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Published on: May 18, 2021
Definition of current density in the presence of a non-local potential
Changsheng Li1, Langhui Wan, Yadong Wei
1Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, Anhui, People's Republic of China.
Abstract:
In the presence of a non-local potential arising from electron-electron interaction, the conventional definition of current density J(c) = (e/2m)([(p-eA)ψ](*)ψ-ψ(*)[(p-eA)ψ]) cannot satisfy the condition of current conservation, i.e., [Formula: see text] in the steady state. In order to solve this problem, we give a new definition of current density including the contribution due to the non-local potential. We show that the current calculated based on the new definition of current density conserves the current and is the same as that obtained from the Landauer-Büttiker formula. Examples are given to demonstrate our results.
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