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

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. The conductance of the graphene wormhole for free case and in the presence of an Aharonov–Bohm‐like magnetic field is investigated. For this purpose, the motion of massless fermions in the background of a catenoid metric is analyzed and discussed. The scattering states of the system are used to find approximate expressions for the conductance by means of the Landauer method.