  Nonuniform elastic strain is known to induce pseudo-Landau levels in Dirac
materials. But these pseudo-Landau levels are hardly resolvable in an analytic
fashion when the strain is strong, because of the emerging complicated space
dependence in both the strain-modulated Fermi velocity and the strain-induced
pseudomagnetic field. We analytically characterize the solution to the
pseudo-Landau levels in experimentally accessible strongly bent graphene
nanoribbons, by treating the effects of the nonuniform Fermi velocity and
pseudomagnetic field on equal footing. The analytic solution is detectable
through the angle-resolved photoemission spectroscopy (ARPES) and allows
quantitative comparison between theories and various transport experiments,
such as the Shubnikov-de Haas oscillation in the complete absence of magnetic
fields and the negative strain-resistivity resulting from the valley anomaly.
The analytic solution can be generalized to twisted two-dimensional materials
and topological materials and will shed a new light on the related experimental
explorations and straintronics applications.
