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The effect of a varying pseudo-magnetic field, which falls as $1/x^2$, on atwo dimensional electron gas in graphene is investigated. By considering thesecond order Dirac equation, we show that its correct general solution is thatwhich might present singular wavefunctions since such field induced by elasticdeformations diverges as $x\rightarrow0$. We show that only this considerationyields the known relativistic Landau levels when we remove such elastic field.We have observed that the zero Landau level fails to develop for certain valuesof it. We then speculate about the consequences of these facts to the quantumHall effect on graphene. We also analyze the changes in the relativisticcyclotron frequency. We hope our work being probed in these contexts, sincegraphene has great potential for electronic applications.

Influence of spatially varying pseudo-magnetic field on a 2D electron gas in graphene