On the electronic spectrum in curved graphene nanoribbons

Using the formalism of the Dirac equation for curved space-time in the Friedmann model of a non-stationary universe, we calculate the electronic spectrum and density of states in curved graphene nanoribbons. Based on the obtained density of states we further study the current-voltage ($IV$) characteristics of the nanoribbon – metal tunnel junction. The dependence on the geometric characteristics of the nanoribbon has been revealed, showing a great influence of such parameters like the number of carbon atoms and the characteristic frequency of distortion.