[Deep Dive] Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness
Coexistence and Interconversion of Multiple-Order Majorana Modes in Topological Superconductor Films with Varying Thickness
Superconductivity ⢠September 22, 2026
Reading time: ~12 minutes
š Contents
š Executive Summary
Majorana research spent most of the past decade chasing a single object: one zero-energy bound state, in one device geometry, confirmed by one tunneling peak. That framing is breaking down. A new theoretical study of C2h-symmetric topological superconductor films (posted to arXiv on 21 September 2026 by Zhizhong Ding, Chuanbao Zhang and Shunhong Zhang) treats film thickness and proximity-induced exchange field as two knobs on a single phase diagram, and finds that Majorana modes of different topological order coexist in the same crystal and convert into one another as those knobs turn. In thick films, two Majorana bound states sit at opposite ends of a vortex line, at the free surface and at the magnetic interface. Push the exchange field and the interfacial mode unwinds into a chiral Majorana edge mode. The candidate material, 2M-WS2, superconducts at 8.8 K and already shows anisotropic vortex bound states in experiment. The practical payoff is a topological qubit platform where the mode type is tunable by growth parameters rather than fixed at fabrication.
A zero-dimensional Majorana bound state becoming a one-dimensional chiral edge mode without changing the sample, only the field, turns mode order into a design parameter instead of a fabrication accident.
š¬ Technical Deep Dive
Current State
The field's workhorse recipe is still Fu and Kane's 2008 proposal: gap a topological insulator surface with proximity-induced s-wave superconductivity, thread a vortex, and a Majorana zero mode binds to the vortex core. Everything since has been an argument about materials and artifacts. Semiconductor nanowires gave clean fabrication and dirty physics, with zero-bias conductance peaks that trivial Andreev states could imitate. Iron-based superconductors such as FeTe0.55Se0.45 (Tc around 14.5 K) moved the game to intrinsic materials where the topological surface band and the superconducting condensate live in one crystal, removing the interface problem entirely.
2M-WS2 belongs to that second camp. It is a metastable monoclinic phase, space group C2/m, obtained by deintercalating potassium from KxWS2, superconducting at 8.8 K, with topological surface states confirmed by ARPES and anisotropic vortex bound states reported by scanning tunneling spectroscopy. The new preprint's contribution is to stop treating the film as a semi-infinite slab. Thickness becomes a control parameter, and the C2h point group (a twofold rotation plus inversion, no mirror perpendicular to the layers) permits second-order topology that a higher-symmetry crystal would forbid.
The resulting regime map is the useful part:
| Regime | Film thickness | Exchange field | Dominant Majorana object | Experimental signature |
|---|---|---|---|---|
| Thick film, weak field | Above hybridization length (roughly 6 to 10 nm class) | Below gap scale | Two vortex-line end MBS, surface plus interface | Zero-bias peak at both terminations of one vortex |
| Thick film, strong field | Same | Above topological transition | Surface MBS survives, interface mode becomes chiral edge mode | Asymmetric spectra: point-like peak on top, dispersing edge channel at interface |
| Intermediate film | Near crossover | Tunable | Mixed first- and second-order coexistence | Hinge or corner localization along C2-preserving terminations |
| Ultrathin film | Below crossover | Any | Hybridized pair, finite-energy Andreev state | Split peak, splitting scaling exponentially with thickness |
The table is the design document. Instead of asking whether a device hosts a Majorana mode, it asks which order of Majorana mode a given growth run will produce.
Recent Breakthroughs
The central claim is interconversion. In thick C2h films, a vortex line terminating at the free surface and at the magnetic insulator interface binds one Majorana bound state at each end, the standard two-end picture. Raising the proximity exchange field from the magnetic layer drives the interfacial region through a topological transition when the Zeeman energy exceeds the combined pairing and chemical potential scale. On the far side, that localized zero mode is gone and a one-dimensional chiral Majorana edge mode runs along the interface boundary instead. A zero-dimensional object has become a one-dimensional one without changing the sample, only the field. Below the hybridization thickness, the crystal's C2h symmetry takes over and supports second-order modes pinned to specific terminations, which is where corner and hinge physics enters. That coexistence of orders in one material matters for a reason that goes beyond taxonomy. Braiding schemes need localized, addressable, well-separated zero modes. Readout and parity transport benefit from extended chiral channels that carry information ballistically along an edge. Most proposed architectures stitch these together across material boundaries, which is where coherence dies. A single film that can host both, with the boundary between regimes set by local gating of the magnetic layer or by a thickness step engineered during growth, collapses a heterostructure problem into a growth problem. The theoretical machinery is standard and therefore checkable: Bogoliubov-de Gennes lattice models on a slab geometry, vortex profiles inserted by phase winding, open boundary diagonalization to extract local density of states maps, and symmetry indicators plus Wilson loop spectra to assign topological order. Nothing exotic is assumed about the pairing symmetry, which keeps the prediction falsifiable by an STM group with a dilution refrigerator and a good exfoliation protocol.
Remaining Challenges
Material handling is the first wall. 2M-WS2 is metastable. It is produced by chemical deintercalation, it degrades in air, and flakes are small and irregular. Precise thickness control at the one to two layer level, across a flake large enough to define a vortex and probe both terminations, is not routine anywhere. The prediction depends on hitting a thickness window, and the window is set by the surface-state decay length, a quantity that is not yet tightly measured for this compound. The second wall is the interpretation problem that has haunted this field since 2018. Zero-bias peaks are cheap. Disorder, smooth confinement potentials and quasi-Majorana states produce robust-looking peaks that are topologically trivial. The 2021 retraction of a high-profile Nature nanowire result and the 2022 retraction of a Science paper claiming half-quantized chiral Majorana conductance both came down to that ambiguity. The new work's saving grace is that it predicts a correlated pair of signatures on a single vortex line, at two different terminations, evolving in opposite directions as one field is swept. Correlation across independent observables is much harder for disorder to fake than a single peak. Third, energy scales. Vortex bound state splitting scales roughly as the pairing gap squared over the Fermi energy, so a large Fermi energy smears the zero mode into a dense Caroli-de Gennes-Matricon ladder. At 8.8 K the gap is decent, but the chemical potential in 2M-WS2 flakes will need careful gating. STM resolution around 20 microelectronvolts at base temperature is achievable but leaves little headroom. One honest limitation: this is a theory paper with no accompanying measurement. Every claim about coexistence and interconversion currently lives inside a model Hamiltonian whose parameters were chosen to be reasonable, not fitted to a specific grown sample.
Expert Perspectives
The community remains split along lines that have not moved much in five years. Sankar Das Sarma, whose group did foundational work on the nanowire proposals, has repeatedly argued in public commentary that tunneling peaks alone cannot establish topological order and that the field needs non-local and interferometric evidence. Sergey Frolov and Vincent Mourik have pressed hardest on data selection practices in the nanowire literature, and Henry Legg has published technical critiques of the topological gap protocol used to validate Microsoft's devices. Chetan Nayak, who leads Microsoft's quantum hardware effort, has defended the interferometric single-shot parity measurement published in Nature in February 2025 while acknowledging that the topological character of those devices is still under active argument, a point Nature's editors flagged explicitly. What the intrinsic-material camp (including the groups behind the FeTeSe and 2M-WS2 vortex measurements) contributes is a different experimental grammar: spatially resolved spectroscopy inside a single crystal, where the Majorana candidate can be imaged, moved and counted rather than inferred from a transport curve. Thickness-dependent predictions play directly to that strength. A study that says the number and character of modes should change at a specific layer count is a study an STM group can attack immediately, and it fails loudly if wrong.
š¢ Market Landscape
Key Players
Microsoft remains the only large company betting its entire quantum roadmap on topological qubits. The Majorana 1 chip announced on 19 February 2025 carries eight topological qubits built on an InAs/aluminum topoconductor, with a stated architecture target of one million qubits on a single palm-sized chip. Microsoft was also selected, alongside PsiQuantum, for the final stage of DARPA's Quantum Benchmarking Initiative in February 2025, a program designed to test whether any vendor can reach utility-scale fault tolerance by 2033. The company's advantage is that a working topological qubit would need far fewer physical qubits per logical qubit than transmon or trapped-ion approaches. The risk is total: if the physics does not hold, there is no fallback product line. Everyone else has hedged. IBM, Google Quantum AI, IonQ, Rigetti, Quantinuum and IQM are all building error-corrected machines from non-topological qubits, and Google's Willow result in December 2024 (below-threshold surface code scaling) plus IBM's Starling roadmap targeting 2029 set the bar that topological approaches have to beat. Delft's QuTech, the Niels Bohr Institute in Copenhagen and Chinese groups at Tsinghua, IOP CAS and SUSTech supply most of the materials-side output, and a meaningful share of the 2M-WS2 and iron-based superconductor vortex spectroscopy comes out of Chinese national laboratories. The picks-and-shovels layer is where revenue is real today. Bluefors and Oxford Instruments dominate dilution refrigerators. Lake Shore Cryotronics, Montana Instruments, attocube and Scienta Omicron supply the millikelvin STM and cryogenic measurement hardware that any thickness-resolved Majorana experiment needs. Riber and Veeco sell the molecular beam epitaxy systems required to grow magnetic insulator and topological superconductor stacks with layer control. None of these firms is a quantum pure play, which is precisely why they survive a bad year in the sector.
Investment Trends
Private funding into quantum technology startups reached roughly $2.0 billion in 2024 by McKinsey's count, up about 50 percent year over year, and 2025 ran hotter still on the back of PsiQuantum's $1 billion Series E and large public commitments. Government money is the larger pool: the US National Quantum Initiative, the EU Quantum Flagship at 1 billion euros over ten years, the UK's National Quantum Computing Centre, Japan's Moonshot program and China's state-backed effort together represent north of $40 billion in announced public commitments globally. Virtually none of that flows directly into Majorana materials science. Topological superconductivity research is funded through condensed matter physics grants measured in hundreds of thousands of dollars per group per year, not venture rounds. Microsoft's internal spend is the exception and is not disclosed separately. The practical consequence for investors is that a result like the C2h film phase diagram has no tradeable instrument attached to it. Its financial relevance runs through the option value it adds to Microsoft's approach and through the instrumentation vendors who sell the cryostats and MBE chambers used to test it.
Competitive Dynamics
The competitive question is not topological versus superconducting circuits in the abstract. It is whether topological qubits arrive before conventional error correction makes their coherence advantage economically irrelevant. Google and IBM are compounding on engineering at a rate that shortens the window every year. If surface-code logical qubits reach useful error rates around 2029 to 2031 on transmon hardware, a topological qubit demonstrated in 2032 is a physics achievement with a hard commercial case. A second dynamic is the intrinsic versus hybrid materials split. Hybrid semiconductor-superconductor devices are fabricable at scale using existing semiconductor tooling, which is why Microsoft chose them. Intrinsic topological superconductors like 2M-WS2 and FeTeSe offer cleaner physics and much worse manufacturability. Thickness-dependent predictions sit awkwardly between the two, since they demand both intrinsic material quality and atomically controlled growth. Whoever solves layer-precise growth of a metastable TMD phase over wafer scale changes that balance, and that capability would most plausibly emerge from a 2D materials foundry effort rather than a quantum computing company.
Market Projections
McKinsey's 2025 Quantum Technology Monitor puts quantum computing revenue at $28 billion to $72 billion by 2035, with the broader quantum technology sector (including sensing and communications) reaching $97 billion. Boston Consulting Group has projected $450 billion to $850 billion of annual value creation for end users by 2040. These are the numbers that get quoted in earnings calls, and they should be read as scenario ranges rather than forecasts, because the wide spread reflects genuine uncertainty about whether fault tolerance arrives this decade or next. The topological share of that market is currently zero and will likely stay near zero through 2030. Model it as an option rather than a revenue line: low probability of success, very high payoff if the physics closes, with the payoff concentrated in one large-cap balance sheet that would barely move on the news.
š Timeline & Milestones
2026 Expectations
Expect the experimental response to arrive as thickness-series scanning tunneling spectroscopy. The natural first test is a set of 2M-WS2 flakes at controlled layer counts on a magnetic insulator such as CrBr3, Cr2Ge2Te6 or EuS, measured at 30 millikelvin, looking for the predicted correlation: zero-bias peaks at both vortex terminations in thick samples, splitting that grows exponentially as thickness drops below the hybridization length. Parallel work should come from the iron-based superconductor community, where FeTe0.55Se0.45 thin films already permit thickness variation and where vortex Majorana signatures are better established. On the engineering side, Microsoft's public commitments under the DARPA Quantum Benchmarking Initiative require a demonstrated multi-qubit topological operation, and any slippage there will be read as a verdict on the whole approach.
2027-2030 Outlook
The decisive measurement for the chiral half of this prediction is transport, not spectroscopy: a half-quantized two-terminal conductance plateau at 0.5 e2/h from a single chiral Majorana edge channel. That claim has been made and retracted once already (Science 2017, retracted 2022), so the bar for acceptance is now very high and will require multiple independent groups and non-local measurements. Between 2027 and 2030 I would expect the first credible claims of controlled interconversion, meaning a single device where sweeping a gate or exchange field moves the system between localized and chiral Majorana regimes with both signatures observed in the same cooldown. In parallel, wafer-scale growth of metastable TMD superconductors becomes the rate-limiting engineering problem, and progress there will come from 2D materials foundries rather than quantum hardware companies. Conventional error-corrected machines from IBM and Google should reach commercially interesting logical qubit counts in this window, which will compress patience for topological timelines.
Beyond 2030
If layer-precise growth and unambiguous interconversion both land, the architectural payoff is a chip where localized Majorana modes serve as memory and chiral edge channels serve as buses, all in one crystal, with the boundary between them defined lithographically in the magnetic layer. That would cut the physical-to-logical qubit overhead by roughly an order of magnitude versus surface-code transmons, which is the only argument that makes topological qubits worth the wait. The realistic scenario is slower: topological superconductor films become an important condensed matter platform for studying non-Abelian statistics and higher-order topology, with quantum computing applications arriving in the late 2030s or not at all, while the growth and cryogenic techniques developed along the way feed into quantum sensing and superconducting electronics.
š° Investment Perspective
Opportunities
The cleanest exposure to this specific research direction is instrumentation. Every experiment implied by the C2h film phase diagram requires a dilution refrigerator, a millikelvin STM or cryogenic transport rig, and molecular beam epitaxy or glovebox exfoliation capability. Oxford Instruments (LSE: OXIG) sells into that stack and has a diversified industrial base. Bruker (NASDAQ: BRKR) and Coherent (NASDAQ: COHR) touch adjacent metrology and materials. Riber (EPA: ALRIB) is a small-cap MBE pure play with real operating leverage to academic and industrial growth-system orders, and correspondingly thin liquidity. Bluefors remains private. For diversified sector exposure, the Defiance Quantum ETF (QTUM) holds roughly 70 to 80 names across quantum and adjacent computing and rebalances away from single-name blowups, which matters in a sector this headline-driven.
Risk Factors
Three risks dominate. First, scientific risk: the claim under discussion is a model prediction with no measurement attached, and topological superconductivity has a documented history of high-profile results that did not survive scrutiny, including a 2021 Nature retraction and a 2022 Science retraction. Second, timing risk: even total success in the lab is a decade from product, and conventional error correction may make the coherence advantage commercially moot before topological qubits scale. Third, valuation risk: quantum pure-play equities including IonQ, Rigetti and D-Wave trade at revenue multiples that price in outcomes far beyond current bookings, and they move violently on announcements that have no bearing on their own technology. Buying them as a proxy for Majorana progress is a category error, since none of them work on topological qubits.
Recommendations
Core: QTUM for diversified sector beta. Instrumentation sleeve: OXIG, BRKR, with ALRIB only as a small speculative position sized for illiquidity. Large-cap option value: MSFT, where the topological program is a free option inside a business whose valuation rests on cloud and AI, so you are not paying for the physics. Avoid sizing IONQ, RGTI or QBTS to this thesis; they are unrelated technology and behave like high-beta sentiment instruments. For anyone with a long horizon and academic access, the highest-return move is not a trade at all but tracking which groups secure layer-controlled growth of metastable TMD superconductors, because that capability precedes any investable outcome by several years.
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š” Key Takeaways
The new arXiv preprint (2609.24311, 21 September 2026) reframes Majorana modes as a tunable phase diagram in film thickness and exchange field, rather than a single fixed device property.
Two Majorana bound states can occupy opposite ends of one vortex line in thick C2h films, and the interfacial one converts into a chiral Majorana edge mode as the proximity exchange field increases.
2M-WS2 is the named candidate: monoclinic C2/m, Tc of 8.8 K, with anisotropic vortex bound states already reported in Nature Physics, which makes the prediction testable now.
The strongest experimental argument here is correlation: two signatures on a single vortex line evolving in opposite directions under one swept parameter is much harder for disorder to imitate than an isolated zero-bias peak.
Material handling is the binding constraint. 2M-WS2 is metastable, air-sensitive and produced by deintercalation, and the prediction requires thickness control near the surface-state hybridization crossover.
Microsoft is the only major commercial player on topological qubits (Majorana 1, eight qubits, February 2025), and its approach uses hybrid InAs/Al rather than intrinsic topological superconductors.
Watch for a credible, independently replicated half-quantized 0.5 e2/h chiral edge conductance plateau, and for any group demonstrating wafer-scale layer-controlled growth of a metastable TMD superconductor. Those two milestones gate everything downstream.
š” Lab Test Report
š Sources & References
š¤ AI Research System
Research & Analysis: Claude Opus 4.7
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Published: September 22, 2026
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