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    Topological insulators and topological materials

    Also known as topological insulator, topological matter, topological phases of matter, Bi2Se3

    Topological insulators are materials whose interior insulates while their surfaces carry electronic states protected by symmetry; the ideas behind them won the 2016 Nobel Prize in Physics.[1][2] They matter because topologically protected states are candidates for robust electronics and quantum computing, including Microsoft's disputed Majorana 1 chip announced in 2025.[3][4]

    Editor reviewedUpdated Materials sciencePhysicsScience
    Key facts

    The idea

    Topology is the branch of mathematics that deals with properties that change only in steps, never smoothly. Physicists showed in the 1980s that some properties of matter behave this way. In very thin conducting layers, for example, conductance was measured to come in exact integer steps, and those integers turned out to be topological.[5] This work won the 2016 Nobel Prize in Physics “for theoretical discoveries of topological phase transitions and topological phases of matter”.[2]

    Topological insulators

    A topological insulator is a quantum material that carries, on its surface, electronic states that are “protected by the time-reversal symmetry”.[1]

    The archetype is bismuth selenide (Bi2Se3). Calculations published in 2009 predicted that it has a single cone-shaped band of surface states (a “Dirac cone”). They also predicted a 0.3 eV topological gap, large enough for room-temperature applications.[6] The same study examined the related compounds Bi2Te3, Sb2Te3 and Sb2Se3.[6]

    The protection is the point. Because the surface states are tied to a symmetry of the material rather than to its fine details, topological materials are discussed for new generations of electronics and for quantum devices.[1][3]

    Topology in 2D and moiré materials

    Topological states also appear in engineered 2D stacks. Since 2023, twisted MoTe2 and rhombohedral graphene have shown fractional quantum anomalous Hall states with no external magnetic field.[7][8] In July 2026 a twisted graphene stack showed Chern numbers from 1 to 7 and an exotic fractional C = 7/3 state.[9] See twisted-bilayer-graphene.

    Why quantum computing cares

    The Nobel committee pointed to possible uses in new electronics and superconductors and in future quantum computers.[3] One industrial bet is Microsoft’s. In February 2025 the company announced Majorana 1, which it called the first quantum processor with a “topological core”. It is built from an indium arsenide-aluminium “topoconductor” designed to enter a topological superconducting state.[4] Microsoft said the chip holds eight topological qubits and is designed to scale to a million.[10] The claim is disputed: Nature’s reviewers said the underlying paper was not evidence of Majorana modes.[11] The dispute is covered on topological-qubits.

    Why it matters for materials science

    Topological materials show a recurring pattern at the frontier: theory, here recognised by a Nobel Prize, predicts specific materials, which experimenters then make and test.[2][6] The same pattern now runs through moiré materials, where stacking and twist angle are used to create topological states.[9] Whether such states can be made robust and reproducible enough for devices is open; Microsoft’s disputed chip shows how hard that is to prove.[4][11]

    Where the ideas came from

    The 2016 Nobel Prize in Physics went half to David Thouless and half jointly to Duncan Haldane and Michael Kosterlitz.[12] In the early 1970s Kosterlitz and Thouless overturned the then-accepted view that superconductivity could not occur in thin layers. They also explained the phase transition that destroys it at higher temperatures. Haldane later showed how topological ideas explain chains of small magnets found in some materials.[13] The Kosterlitz-Thouless transition reappears in today’s ultrathin nickelate superconductor films.[14] Topology is not confined to flat systems. The Nobel committee noted that many topological phases are now known in ordinary three-dimensional materials, of which bismuth selenide is one.[15][6]

    The Majorana bet in detail

    Microsoft says its topoconductor devices, cooled near absolute zero and tuned with magnetic fields, form topological superconducting nanowires with Majorana zero modes at their ends. It also says Majorana 1 is part of the final phase of DARPA’s US2QC programme.[16] Peer reviewers were more cautious. Nature’s review file for the accompanying paper stated that its results do not represent evidence for Majorana zero modes.[11] See topological-qubits for the quantum-computing side.

    Questions readers ask

    What is a topological insulator?

    A material that behaves as an insulator inside but has conducting surface states protected by time-reversal symmetry.[1]

    What does topology have to do with materials?

    Topology describes properties that change only in steps. In materials it explains why some quantities, such as certain conductances, come in exact integer steps.[5]

    Is Bi2Se3 a topological insulator at room temperature?

    Calculations published in 2009 predicted that Bi2Se3 is a topological insulator with a 0.3 eV gap, large enough for room-temperature applications.[6]

    Has Microsoft built a topological qubit?

    Microsoft announced Majorana 1 in February 2025 as the first processor with a topological core, but the claim is disputed; reviewers said the underlying paper was not evidence of Majorana modes.[4][11]

    Sources

    Each numbered claim is a statement we checked against the sources listed with it. Status shows how well established it is.

    1. [1]

      Topological insulators are quantum materials whose surface states are protected by time-reversal symmetry. confirmedas of 2026-10-10

    2. [2]

      The 2016 Nobel Prize in Physics honoured "theoretical discoveries of topological phase transitions and topological phases of matter". confirmedas of 2026-10-10

    3. [3]

      The Royal Swedish Academy of Sciences said topological materials could find uses in new generations of electronics and superconductors and in future quantum computers. confirmedas of 2026-10-10

    4. [4]

      In February 2025 Microsoft announced Majorana 1, which it described as the first quantum processor powered by a topological core, built from an indium arsenide-aluminium "topoconductor". confirmedas of 2026-10-10

    5. [5]

      Topology is the branch of mathematics describing properties that change only in steps; in physics it explains why some quantities, such as certain conductances, come in exact integer steps. confirmedas of 2026-10-10

    6. [6]

      A 2008-2009 study predicted that Bi2Se3 is a topological insulator with a 0.3 eV gap, large enough for room-temperature applications, and a single Dirac cone of surface states. confirmedas of 2026-10-10

    7. [7]

      In 2023 researchers observed the fractional quantum anomalous Hall effect, fractionally quantised Hall resistance with no applied magnetic field, in twisted bilayer MoTe2, enabling research into charge fractionalisation and anyonic statistics without external magnetic fields. confirmedas of 2026-10-10

    8. [8]

      A rhombohedral five-layer graphene/hBN moiré superlattice showed integer and fractional quantum anomalous Hall effects at zero magnetic field at several filling factors, reported in Nature in 2024. confirmedas of 2026-10-10

    9. [9]

      A Nature paper published on 15 July 2026 reported quantum anomalous Hall insulators with Chern numbers from 1 to 7 and an exotic fractional Chern insulator with C = 7/3 in a moiré system of Bernal bilayer and rhombohedral tetralayer graphene. confirmedas of 2026-10-10

    10. [10]

      Microsoft said it had placed eight topological qubits on Majorana 1, a chip designed to scale to a million qubits. confirmedas of 2025-02-19

    11. [11]

      The Nature peer-review file for Microsoft's 2025 paper stated that its results do not represent evidence for Majorana zero modes, and the paper itself did not claim a topological qubit. confirmedas of 2025-02-25

    12. [12]

      The 2016 physics Nobel went half to David Thouless and half jointly to Duncan Haldane and Michael Kosterlitz. confirmedas of 2016-10-04

    13. [13]

      In the early 1970s Kosterlitz and Thouless showed that superconductivity can occur in thin layers at low temperatures, overturning the prevailing theory, and explained the phase transition that destroys it at higher temperatures; Haldane later applied topology to chains of small magnets. confirmedas of 2016-10-04

    14. [14]

      In the 45 K ultrathin films, zero resistance appeared through a Berezinskii-Kosterlitz-Thouless-like transition at about 9 K and the Meissner effect at 8.5 K, with about 2% compressive strain in the nickel-oxide planes. confirmedas of 2024-12-21

    15. [15]

      The Nobel committee noted that many topological phases are now known, not only in thin layers and threads but also in ordinary three-dimensional materials. confirmedas of 2016-10-04

    16. [16]

      Microsoft said its topoconductor devices, cooled near absolute zero and tuned with magnetic fields, form topological superconducting nanowires with Majorana zero modes at their ends, and that Majorana 1 is part of the final phase of DARPA's US2QC programme. confirmedas of 2025-02-19

    Revision history (2)
    1. Page created.
    2. Added the 2016 Nobel laureates and their discoveries, topology in 3D materials, and how Microsoft describes its topoconductor.

    Created Oct 10, 2026. Last reviewed by an editor on Oct 10, 2026. Next scheduled review: Jan 10, 2027.

    Cite this page

    "Topological insulators and topological materials." ContentLora, updated Oct 10, 2026. https://contentlora.com/wiki/topological-insulators

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