Polaron formation as origin of unconventional isotope effects in cuprate superconductors

Abstract

Various unconventional isotope effects have been reported in high-temperature superconducting copper oxides which are beyond the scheme of BCS theory. Their origin is investigated within polaron theory which leads to a renormalization of the single particle energies and introduces a level shift here. It is found that the exponential squeezing of the second nearest neighbour hopping integral carries the correct isotope effect on the superconducting transition temperature T c , as well as the one on the penetration depth. The average superconducting gap is predicted to have an isotope effect comparable to the one on the penetration depth. The results imply that the coupling of the electronic degrees of freedom to the Jahn-Teller Q 2 -type mode is the origin of these isotope effects.High-temperature cuprate superconductors (HTSC) are one of most intensely studied systems due to the yet lacking understanding of the pairing mechanism. The antiferromagnetic properties of the undoped compounds are a consequence of the large Coulomb repulsion at the copper site. The energy scale given by it is the largest, and this has been taken as evidence that it must play a crucial role for the pairing mechanism. Consequently effects stemming from the lattice have mostly been ignored, especially in view of the fact that the isotope effect on the superconducting transition temperature T c almost vanishes at optimum doping 1,2 . The failure of BCS theory to account for many of the observed exotic properties has contributed to interpret the pairing mechanism in terms of a purely electronically driven one. However, various unexpected isotope effects have been reported 3,4,5 which are neither expected within the BCS mechanism nor within m odels based on strong correlations only. Since the Cu ion is one of the strongest Jahn-Teller systems 6 , polaron formation can take place here and be the origin of unconventional isotope effects. In spite of that the majority thought that the physics of high-temperature cuprate superconductors are dominated by a purely electronic mechanism, we address here the possibility of unconventional charge lattice coupling leading to Jahn-Teller polaron formation. We are motivated by various experimental findings as e.g. the observation of an isotope effect on the London penetration depth λ L 3,4 , the isotope dependence of the electronic energy bands 5 , the interpretation of EPR data in terms of three spin polarons 7 , the EXAFS data revealing the coexistence of different length scales 8 , the isotope effect on T c 1,2 , which exceeds the BCS value in the underdoped regime, the strain induced enhancement of T c in HTSC films 9,10 . In addition, we address the inherent inhomogeneity observed in HTSC as revealed by EXAFS 8 , STM 11 , NMR 12 , EPR 13 , which requires that a multi-component scenario has to be considered. Especially the observation of not only a d-wave order parameter but also an swave order parameter 14 is included in the modelling of HTSC.For the undoped parent compounds we start with the t -J sce...

Unified picture of the oxygen isotope effect in cuprate superconductors

“…Therefore, this model predicts that both the maximum T c and ␣ in these optimally doped cuprates are in reality related to the modification of the electronic structure through the change of tЈ eff . The crucial role of tЈ eff has been proposed (35) to be associated to the Jahn-Teller active Q 2 -type mode. Our results imply that the coupling of the electronic degrees of freedom to the Jahn-Teller Q 2 -type mode is responsible for the material dependence of the isotope effect.…”

Oxygen Isotope Effect in Cuprates Results from Polaron-induced Superconductivity

“…It quantitatively yields the correct behavior for polarons sited in the CuO 2 plane. Now the vibronic theory of Bussmann-Holder and Keller [6,11] reproduces  || n) quite well near optimum doping, see Fig. 1.…”

“…This is because the hole density present was shown to reside mainly in the planar CuO 2 [6]. Accordingly, the carrier density is mainly planar n || .…”

“…The latter comprises two electronic bands present in the cuprates, a lower t-J-type dband and a nearby, higher-lying s-band coupled by a linear vibronic term [6,11,12]. Within this model, the oxygen isotope effects on T c result from considering in-plane bands with first t 1 , second t 2 , third neighbor t 3 , and interplanar hopping integrals t 4 [6,11]. The polaronic renormalizations of the second-nearest-neighbor hopping integral t 2 and the interplanar hopping term t 4 yield the correct trend for  || (n) close to optimal doping.…”

Evidence for Polaron Formation in High-Temperature Superconducting Cuprates: Experiment and Theory

“…First, we consider the consequences arising from (2a), from which we conclude that the electronic energy bands experience a substantial renormalization [18,19,22]. By using the LDA-derived band structure for the cuprates [23], i.e.,…”