Topological superconductivity

Also called topological superconductor

In plain words

whose paired electrons carry a twist that cannot be undone smoothly – the superconducting cousin of a . Inside, the material behaves like an ordinary superconductor, but its edges, surfaces and the cores of its vortices must hold special states, among them , which could store quantum information in a way that local disturbances cannot easily spoil. Few materials are clearly topological superconductors on their own, so researchers also build them by bringing an ordinary superconductor into contact with a or magnetic material.

Not to be confused with

Majorana mode

Topological superconductivity is the state of a material; a Majorana mode is one of the states it must hold at its edges, wire ends or vortex cores. Finding a state at zero energy is not the same as finding a topological superconductor: ordinary defects can produce look-alikes, which is why a claimed Majorana mode needs more than one signature.

As the site uses it

Because the pairing looks conventional, any topological superconductivity would come from the normal-state topology rather than from an exotic order parameter, which makes the surface states and their response to disorder the interesting quantity to compute.

PbTaSe₂ · Nodal-line superconductor PbTaSe₂

Mixing in tellurium gives a crystal whose surface becomes a topological superconductor, one of the leading places to look for Majorana states.

FeSe, FeTeSe · Iron selenide and iron telluride selenide

Going deeper

A topological superconductor is gapped inside but must carry states at its edges and in its vortex cores. Few materials are one by nature; most attempts combine an ordinary superconductor, strong spin–orbit coupling and a magnetic field.

Topology meets pairing

In a superconductor electrons pair up, and the excitations above the ground state are mixtures of an electron and a missing electron. Their bands can carry a topological twist, just as the bands of a topological insulator do: the inside is then gapped, but the boundary must carry states inside the gap. Because each of these states mixes particle and hole, some of them are their own antiparticles – Majorana modes. The textbook case is a chain of spinless electrons with p-wave pairing, whose two ends each hold one Majorana mode.

Building one

Topological superconductors are rare in nature, so most are built. In 2008 Fu and Kane showed that an ordinary superconductor laid on the surface of a topological insulator turns its topological. Similar recipes combine a superconductor with a nanowire with strong in a magnetic field, or with a chain of magnetic atoms. Among layered crystals, the surface of FeTe₀.₅₅Se₀.₄₅ was shown in 2018 to meet the conditions by itself, PtBi₂ has superconducting topological surface states, and NbSe₂ junctions with magnets or topological layers are being explored.

Why proof is hard

The signature most experiments look for, a peak in the tunnelling conductance at zero bias, has ordinary causes too: and Andreev bound states that are not topological can produce it, and several prominent claims have been withdrawn or reinterpreted. Stronger tests check that the peak keeps a quantised height, appears and vanishes with the predicted magnetic field and position, or shows the exchange statistics that topological quantum computing would rely on.

For specialists

Superconductivity whose Bogoliubov bands carry a nontrivial topological invariant, so that a full or nodal bulk gap coexists with protected Andreev boundary states, including Majorana zero modes bound to vortices and wire ends. Intrinsic candidates include odd-parity pairing and strongly –orbit-coupled systems such as the surface of FeTe₀.₅₅Se₀.₄₅, PtBi₂ and UTe₂; engineered versions combine s-wave pairing with spin–orbit coupling and broken , following the Fu–Kane proposal for topological-insulator surfaces, semiconductor nanowires and magnetic atom chains. A zero-bias conductance peak alone is not proof: disorder and ordinary Andreev bound states mimic it.

Where this comes from

Unpaired Majorana fermions in quantum wires Kitaev · Physics-Uspekhi 44, 131 (2001) cited by 4,766
Superconducting proximity effect and Majorana fermions at the surface of a topological insulator Fu and Kane · Physical Review Letters 100, 096407 (2008) cited by 4,886
Topological superconductors: a review Sato and Ando · Reports on Progress in Physics 80, 076501 (2017)
Observation of topological superconductivity on the surface of an iron-based superconductor Zhang et al. · Science 360, 182 (2018) cited by 722

In the news

The newest items in the site’s news feed that use the term, one from each source.

Preprintnot yet peer reviewed 24 Sep 2026 arXiv

Repulsion-Driven p - i p Superconductivity in a Single Valley Revealed by DMRG

We demonstrate repulsion-driven topological superconductivity of a single species of , motivated by -polarized phases observed in two-dimensional materials such as graphene. Using density-matrix renormalization group calculations on the Qi-Wu-Zhang lattice model on cylinders of width up…

TheoryTwisted graphene Graphene

Preprintnot yet peer reviewed 9 Sep 2026 arXiv

A First-Principles Multiscale Framework for Topological Superconductivity

A microscopic understanding of topological superconductivity (TSC) in real materials requires a materials-informed approach that integrates , superconductivity, and topology within a unified computational framework. Here, we develop such an approach by combining density functional…

TheoryFeSe, FeTeSe

Preprintnot yet peer reviewed 3 Sep 2026 arXiv

Hierarchy of topological superconductivity generated via heterostructures of unconventional p-wave magnets

A theoretical framework is proposed to engineer both first and second-order topological superconducting phases in a two-dimensional (2D) , consisting of a quantum spin Hall insulator (QSHI) and an unconventional p-wave magnet in presence of proximity-induced s-wave superconducting pairing. Our analysis…

Theory

Search the news for this term

Majorana mode

A state that can appear at the ends of certain superconducting wires, or in the whirlpools of a superconductor, and that is its own antimatter twin. Two of them together make up one ordinary electron state split in half and kept in two separate places, so no disturbance at either place alone can read or destroy what it holds – which is why they are pursued for quantum computing.

A zero-energy state equal to its own conjugate, appearing at defects of a topological superconductor – wire ends, vortex cores, domain walls. A pair defines one non-local fermionic state, so exchanging them realises non-Abelian statistics and topologically protected operations. Recipes combine strong spin–orbit coupling, magnetism and superconductivity, which is what makes van der Waals stacks attractive; proximity-induced pairing on a topological surface is the canonical route, and a zero-bias conductance peak on its own is not proof.

Full explanation

Topological phase

A state of matter told apart not by how its atoms are arranged but by a whole number that describes how its electrons’ waves twist across the crystal – the way a doughnut differs from a ball by its one hole. A whole number cannot change a little, so what it guarantees, such as current running along an edge without loss, survives defects and dirt until the band gap itself closes.

A gapped phase characterised by a topological invariant of its occupied bands – a Chern number, a Z₂ index, a winding number – that cannot change under deformations that keep the gap open and any protecting symmetry intact. Where regions with different invariants meet, the gap must close, which forces boundary states: chiral edge channels in Chern insulators, helical ones in quantum spin Hall insulators, Fermi arcs in Weyl semimetals, Majorana modes in topological superconductors. Topological order in the strict sense – the long-range entanglement of fractional quantum Hall states and spin liquids – is a distinct, stronger notion.

Full explanation

Surface state

Electron states that exist only at the surface of a crystal, because the crystal stops there. Atoms at a surface have lost their neighbours on one side, so electrons can take energies there that the inside of the crystal does not allow. Usually such states are a nuisance that traps charge. In a topological insulator they are the point: the inside insulates while the surface is guaranteed to conduct, with each electron’s spin tied to its direction of motion.

States localised at a crystal surface and decaying into the bulk, at energies forbidden in the bulk for that in-plane momentum. Ordinary Tamm and Shockley states come from the broken periodicity, dangling bonds or reconstruction, and can be removed or shifted by passivation. Topological surface states are required by a non-trivial bulk invariant: a single spin–momentum-locked Dirac cone in Bi₂Se₃-family topological insulators, protected against backscattering by time-reversal symmetry, and Fermi arcs joining the projections of Weyl points in Weyl semimetals. In thin films the top and bottom surface states hybridise and open a gap below a critical thickness, about six quintuple layers for Bi₂Se₃. In a 2D material the boundary of a topological phase is its edge, and the counterpart of the surface state is the edge state.

Full explanation

Disorder and localisation

Every real crystal has some disorder: missing or misplaced atoms, impurities, stray charges in the substrate, a random mixture of elements in an alloy. Electrons moving through it scatter off these imperfections, which raises the resistance. If the disorder is strong enough, electron waves become trapped in small regions – localised – and the material stops conducting, even if it would be a metal when perfect. In a sheet one atom thick, disorder in its surroundings matters especially.

Deviations from perfect periodicity – point defects, substitutional or alloy disorder, interface roughness, charged impurities and strain variations in the substrate – that scatter carriers and, beyond a threshold, localise their wavefunctions through interference (Anderson localisation). Scaling theory predicts that non-interacting electrons in two dimensions without spin–orbit coupling are localised by any disorder; its precursor, weak localisation, appears as a logarithmic rise of resistance at low temperature that a magnetic field suppresses, while strong spin–orbit coupling gives weak antilocalisation. In graphene on SiO₂, charged impurities break the sheet near charge neutrality into electron–hole puddles, which hBN encapsulation reduces. Strong disorder leads to hopping conduction, broadens optical lines and smears phase transitions; in frustrated magnets and correlated oxides, structural or cation disorder can mimic exotic states.

Full explanation

Quasiparticle

An electron moving through a crystal is never alone: it pushes and pulls on all the other electrons and atoms around it, and drags a little cloud of disturbance along. Physicists treat the electron together with its cloud as a new particle – a quasiparticle – with its own mass and lifetime. The idea goes further: holes, excitons, vibrations of the lattice and waves of spins also behave like particles, and describing a solid as a gas of such quasiparticles is how most of its properties are understood.

An elementary excitation of an interacting many-body system that behaves like a particle with a defined energy–momentum relation, charge or spin, and a finite lifetime, as in Landau’s Fermi-liquid theory. Dressed electrons and holes (renormalised by screening, phonons or correlations, with effective masses that can reach hundreds of free-electron masses in heavy-fermion systems), excitons, trions and polarons, and bosonic collective modes such as phonons, magnons, plasmons and polaritons are all quasiparticles. Their energies are poles of the Green’s function; the GW approximation computes quasiparticle band structures, which in 2D semiconductors are strongly renormalised by the reduced screening, so that the quasiparticle gap exceeds the optical gap by the large exciton binding energy.

Full explanation

Spin

A built-in property of every electron that makes it a tiny magnet. Measure it along any direction and you only ever find one of two answers, ‘up’ or ‘down’. Despite the name, nothing is actually spinning – the word stuck from an early picture – but the magnetism is real: countless electron spins lined up are what make a fridge magnet stick. Spintronics tries to carry information in spin rather than in charge.

The intrinsic angular momentum of the electron, ħ/2, with a magnetic moment of almost exactly one Bohr magneton; a measurement along any axis yields one of two values. In solids spin couples to orbital motion through spin–orbit coupling and to other spins through exchange; in 2D materials it sets magnetic order, spin–valley locking and how long a spin survives as a carrier of information.

Full explanation

Time-reversal symmetry

The idea that the laws governing electrons would look just as valid if you ran a film of them backwards. Reversing time flips every motion and every spin, so a material with no magnetism of its own usually keeps this symmetry, while a magnet – or a magnetic field – breaks it. Which case applies decides a lot: some protected edge currents need the symmetry, and others need it broken.

The antiunitary operation t → −t, which reverses momenta and spins; for spin-½ electrons T² = −1, giving Kramers degeneracy of every state at time-reversal-invariant momenta. It is broken by magnetic order or applied fields. Its presence protects the helical edge states of quantum spin Hall insulators and makes Berry curvature odd in k, so valley Hall but not anomalous Hall effects survive; its breaking allows Chern insulators, the anomalous Hall effect and Kerr rotation, the standard probes of spontaneous breaking in correlated phases.

Full explanation

Bernal and rhombohedral stacking

The two ways graphene sheets usually sit on one another in graphite. In Bernal, or AB, stacking every second layer lines up with the one two below it; in rhombohedral, or ABC, stacking each layer is shifted the same way as the one before, so the pattern repeats only every third layer. Natural graphite is mostly Bernal with some rhombohedral regions, and the difference matters: a few rhombohedral layers have very flat electron bands, and such flakes have turned out to superconduct and to hold unusual kinds of magnetism.

The two common stacking sequences of graphene layers: Bernal (AB, hexagonal graphite) and rhombohedral (ABC), which differ in the lateral position of every third layer; 3R TMDCs follow the same rhombohedral sequence. In the simplest model the low-energy bands of N-layer ABC graphene disperse as the Nth power of momentum and sit on the two outer layers, so they flatten with thickness and a perpendicular displacement field opens a tunable gap; Bernal multilayers instead decompose into bilayer-like bands plus, for odd N, a monolayer-like one. Rhombohedral stacking is metastable and relaxes to Bernal under heat, strain or processing.

Full explanation

Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

Full explanation

Band structure

The map of the energies an electron may have in a crystal. The allowed energies come in ranges called bands, with forbidden gaps between them – like the decks of a multi-storey car park, where a car can stand on a deck but never between two. Whether a material conducts, gives off light or lets its electrons move easily can all be read from it, and in a layered material the map changes with the number of layers.

The electron energies E(k) of a periodic crystal as functions of crystal momentum, one branch per band, usually plotted along high-symmetry lines of the Brillouin zone. Band edges, slopes and curvatures give the gap, group velocities and effective masses; crossings and inversions give the topology. In layered crystals interlayer hybridisation makes it depend on thickness: the valence-band maximum of MoS₂ moves from Γ in the bulk to K in the monolayer, turning an indirect gap into a direct one.

Full explanation