Some Electric, Thermal, and Thermoelectric Properties of Suspended Monolayer Graphene

Mascali, Giovanni

doi:10.1137/22m147548x

SIAM J. Appl. Math.

2023

DOI: 10.1137/22m147548x

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Some Electric, Thermal, and Thermoelectric Properties of Suspended Monolayer Graphene

Giovanni Mascali

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Wigner Equations for Phonons Transport and Quantum Heat Flux

Camiola,

Romano,

Vitanza

2023

J Nonlinear Sci

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Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the acoustic, optical and Z phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties, the pseudo-differential operators are expanded up to the second order in $$\hbar $$ ħ . An energy transport model is obtained by using the moment method with closure relations based on a quantum version of the Maximum Entropy Principle by employing a relaxation time approximation for the production terms of energy and energy flux. An explicit form of the thermal conductivity with quantum correction up to $$\hbar ^2$$ ħ 2 order is obtained under a long-time scaling for the most relevant phonon branches.

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Wigner Equations for Phonons Transport and Quantum Heat Flux

Camiola,

Romano,

Vitanza

2023

J Nonlinear Sci

View full text Add to dashboard Cite

show abstract

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Some Electric, Thermal, and Thermoelectric Properties of Suspended Monolayer Graphene

Cited by 1 publication

References 33 publications

Wigner Equations for Phonons Transport and Quantum Heat Flux

Wigner Equations for Phonons Transport and Quantum Heat Flux

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