Correlation of optical conductivity and angle-resolved photoemission spectra of strong-coupling large polarons and its display in cuprates

Abstract

A common approach is used to calculate a band due to strong-coupling large polaron (SCLP) photodissociation in angle-resolved photoemission spectroscopy (ARPES) and in optical conductivity (OC) spectra. It is based on using the coherent-state representation for the phonon field in SCLP. The calculated positions of both band maxima are universal functions of one parameter---the SCLP binding energy ${E}_{p}$: a maximum of the band in the ARPES spectrum lies at a carrier binding energy of about $3.2{E}_{p}$; the OC band maximum is at a photon energy of about $4.2{E}_{p}$. The half-widths of the bands are mainly determined by ${E}_{p}$ and slightly depend on the electron-phonon coupling constant $\ensuremath{\alpha}$; for $\ensuremath{\alpha}=6--8$, the half-width of the band in the ARPES spectrum is $1.7\ensuremath{-}1.3{E}_{p}$ and the OC band half-width is $2.8\ensuremath{-}2.2{E}_{p}$. By using these results, one can predict the approximate maximum position and half-width of the band in the ARPES spectrum from the maximum of the mid-IR OC band and vice versa. Comparison of the results with experiments leads to the conclusion that underdoped cuprates contain SCLPs with ${E}_{p}=0.1--0.2\text{ }\text{eV}$, which is in good conformity with the medium parameters in cuprates. The values of the polaron binding energy determined from experimental ARPES and OC spectra of the same material are in good conformity, too: the difference between them is within 10%.