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Prof. Paolo Marconcini, Dipartimento di Ingegneria dell’Informazione, Università di Pisa, "Envelope-function method for the study of charge transport in graphene and graphene-related materials", 18-20 July 2022

12 hours (3 credits)


Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

After a general introduction on the use of the envelope-function method in the study of semiconductors, the course will focus on the application to graphene and graphene-related materials. Due to its particular lattice structure, in monolayer graphene the envelope-function equation takes the form of the Dirac-Weyl equation (i.e., the same relation that describes the behavior of relativistic massless quantum particles, which explains why in graphene several exotic relativistic effects, such as Klein tunneling, appear at non relativistic speeds). The course will describe the derivation of the Dirac envelope-function equation in graphene and related materials, the numerical methods that can be adopted for its solution, and the way in which this description can be applied for the study of transport of graphene-based devices. Particular care will be devoted to the discretization and ill-conditioning numerical problems which may emerge using this modelization and to the methods which can be used to overcome them.

Course Contents in brief:

  1. General introduction to the envelope-function method in semiconductors.
  2. Derivation of the Dirac envelope function equation in graphene and graphene-related materials.
  3. Numerical solution of the Dirac equation and related discretization problems.
  4. Application to the study of charge transport in graphene-based devices, in the presence of a generic potential profile and of an orthogonal magnetic field.


  1. 18/07/2022: h. 14.00-18.00
  2. 19/07/2022: h. 14.00-18.00
  3. 20/07/2022: h. 14.00-18.00