT calculations we were capable to identify some structural parameters, like the preferred position that one layer sits on the other, as well as to understand how the electronic properties are changed when this two materials are brought close to each other. This helped us to understand that some paramount ingredients for the emerging of Majorana fermion edge nodes were present in the heterostructure, and the DFT results were used to “feed” another methodology that deals with this exotic state, Foster continues.

– This discovered novel phase, known as topological superconductivity, is believed to support exotic quantum excitations known as Majorana particles. These new particle-like excitations have been envisioned as building blocks of quantum computers, Ojanen says.

– It is extremely challenging to detect topological superconductivity directly but Majorana particles provide a smoking-gun evidence of its presence. The observed signal is in excellent agreement with the theoretical expectations of Majorana edge modes,” concludes Ojanen.

Now the team is sure that they can make 1D MZMs in 2-dimensional materials, the next step will be to attempt to make them into topological qubits. This step has so far eluded teams who have already made 0-dimensional MZMs, and the Aalto team are unwilling to speculate on if the process will be any easier with 1-dimensional MZMs, however they are optimistic about the future of 1D MZMs.

– The cool part of this paper is that we’ve made MZMs in 2D materials. In principle these are easier to make and easier to customise the properties of, and ultimately make into a usable device, says Professor Liljeroth.

Sources: an e-interview with Adam Foster and press releases by Aalto University and Tampere University.

Kezilebieke, S., Huda, M.N., Vaňo, V. et al. Topological superconductivity in a van der Waals heterostructure. Nature 588, 424–428 (2020).

Writer: Tommi Kutilainen