Adiabatic confinement and number-theoretic spectra of massless Dirac fermions in twisted trilayer graphene

Abstract

Electrons in graphene move like massless relativistic particles, making them exceptionally mobile but difficult to trap because Klein tunnelling permits unimpeded passage through electrostatic barriers. This challenge extends to atomic collapse and hadron confinement. Twisted trilayers form Bernal and rhombohedral domains joined by smooth boundaries, bringing their carriers into contact. Here we show that a new mechanism, distinct from established approaches, confines massless fermions in equilateral triangular Bernal domains without mass barriers, bulk gaps or physical edges. Simulations and analytical modeling reveal that massless carriers have no adiabatic continuation into rhombohedral domains, while escape through nonadiabatic coupling to massive carriers is exponentially suppressed by smooth stacking variation. Perfect reflection in the adiabatic limit turns Bernal domains into quantum cavities in a gapless, edgeless metal. Striking density-of-states oscillations encode Eisenstein-integer arithmetic, linking energies and degeneracies to norms and prime factorizations. These findings bring relativistic confinement and number theory into experimentally accessible electronic spectra.