Microscopic theory of Raman spectra of superconducting heavy fermion system

Microscopic theory of Raman spectra of heavy fermion systems in the normal state

“…However, this value of the EP coupling is smaller compared to g ' 0:11-0.15 for CDW superconductors [21][22][23][24]26] and for high-T c superconductors containing f-electron levels of rareearth ions and g ' 0:042 for YBa 2 Cu 2 O 7Àd [29] and g ' 0:037-0.041 for GdBaSrCu 2 O 7Àd [30] high-temperature superconductors. However, a still smaller EP coupling (g ' 0:0065) has been recently reported [17] to produce phonon excited superconducting peaks in superconducting HF systems at T ¼ 0 K. The present study gives the strength of EP coupling to the bare f-electrons a minimum value g f ¼ 2:53 Â 10 À8 . This agrees with the fact that the phonon coupling f 1 ð0Þ to the hybridization is stronger than that of the phonon coupling f 2 ð0Þ to the bare f-electron to explain the phonon anomalies and superconductivity in some HF systems [9].…”

“…For example, the value of the coupling is much smaller as compared to that in case of the CDW phase superconductor (g ¼ 0:11-0.15) [21][22][23]26]. In the earlier study [17] (as small as g ' 0:0065) was considered to produce phonon excitation peaks in HF systems in superconducting state at 0 K. Fig. 1 shows the phonon SDF as a function of the reduced phonon frequency ðõÞ for the choice of g; g f ; d; v; u; t; e and p the parameters mentioned above for the normal state of the HF systems.…”

“…Later on several authors have [21][22][23][24] explained the origin of the collective modes of the CDW state as well as the superconducting state appearing in Raman spectrum. Recently, Rout et al [17] have reported a model study of the Raman intensity of the HF superconductors using the PAM in presence of BCS-like Cooper pairing mechanism, with the HF behaviour arising from the hybridization of the f-level with the conduction electrons. The superconducting gap excitation is observable in the Raman spectra due to coupling of the superconducting gap to the normal phonons.…”

“…In the present work, we undertake to investigate the behaviour of these high-frequency collective modes in the HF systems, associated with the hybridization gap in ARTICLE IN PRESS the quasi-particle spectrum, appearing in the normal state Raman spectra as first indicated in Ref. [17]. Different dimensionless parameters involved in the numerical calculations are the coupling strength (g) of phonons with hybridization, the coupling strength (g f ) of the phonons with the f-level, the position of the bare f-level (d), hybridization strength (v) between the conduction electrons and f-level, Coulomb correlation energy (u), the renormalized phonon frequency (c), the bare phonon frequency (p) and the reduced temperature ðt ¼ k B T=w D Þ.A standard set of values for these parameters as given by g ¼ 0:0253; g f ¼ 2:53 Â 10 À8 ; v ¼ 0:015; o D ¼ 200 K; t ¼ 0:09 ðT$18 KÞ; e ¼ 0:018 and p ¼ 1:0 are used to study the detailed variation of the Raman active phonon modes in the Raman spectra.…”

“…More recently, Rout et al [17] have reported a theoretical study of Raman spectra of the HF superconductors. They have considered the Periodic Anderson Model (PAM) in presence of BCS mean-field approximation of Cooper pairing mechanism and Hartree-Fock-type mean-field approximation for Coulomb correlation effects of localized f-electrons of rare-earth ions.…”