Wang et al. (Science 336, 52, 2012) demonstrated that molecular-beam-epitaxial Bi2Se3 thin films on superconducting NbSe2 combine a proximity-induced superconducting gap at the film surface with topological Dirac surface states, explicitly as groundwork for realizing Majorana fermions in the Fu–Kane vortex-core scenario. The problem they left open, and which remains open after more than a decade of follow-up work, is to determine the precise conditions — Bi2Se3 film thickness, Fermi-level position (in particular tuning the Fermi level into the bulk band gap by gating, which the original samples did not achieve), interface and substrate/buffer choices, and possible magnetic or interface engineering — under which a single, isolated Majorana zero mode can be realized and unambiguously detected in a surface vortex core of this heterostructure, together with the microscopic modeling of the tunneling spectra needed to discriminate it from trivial bound states. The coexistence observation itself has since been corroborated, but no independent, consensus-level Majorana detection exists in this platform: the same research group's claimed vortex Majorana evidence in sibling Bi2Te3/NbSe2 is contested by same-platform works, recent experiments explicitly report no evidence of Majorana bound states in Bi2Se3/NbSe2 devices, and photoemission shows that proximity pairing is massively suppressed in exactly the bulk-insulating regime the Fu–Kane mechanism requires.

Background

Three-dimensional topological insulators (TIs), such as bismuth selenide (Bi2Se3), are bulk semiconductors whose surfaces host massless Dirac fermions: conducting states whose spin is locked perpendicular to their momentum and which are protected by time-reversal symmetry against backscattering from nonmagnetic disorder. Bi2Se3 crystallizes in quintuple-layer (QL) slabs, about 1 nm thick, stacked along the (111) axis; in films thinner than roughly 6 QL the top and bottom surfaces tunnel-couple and hybridize, which gaps the Dirac surface bands, while thicker films recover decoupled Dirac cones.

In 2008, Fu and Kane proposed that placing a conventional s-wave superconductor on a TI surface creates, through the superconducting proximity effect (the leakage of Cooper-pair pairing amplitude from a superconductor into an adjacent normal layer), an effectively spinless topological p-wave superconductor on the Dirac surface. In that state, each vortex core — the normal region threading a superconducting film when a magnetic flux quantum pierces it — should bind a single Majorana zero mode (MZM), a zero-energy excitation that is its own antiparticle and obeys non-Abelian exchange statistics, making it a candidate building block for fault-tolerant topological quantum computation. The mechanism requires the chemical potential to lie inside the bulk band gap, so that only the topological surface band crosses the Fermi level.

Wang et al. (2012) reported the first heterostructure aimed at this regime: Bi2Se3 films of 3 to 12 QL grown by molecular-beam epitaxy (a layer-by-layer ultrahigh-vacuum growth technique) on the s-wave superconductor NbSe2 (critical temperature TcT_c of about 7.2 K) with an intervening Bi(110) bilayer buffer. Scanning tunneling spectroscopy (STS, which measures the differential conductance dI/dV\mathrm{d}I/\mathrm{d}V of a tunneling tip and thereby the local density of states) showed a superconducting-like gap with coherence peaks near ±1\pm 1 meV that closed near 7 K, deepened on cooling, and weakened systematically as the film thickness increased — the signature expected of proximity induction. Angle-resolved photoemission spectroscopy (ARPES, which maps electronic band dispersion versus momentum) showed that films of 6 QL and above recover the topological Dirac cone, so superconducting order and topological surface order coexist on one platform. Three limitations were acknowledged. First, the Dirac point sat about 0.45 eV below the Fermi level, so the Fermi level was in the bulk conduction band, not in the bulk gap the Fu–Kane mechanism requires; bringing it into the gap, for example by a top gate, was identified as a necessary control knob whose workable range was unknown. Second, Bardeen–Cooper–Schrieffer (BCS)-like and elementary proximity-effect fits to the tunneling lineshape of the 3 QL film were, by the authors' own account, not good; the film-specific quantum-well subbands (discrete confined states of the thin film), a Rashba-type spin-orbit splitting of the bands (a spin splitting caused by inversion-symmetry breaking at the interface), interface electric fields, and possibly modified pairing symmetry were all expected to shape the spectrum and lacked a microscopic model. Third, how interface quality, residual charge transfer, and substrate/buffer choices quantitatively control the induced gap, coherence length, and robustness of the Dirac surface state was unmeasured beyond a few thicknesses.

The Fu–Kane program also has engineered extensions on the same material family: magnetically doped TIs realizing the quantum anomalous Hall effect (QAHE, a quantized Hall conductance produced by time-reversal-symmetry breaking without an external magnetic field) coupled to a superconductor were predicted to host chiral Majorana edge modes, and magnetic or interface engineering was suggested as a route to effective px+ipyp_x+ip_y pairing. Whether any of these can be realized on the Bi2Se3/NbSe2 platform remains experimentally untested.

Problem Statement

Determine the conditions under which a single, isolated Majorana zero mode can be realized and unambiguously detected in a surface vortex core of the Bi2Se3/NbSe2 superconductor–topological-insulator heterostructure, and demonstrate it. The source work and its follow-ups make the objective explicit as a set of jointly supporting questions: (1) the experimental parameter window — Bi2Se3 film thickness (balancing top/bottom surface hybridization below about 6 QL against pairing decay at large thickness), Fermi-level position (in particular whether top or other gating can place the Fermi level inside the bulk band gap, which the original samples did not achieve), and the interface/buffer-layer and substrate choices — in which the proximitized topological surface state is decoupled from the substrate yet retains superconducting pairing; (2) whether proximity pairing survives at all in the bulk-insulating regime the Fu–Kane mechanism requires, given the reported massive suppression of proximity pairing in bulk-insulating topological films on niobium; (3) microscopic theory of the tunneling spectra in that window, incorporating film-specific quantum-well states, interface electric fields, Rashba-type spin-orbit splitting, and possible modified or unconventional pairing symmetry, sufficient to discriminate a Majorana zero mode from trivial vortex-core bound states and other zero-bias anomalies; (4) a detection protocol that establishes a single isolated Majorana zero mode per vortex rather than an ensemble effect or a conventional state; and (5) quantitative characterization of how interface quality, residual charge transfer, and substrate/buffer choices control the induced gap magnitude, coherence length, and robustness of the Dirac surface state. The proposed extensions — magnetic doping toward a quantum anomalous Hall–superconductor combination and induced effective px+ipyp_x+ip_y pairing under magnetic or interface engineering — are secondary arms of the same objective of engineering this platform into a topological superconductor. The question is resolved affirmatively by a single, isolated Majorana zero mode realized, reproducibly parameterized, and unambiguously detected in a surface vortex core under the conditions of (1)–(5). It is resolved negatively by a demonstration that a single, isolated Majorana zero mode is precluded in this heterostructure, with the physical mechanism of the obstruction and the parameter range over which it holds. The two secondary arms extend the same objective rather than forming additional jointly posed questions. Unambiguous detection means a single zero-energy mode spatially bound to a vortex core whose measured signatures exclude the trivial alternatives named in sub-question (3) — Caroli–de Gennes–Matricon vortex-core levels, Andreev bound states, and disorder-induced zero-bias anomalies — and exclude an ensemble of such states or a conventionally bound state.

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