- Open Access
Mass-gap control of Lorentzian graphene zero modes: Exact retuning, multiplet splitting, and local density of states resonances
Phys. Rev. B 114, 285413 – Published 13 November, 2026
DOI: https://doi.org/10.1103/bbps-dcjq
Abstract
Smooth electrostatic wells in graphene can support normalizable states at the charge-neutrality (Dirac) point even though electrostatic confinement at nonzero energy is generally leaky. We examine how a spatially varying mass gap reorganizes this mechanism for a circular Lorentzian well under the explicit assumption that the localized mass and scalar potential are strictly coprofiled. A constant spinor-component rescaling gives an exact covariance of the radial equations at finite energy and background gap; the Lorentzian specialization then yields a closed critical-retuning law. The zero-mode manifold contains two regular angular families in each valley, and a weak uniform background gap produces opposite-sign slopes within a restricted localized-mass range, with asymmetric magnitudes when the localized mass is nonzero. Tail-corrected two-point shooting confirms the analytic slopes down to small background gaps and follows all six descendants of the multiplet. The Lorentzian inverse-square tail additionally generates idealized geometric towers of near-edge states in supercritical low-angular-momentum channels. In a gapless exterior, the two angular sectors appear as paired local density of states resonances whose positions approach zero and whose widths collapse rapidly near criticality. These results connect exact coprofile covariance, zero-mode retuning, angular-pair splitting, threshold towers, and tunneling signatures within one two-dimensional Dirac model.
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