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Article

Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials

Department of Information Engineering, Marche Polytechnic University, 60131 Ancona, Italy
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Author to whom correspondence should be addressed.
Academic Editors: Vasili Perebeinos and Antonio Bartolomeo
Appl. Sci. 2021, 11(5), 2398; https://doi.org/10.3390/app11052398
Received: 5 February 2021 / Revised: 2 March 2021 / Accepted: 4 March 2021 / Published: 8 March 2021
(This article belongs to the Section Applied Physics)
Starting from the four component-Dirac equation for free, ballistic electrons with finite mass, driven by a constant d.c. field, we derive a basic model of scalar quantum conductivity, capable of yielding simple analytic forms, also in the presence of magnetic and polarization effects. The classical Drude conductivity is recovered as a limit case. A quantum-mechanical evaluation is provided for parabolic and linear dispersion, as in graphene, recovering currently used expressions as particular cases. Numerical values are compared with the ones from the literature in the case of graphene under d.c. applied field. In particular, the effect of the sample length and field strength on the conductivity are highlighted. View Full-Text
Keywords: Dirac equation; quantum conductivity; graphene Dirac equation; quantum conductivity; graphene
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MDPI and ACS Style

Pierantoni, L.; Pelagalli, N.; Mencarelli, D.; Di Donato, A.; Orlandini, M.; Pagliuca, J.; Rozzi, T. Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials. Appl. Sci. 2021, 11, 2398. https://doi.org/10.3390/app11052398

AMA Style

Pierantoni L, Pelagalli N, Mencarelli D, Di Donato A, Orlandini M, Pagliuca J, Rozzi T. Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials. Applied Sciences. 2021; 11(5):2398. https://doi.org/10.3390/app11052398

Chicago/Turabian Style

Pierantoni, Luca; Pelagalli, Nicola; Mencarelli, Davide; Di Donato, Andrea; Orlandini, Matteo; Pagliuca, Jacopo; Rozzi, Tullio. 2021. "Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials" Appl. Sci. 11, no. 5: 2398. https://doi.org/10.3390/app11052398

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