THE QUANTUM INTELLIGENCER

Tetralayer kagome borophene, a crystal of boron in four stacked layers, has been predicted to superconduct at 102 kelvin, a temperature above that of liquid nitrogen and a record for any elemental superconductor. The result, obtained from first-principles calculations and fully anisotropic Migdal-Eliashberg theory, is set out in a paper now on the arXiv. The authors describe a mechanism distinct from that of known high-temperature boron superconductors: the pairing is carried by low-frequency vibrations of boron atoms moving out of the plane, coupled to interlayer s-pz bonding states at the Fermi level, rather than by the high-frequency in-plane stretching modes that dominate elsewhere. They propose covalent stacking engineering, the deliberate ordering of boron layers, as a route to high-temperature superconductivity in two-dimensional materials. No measurement has yet been reported; the record is at present a calculated one, awaiting the verdict of the laboratory. One structural figure not yet set down: the paper specifies the four-layer material as an ABAB covalent stacking, and it is this ordered alternation of the sheets that opens the out-of-plane bonding states at the Fermi level. The announcement carries its own vocabulary, and the terms reward a patient reader. A superconductor is a material which, below a particular temperature, carries an electric current without resistance. That temperature is the critical temperature; the prediction places this one at 102 kelvin, above the temperature at which nitrogen becomes liquid. The word elemental fixes the scope of the record: the crystal is boron alone, not a compound of boron with other elements, and the predicted value exceeds the critical temperatures previously reported for any elemental superconductor. The calculations are called first-principles because they begin from the laws of quantum mechanics and the identities of the atoms themselves, without borrowing a fitted answer from experiment. The crystal, for its part, is not still. Its atoms vibrate about their appointed stations, and the vibrations pass through the lattice in discrete packets known as phonons. Superconductivity of the conventional kind is a partnership between electrons and phonons: a moving electron deforms the lattice, and the deformation, carried by phonons, draws electrons into pairs that flow without friction. The strength of this partnership is the electron-phonon coupling. The fully anisotropic Migdal-Eliashberg theory, by which the present prediction was computed, takes the measure of that coupling in every direction through the crystal rather than treating the material as uniform. The word anisotropic is essential, for the crystal has layers, and motion within a layer is not the same as motion between layers. At the Fermi level, the energy boundary between occupied and unoccupied electron states, lie the states that matter for conduction. In this material they are interlayer states, formed from the s and pz orbitals of the boron atom, the lobes of which point out of the plane of each sheet and reach toward the next. The vibrations that pair the electrons are likewise directed out of the plane: low in frequency, the boron atoms moving perpendicular to the layers. The mechanism is thus a vertical one, depending on bonds between sheets, whereas the better-known high-temperature boron superconductors depend on strong bonds and high-frequency motion within the sheets. The lattice pattern of the sheets takes its name from the kagome, a Japanese weave of triangular openings. The paper's own term for its proposal is covalent stacking engineering: the deliberate ordering of layers, here in the alternating ABAB arrangement, so that bonds form between them. —Dr. Octavia Blythe Dispatch from The Prepared E0