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Electrons in metals form a Fermi surface separating occupied from unoccupiedstates in momentum space at zero temperature. Interactions between electronsare usually accounted for by the Landau theory of Fermi liquids; however,little is known about the stability of the Fermi liquid when the Fermi levelintercepts the crossing point between two bands, shrinking the Fermi surface toa set of points known as conical intersections. Here we consider thepossibility of pairing electronic states across conical intersections thatresults in a Bardeen-Cooper-Schrieffer-like state restricted to a finite rangeof energies around the crossing point, hence, "floating" over an ordinary Fermisea of occupied states in the lower band. Although this state is notsuperconducting in the usual sense and does not exhibit a gap in its excitationspectrum, it is nevertheless immune to elastic scattering caused by any kind ofdisorder, and is therefore expected to exhibit high electric conductivity atlow temperature, similar to a real superconductor. The stability of thiscorrelated state requires high density of electronic states in the vicinity ofthe crossing point -- a feature that may occur in twisted multilayer graphenestructures, which are experimentally available. Our findings thus open anexciting opportunity for creating a new class of highly conductive materials.

Electron pairing across a band intersection may create a highly conductive state