Deriving the Dirac Hamiltonian in Graphene

In this video, we will continue our discussion on the electronic structure of graphene, a two-dimensional layer of carbon atoms. In a previous video, we showed that the band structure of graphene exhibits a pair of crossing bands right at the Fermi energy. Hence, the nature of these states will dictate the conduction properties of this two-dimensional material. Here, we will show that electrons in graphene obey a two-dimensional version of the famous Dirac equation, a relativistic wave equation for spin half fermions firstly proposed by Paul Dirac. Hence, electrons in graphene behave as relativistic particles, an unique behavior that has enabled the study of relativistic quantum mechanical phenomenon at the table-top.
Technical Content: Duarte Sousa, Tony Low
Video Production: Katie Low, Tony Low

[@peterasamoah8779]

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[@professornanoscience]

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[@alanthayer8797]

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[@thiagoescobarcolla302]

Great video! Very nice and well exposed overview of graphene Hamiltonian. Thanks a lot for this video!

[@arthurmarazza6554]

Hello sir, I hope you would make some videos regarding the nonlinear Schrodinger and Dirac equation. Thank you!

[@LL-mq7gj]

Where can I find a derivation of the expansion around K at 5:55?

[@professornanoscience]

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