Aharonov–Bohm‐Like Flux Effects on the Landauer Conductance in Graphene Wormholes

Abstract

In this work, the graphene wormhole in two cases, i) free case and ii) in the presence of an Aharonov–Bohm (AB)‐like magnetic field are studied. To achieve the objective, the massless Dirac equation is solved in the background of a catenoid metric. As this system does not support exact solutions due to the considered background, the scattering‐state solutions are obtained by means of the Born approximation. In both cases, the Landauer formalism is used to obtain approximate expressions for the conductance. For the free case, a minimum conductance, which is independent of system parameters is found. For the case with an AB‐like magnetic field, the results show that the conductance can be modulated by means of the parameter related to magnetic flux. In addition, a special case where a null magnetic flux generates an oscillatory conductance is analyzed.

Charged scalar bosons in a Bonnor–Melvin-$$\varLambda $$ universe at conical approximation

“…To accomplish this, we consider a four-vector potential, A μ , in curved space associated with this external field. This potential is defined as A μ = e μ ā A ā , where A ā represents the fourvector potential in flat space-time [39][40][41]. In this case, we consider A ā in the form…”