A new class of solvable two-dimensional scalar potentials for graphene
Saint Petersburg State University, 7/9 Universitetskaya nab., 199034, St. Petersburg, Russia
2 Akaki Tsereteli State University, 4600, Kutaisi, Georgia
Accepted: 25 September 2022
Published online: 29 October 2022
In the present paper, a systematic approach is presented for solution of two-dimensional massless Dirac equation with external electrostatic potential applied. This approach is based on the new—asymmetric—form of SUSY-like intertwining relations. It allows to build a wide variety of pairs of SUSY-partner external scalar potentials. If one of them is simple enough to be solvable, its partner is also solvable although it may have a non-trivial dependency on both coordinates. Physically, this kind of problems is related to the description of graphene and some other materials with external potential. Solvability obtained by means of asymmetric form of SUSY intertwining relations allows to extend the class of analytically solvable two-dimensional models.
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