image: Comparison of a system without an impurity and one with a local impurity at the centre of the vortex. The distribution of the wave function of a low-energy bound state in the non-topological regime (B/F): in the absence of an impurity, the state is more strongly localised at the vortex core, whereas in the presence of an impurity, its profile is significantly modified. The spatial distribution of the modulus of the MZM wave function in the topological regime (C/G): although the impurity alters the spatial profile, the state remains localised in the vortex region. The average local density of states at the vortex centre for both topological and conventional regimes (D/H): without an impurity, low-energy signals strongly overlap, while in the presence of an impurity, the differences between them become more pronounced.
Credit: © Vyacheslav D. Neverov, Tairzhan Karabassov, Andrey V. Krasavin, Dimitri Roditchev, Vasily S. Stolyarov, Alexei Vagov. Revealing Majorana Zero Modes in Vortex Cores via Nonmagnetic Impurities. Research. 2026;9:1087.DOI:10.34133/research.1087
An international team of researchers, including physicists from HSE MIEM, has demonstrated that nonmagnetic impurities can help more accurately reveal Majorana zero modes—quantum states considered promising building blocks for quantum computing. The researchers found that these impurities shift the energy levels that typically obscure the Majorana signal, while leaving the mode itself largely unaffected, thereby making its spectral peak more distinct. The study has been published in Research.
Majorana zero modes (MZMs) are rare quantum states that can emerge in certain superconductors. In particular, they form in magnetic vortices—tiny regions within the material where the magnetic field is concentrated. At the same time, MZMs are robust against random disturbances and material impurities, which makes them promising candidates for realising stable qubits—the units of information in a quantum computer.
The challenge is that MZMs are difficult to detect experimentally: other quantum states with similar energies appear nearby, making the signals easy to confuse. Previous attempts to address this issue focused on selecting superconductors with fewer impurities and fewer extraneous states, in the hope that the Majorana signal would become more pronounced. In practice, however, such systems are difficult to produce and reproduce reliably, and the measurement results often remain ambiguous.
A team of researchers from MIPT, HSE MIEM, MEPhI, and Sorbonne University has shown that a nonmagnetic impurity in a superconductor can serve as a useful element. Using computer modelling, they studied the effect of a defect that creates a local energy barrier and pins the vortex at a specific location. They found that the ordinary states inside the vortex are sensitive to this barrier and shift in energy, while the MZM energy remains unchanged.
As a result, the energy gap between the MZM and the other states increases. Experimentally, this leads to a clearer signal: a pronounced zero-bias peak appears in the spectrum, making it difficult to confuse with other features. Importantly, this approach does not require exotic materials—the effect can also be observed in systems based on commonly used superconductors.
Importantly, this effect is observed only in the presence of nonmagnetic impurities. While magnetic impurities suppress superconductivity and interfere with measurements, nonmagnetic impurities, by contrast, can serve as a controllable separator: they push background states away from zero without affecting the MZM.
'Our study offers a more practical approach to generating and detecting MZMs,' explains Alexey Vagov, Director of the HSE MIEM Centre for Quantum Metamaterials and one of the study authors. 'Instead of searching for rare or exotic materials, we rely on controllable defects in more accessible systems. We hope this will accelerate progress toward building a quantum computer based on topological Majorana states.'
The study was conducted with support from the Russian Science Foundation (Project 075-15-2025-608) and the HSE Basic Research Programme
Journal
Research
Article Title
Revealing Majorana Zero Modes in Vortex Cores via Nonmagnetic Impurities