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We apply the Darboux transformation to construct new exactly-solvable casesof the two-dimensional massless Dirac equation for potential classes ofLambert-W and inverse exponential type. Both of these classes originate fromthe Heun equation. Conditions are devised for transformed potentials to bereal-valued, and to be in terms of elementary functions.

Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation