Alternative representation of the Kubo formula for the optical conductivity: A shortcut to transport properties

Physical Review B - Condensed Matter and Materials Physics

Volumn 90, Issue 1, 2014, Pages

  De Filippis, G ^a   Cataudella, V ^a   De Candia, A ^a   Mishchenko, A S ^b   Nagaosa, N ^b,c  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b RIKEN Center for Emergent Matter Science   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84905395962     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.90.014310     Document Type: Article

References (44)

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41. H. Fröhlich and N. F. Mott, Proc. R. Soc. London A 171, 496 (1939). We note that within this reference, the equations determining the transport scattering time coincide with Eqs. (28) and (29), except for the factor (Equation presented) that is replaced with (Equation presented). Fröhlich and Mott demonstrated, by using the energy conservation, that the factor (Equation presented) is equivalent to the quantity (Equation presented) [(Equation presented) (Equation presented) for one phonon emission (absorption)], where (Equation presented). On the other hand, the inspection of the Boltzmann equation reveals that the contribution (Equation presented) is correct only in the elastic-scattering problems (where (Equation presented) and, in this case, all the approaches provide the same result). We also note that the term (Equation presented) has been neglected by Frohlich in Ref. [30]. Actually it is not clear which is the appropriate factor in the inelastic-scattering problems, and, in general, it is discarded (in this way, transport scattering time and electron lifetime coincide). Then the problem is open and, so far, not solved. This does not allow one to establish which is the correct perturbative limit for the mobility. Within BWFOC, the appropriate factor both in elastic- and inelastic-scattering problems turns out to be (Equation presented). We note, in particular, that the validity of our approach is not related to the nature of the scattering events. 1364-5021 10.1098/rspa.1939.0080
42. Note the strange fact that in the FHIP [28] treatment, mobility is dominated by phonon emission processes [21].
43. We emphasize that within the SKF, the second vertex correction provides a further factor in Eq. (27) of the order of (Equation presented) [7], in agreement, apart from a numerical factor, with the prediction of WBFOC (we note that WBFOC obtains this result at the lowest order).
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