Where are the electrons?
We have published our point of view in the paper indicated below in the journal "Proceedings of IEEE"
This paper wants to be a reflection on how we are educating young engineers that will develop future quantum technologies. Are we providing them with a comfortable understanding of quantum phenomena? What will be our answer when a student asks us "Where are the electrons"? Will we still answer "shut up and calculate"?
We are all fascinated by the mystery of uncomprehensibility and, certainly, there are still many mysteries to be solved. In addition, all physical theories (as human creations) have a limited range of validity. But, it is now clear that a trivial answer to a student asking "Where are the electrons?" is that electrons are obviously "there, inside the transistors". Bohmian mechanics (with an ontology based on particles choreographed by a many-body wave function) gives fully theoretical support to such trivial answer....Then, why don't we provide this trivial answer to the students? If everybody explains the behaviour of electron devices with the sentence "electrons traversing the device", while moving our finger to show their path, why don't we use a theory that supports that "electrons are traversing the device"?
Figure caption: The animated plot above shows an electron traversing a barrier in a 2D gapless graphene structure. The fact that the electron traverse so easily the barrier, with almost a constant velocity (in modulus), is known as the Klein tunneling paradox because it is an unexpected result for typical electronic materials (parabolic bands) where electron tunneling implies that the electron has to pass through regions of forbidden energies, but this is not the case in gapless graphene (linear bands) since there are no forbidden energies for electrons.
Top: The electron is described by a (red solid) moving point in the x-y plane of a 2D graphene sheet. It is guided by a (bispinor) wave function (blue dashed circles) solution of the time-dependent Dirac equation. The wave function is mostly transmitted, but also partially reflected. On the contrary, in this particular experiment, the electron is only transmitted. In other experiments, it can be reflected. But, never both, reflected and transmitted. The vertical lines, perpendicular to the transport direction, show the limits of the central region defined in the bottom plot. The change in the direction of the electron’s trajectory (solid blue line) is explained from the conservation of y-momentum.
Bottom: The potential energy (defined as the Dirac point) in each x-y point of the 2D graphene sheet. The Dirac point in the central (brown) region is 0.3 eV higher than in the left and right (blue) regions. The moving vertical (red) line indicates a constant total energy of 0.1 eV for the electron while traversing the graphene structure (ballistic transport). In the left and right (blue) regions, the electron’s energy coincides with the conduction band, while it coincides with the valence band in the central (brown) region. There is no region of forbidden energy for the electron since graphene is a gapless material.