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The expression for Vel is simplified in the long polaron approximation. Using the notation of Ref., we can neglect terms in i qj (the dispersion in the optical branches) as long as (μ- μ′) / a2, (λ- λ′) / a2 α, where a is the length of the polaron. Since (μ- μ′), (λ- λ′) are the order of the square of the speed(s) of sound in graphene or about 108 m2 s-2, whereas α can be expressed in terms of the graphitelike optical frequency α= ωΓ2 /4∼ 1028 s-2 and we have for the length of the polaron a∼10nm, those ratios are thus of the order of 10-4.
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The expression for Vel is simplified in the long polaron approximation. Using the notation of Ref., we can neglect terms in i qj (the dispersion in the optical branches) as long as (μ- μ′) / a2, (λ- λ′) / a2 α, where a is the length of the polaron. Since (μ- μ′), (λ- λ′) are the order of the square of the speed(s) of sound in graphene or about 108 m2 s-2, whereas α can be expressed in terms of the graphitelike optical frequency α= ωΓ2 /4∼ 1028 s-2 and we have for the length of the polaron a∼10 nm, those ratios are thus of the order of 10-4.
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