Identifying the Majorana phase in extensively studied InSb nanowires has proven to be a notoriously difficult task. In contrast, experiments have observed robust one-dimensional modes at surface atomic steps of SnTe, and subsequent studies have linked these flat bands to a pronounced zero-bias conductance peak at low temperatures—raising speculation about the presence of Majorana modes. Motivated by these findings, the MagTop theory group undertook a detailed investigation of possible topological phases in SnTe nanowires, considering various nanowire geometries: monocrystalline (001) and (110) nanowires (see Fig. 1 and Refs. [1–2]), as well as pentagonal nanowires featuring twin boundaries (see Fig. 3 and Ref. [3]).
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Figure 1: Schematic views of the SnTe nanowires: (a) the (001) nanowire and (b) the (110) nanowire. Yellow/violet balls represent Sn/Te atoms, unit cells are marked with square surfaces and nearest neighbors within a single cell are connected by edges. |
The (001) and (110) nanowires exhibit remarkably similar behavior under the application of a longitudinal Zeeman field. Specifically, we observe a sequence of gap inversions which, in the case of the (110) nanowire, can be attributed to the increasing value of the mirror-reflection topological invariant that protects each insulating phase. These insulating states are interleaved with Weyl semimetal phases. When both a Zeeman field and induced s-wave superconductivity are included, the resulting topological phase diagram becomes unexpectedly rich, displaying a mosaic of distinct Majorana phases (see Fig. 2). Importantly, we find that (110) nanowires offer a more practical platform for realizing Majorana states than their (001) counterparts. In particular, the Majorana phase in (110) nanowires emerges at lower Zeeman fields and remains close to the original Fermi level.
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Figure 2: On the left, Majorana phase diagram of the 12 atoms-thick (110) nanowireas function of chemical potential and longitudinal Zeeman magnetic field. The Majorana phase is marked with navy blue. On the right, edge density of states at zero energy calculated along red line in the left plot revealing Majorana zero-energy end-state. |
A pentagonal SnTe nanowire with twin boundaries was synthesized by the MagTop MBE group. The stability of this non-trivial crystal structure was confirmed by an ab initio DFT study presented in Ref. [3]. Additional investigations revealed the presence of a localized metallic state in the core of the nanowire, resembling chiral edge states observed in Chern insulators. To explain the origin of this state, the theory group employed a model-Hamiltonian approach, which showed that a longitudinal cross-section of the nanowire resembles the so-called 1D SSG model—a system known to support end states due to its non-trivial topology (see Fig. 3). As a result, this structure offers a promising new platform for studying Majorana states in future experiments.
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Figure 3: On the left: (a) longitudinal cut through the pentagonal nanowire, (b)-(c) bands structures of the cut as function of momentum along the nanowire. Bottom: tranverse cut on the nanowire.
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[1] M. Nguyen, W. Brzezicki, T. Hyart, Corner states, hinge states and Majorana modes in SnTe nanowires, Phys. Rev. B 105, 075310 (2022).
[2] A. Kawala, W. Brzezicki, Topological properties of the [110] SnTe nanowires, Phys. Rev. B 112, 035102 (2025).
[3] G. Hussain, G. Cuono, P. Dziawa, D. Janaszko, J. Sadowski, S. Kret, B. Kurowska, J. Polaczynski, K. Warda, S. Sattar, C. M. Canali, A. Lau, W. Brzezicki, T. Story, C. Autieri, Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology, Nanoscale Horiz. 9, 1290 (2024).
As, so far, the experimental signatures that identify a topological superconductor (TSC) are elusive [see, e.g., M. Mandal et al., arXiv:2303.15581] and there has been no conclusive experimental observation of Majorana bound states in proximitized topologically trivial semiconductors [see, e.g., R. Hess et al., Phys. Rev. Lett. 130, 207001 (2023)], particularly timely is search for intrinsic or proximitized superconductivity in topological materials. In addition to MagTop’s comprehensive theoretical effort, MagTop/IFPAN’s growers and experimentalists have been exploring four paths: (i) Weyl semimetals with superconductors’ overlayers; topological crystalline insulators in the form of (ii) bulk crystals; (iii) superlattices, and (iv) nanowires. Surprising and not yet understood results, calling for further work, have been gathered.
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For studies of interface transmission by differential conductance, the (001) surface of the Weyl NbP crystal was covered by several hundred nm thick metallic layers of either Pb, or Nb, or In [1]. Upon cooling across metals’ Tc,s, all junctions show a conductance increase, pointing out to the Andreev reflection. In the case of Pb-NbP and Nb-NbP junctions, the conductance change indicates that the transmission occurs through a small part of the contact area. However, in the In-NbP junction, the peak magnitude and width show that the whole contact area is transmitting and a superconducting
Theory of symmetry-protected topological states in SnTe nanowires in the presence of various combinations of Zeeman field, s-wave superconductivity and inversion-symmetry-breaking field was developed [2]. Encouragingly, Andreev-like spectra have been found is a number of topological materials employing a normal- or ferromagnetic-metal tip, also the case of diamagnetic and ferromagnetic bulk (Pb,Sn)Te and (Pb,Sn,Mn)Te with silver paint contacts [3]. However, no global superconductivity was found, and the effect was discussed in terms of the correlation gap in 1D topological states at surface atomic steps. However, is some PbTe/SnTe strained superlattices, in addition to Andreev-type features, global superconductivity was found (Figure), as observed earlier by other groups. Whether this superconductivity is topological and originates from the dislocation network, as E. Tang and L. Fu [Nat. Phys. 10, 964 (2014)] model predicts or results from superconducting nanoprecipitates, is to be demonstrated.
[1] G. Grabecki, A. Dąbrowski, P. Iwanowski, A. Hruban, B. J. Kowalski, N. Olszowska, J. Kołodziej, M. Chojnacki, K. Dybko, A. Łusakowski, T. Wojtowicz, T. Wojciechowski, R. Jakieła, A. Wiśniewski, Conductance spectra of (Nb,Pb,In)/NbP superconductor/Weyl semimetal junctions, Phys. Rev. B 101, 085113 (2020).
[2] N. M. Nguyen, W. Brzezicki, T. Hyart, Corner states, hinge states and Majorana modes in SnTe nanowires, Phys. Rev. B 105, 075310(2022).
[3] G. P. Mazur, K. Dybko, A. Szczerbakow, J. Z. Domagala, A. Kazakov, M. Zgirski, E. Lusakowska, S. Kret, J. Korczak, T. Story, M. Sawicki, T. Dietl, Experimental search for the origin of low-energy modes in topological materials, Phys. Rev. B 100, 041408(R) (2019) [Editors’ Suggestions].
[4] P. Sidorczak, W. Wołkanowicz, K. Gas, A. Kaleta, S. Gierałtowska, R. Minikayev, S. Kret, M. Sawicki, T. Wojtowicz, D. Wasik, M. Gryglas-Borysiewicz, K. Dybko (unpublished).
One of the most challenging aims in the current condensed matter physics research is the demonstration of non-Abelian Majorana statistics — the underlying fundamental property that would enable the realization of a topological quantum computer. Though not experimentally proven, it is theoretically well established that Majorana zero modes (MZMs) can be realized in semiconducting nanowires with strong Rashba spin-orbit coupling in the presence of induced superconductivity and external magnetic field. MagTop’s team studied theoretically ferromagnetic-semiconducting-superconducting hybrids with MZMs, and demonstrated that this system; (i) constitutes a novel topological charge, spin, and heat transistor; (ii) shows quantization of spin under spin pumping conditions. Furthermore, the dynamics of photons in a microwave cavity coupled to a topological superconducting nanowire that hosts gliding MZMs has been studied.
By exploring the magnetisation dynamics in ferromagnetic-semiconducting-superconducting hybrids, we have unraveled a novel quantised effect—the spin pumping—which characterises the topology of the system similarly to the conductance in static cases. We have demonstrated quantised spin pumping in quantum spin Hall insulting edges hosting Majorana zero modes [1], as well as semiconducting-superconducting nanowires covered with ferromagnets [2], two setups that have been under intense experimental scrutiny in the hunt for Majorana fermions (see Figure). Crucially, we showed that in long nanowires there exists a one-to-one correspondence between the quantized conductance and the quantized spin pumping in the topologically nontrivial nanowires but these observables are uncorrelated in the case of accidental zero-energy Andreev bound states in the trivial phase. The observation of correlated and quantized peaks in the conductance and spin pumping would provide strong evidence of MZMs, and allow to distinguish them from quasi-Majorana modes potentially created by imperfections at the lead-nanowire interface. Furthermore, harnessing the magnetisation dynamics could open the pathway to real technological applications involving MZMs [3].
(a) Rashba nanowire (green) with proximity induced superconductivity (blue) and magnetization (gray) supports MZM (red). The precessing magnetization m(t) pumps spin and charge into the lead due to the normal and Andreev reflection processes. (b) Topological phase diagram of the nanowire as a function of the exchange coupling m0 and the precession angle Q. (c), (d) The pumped charge Q and spin S as a function of m0 for different tunnel barriers µtun. The pump spin is quantized to Sz = ħ/2 in the topologically nontrivial regime (after [2]).
Furthermore, we have investigated the dynamics of photons in a microwave cavity coupled to a topological superconducting nanowire in the ballistic regime that hosts gliding MZMs [4]. We have demonstrate that both the ground-state parity encoded by the MZMs and their gliding dynamics influence the cavity field decay rate into the external lines that can be accessed experimentally. Our approach offers an alternative to tunneling spectroscopy to probe nonlocal features associated with the Majorana zero modes in nanowires.
[1] V. Fernández Becerra, Mircea Trif, and Timo Hyart, Topological charge, spin and heat transistor, Phys. Rev. B 103, 205410 (2021).
[2] V. Fernández Becerra, Mircea Trif, and Timo Hyart, Quantized spin pumping in topological ferromagnetic- superconducting nanowires, Phys. Rev. Lett. 130, 237002 (2023).
[3] V. Fernández Becerra, Mircea Trif, and Timo Hyart, European Patent: Topological charge, spin, and heat transistor (granted 26 March 2025 – European Patent Specification EP3975275B1).
[4] O. Dmytruk, M. Trif, Microwave detection of gliding Majorana zero modes in nanowires, Phys. Rev. B 107, 115418 (2023).
Magnetic impurities in s-wave superconductors provide a viable platform for realizing a topological quantum computer based on Majorana zero modes (MZMs). However, MZMs alone do not provide a universal set of quantum gates and manipulating coherently quantum degrees of freedom in these systems remains an open challenge. MagTop’s team introduced a new type of quantum bit, a Yu-Shiba-Rusinov qubit, stemming from two nearby magnetic impurities on a superconductor and demonstrated how to determine relevant quantum gate and topological characteristics, including interactions with MZMs, by scanning tunneling microscopy-electron spin resonance techniques, couplings to microcavity modes, and dynamic magnetic susceptibility.
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Hybrid structures grown in a two-chamber MBE set-up allowing for magnetooptical probing of exchange coupling between ferromagnetic layers (Co or Fe) and carriers in CdTe QW vs. voltage U (left panel) (after [1]) and distance d (right panel) (after [2]). |
Figure depicts a new type of quantum bit, a Yu-Shiba-Rusinov qubit (YSRQ), stemming from two nearby magnetic impurities on a superconductor [1]. We demonstrated that the coherent rotation and the readout of the qubit states is possible by exploiting the dynamics of the impurity spins. We have established a protocol for generation of Rabi oscillations induced by the dynamics of the magnetic impurities which is robust for a wide range of experimentally feasible parameters. The precession of magnetic impurity also generates a feedback torque acting on the impurity [2] so that the resonance frequency of the impurity spin depends on the qubit state. We showed that it is possible to utilize this effect to readout the YSRQ via the well-established scanning tunneling microscopy-electron spin resonance (STM-ESR) techniques. We estimated that the difference in the resonance frequencies, corresponding to the two qubit states, is well within the STM-ESR resolution.
YSRQs can be integrated with topological qubits based on MZMs, allowing the possibility to transfer quantum information coherently between them [3,4]. In particular, it is possible to manipulate and readout the Majorana qubits via the YSRQ, facilitating implementation of universal set of quantum gates. In the future, we plan to investigate quantum adatom spins, as well as using machine-learning techniques to extract the topology of the Shiba chain from spin susceptibility data .
[1] Archana Mishra, Pascal Simon, Timo Hyart, and Mircea Trif, Yu-Shiba-Rusinov qubit, Phys. Rev. X Quantum 2, 040347 (2021).
[2] Archana Mishra, So Takei, Pascal Simon, and Mircea Trif, Dynamical torque from Shiba states in s-wave superconductors, Phys. Rev. B 103, L121401 (2021).
[3] Pei-Xin Shen, Silas Hoffman, and Mircea Trif, Theory of topological spin Josephson junctions, Phys. Rev. Research 3, 013003 (2021).
[4] Peixin Shen, Vivien Perrin, Mircea Trif, and Pascal Simon, Majorana-magnon interactions in topological Shiba chains, Phys. Rev. Research 5, 033207 (2023)
