It is known that strong electron-phonon interactions can lead to the formation of lattice polarons (quasiparticles dressed by lattice distortions) as a result of the breakdown of the Migdal approximation. In the colossal magnetoresistive (CMR) manganites, such quasiparticles are expected to exist. A direct and clear-cut experimental technique for demonstrating the existence of such quasiparticles in manganites is an observation of a giant oxygen isotope shift of the ferromagnetic transition temperature (see Fig. 1) [1]. Such a novel isotope effect had never been observed before 1996 because conventional theories of magnetism do not predict this isotope effect. This important pioneering work not only shows that the nature of charge carriers in manganites is of polaronic type, but also establishes a powerful experimental technique to determine the strength of electron-phonon coupling and the nature of charge carriers in strongly correlated oxide systems. Following this original work, I have extensively studied various oxygen isotope effects in manganites using different experimental techniques and found many novel oxygen isotope effects in this system [2-4]. In particular, the observed isotope effects on the transport properties in high-quality thin films [3-4] provide crucial and quantitative experimental constraints on the physics of manganites and the microscopic origin of colossal magnetoresistance.

Fig. 1 Temperature dependence of the normalized magnetization of the ¹⁶O and ¹⁸O isotope samples of La_0.80Ca_0.20MnO_3+y. The Curie temperature shifts down by 21 K upon replacing ¹⁶O with ¹⁸O isotope. This giant oxygen-isotope shift of the Curie temperature had never been observed nor expected from conventional theories of ferromagnetism before 1996. After [1].

Fig. 2. The -d²I/dV²-like tunneling spectrum for a slightly over-doped YBa₂Cu₃O₇ (YBCO) crystal (left scale) together with the phonon density of states obtained from inelastic neutron scattering (right scale). The vertical dashed lines mark peak and/or shoulder features in the -d²I/dV²-like spectrum. If strong coupling to phonon modes happens in YBCO, then the peak and/or shoulder features in the -d²I/dV²-like tunneling spectrum should line up with the peak and/or shoulder features in the phonon density of states as well. Indeed, nearly all 13 peak and/or shoulder features in -d²I/dV²-like spectrum match precisely with those in the phonon density of states. The strong coupling features at 7.1 and 90.8 meV in -d²I/dV²-like spectrum cannot compare with these neutron data since the energy positions of these features are outside the energy range of the neutron data. Nevertheless, the phonon peak at about 6.8 meV is clearly seen in the high-resolution neutron data of Bi₂Sr₂CaCu₂O_8+y (BSCCO). The feature at 90.8 meV should be the composite phonon energy of 7.1 and 83.7 meV since the sum of 7.1 and 83.7 meV is equal to 90.8 meV. This is expected from the conventional strong-coupling theory. Such excellent agreement between neutron and tunneling data provides clear evidence that the bosonic modes mediating the electron pairing are phonons and that the tunneling current of this junction is highly directional. After [16].

Although various unconventional isotope effects we have observed over last ten years have provided direct and compelling evidence for strong electron-phonon interactions and the existence of polarons or bipolarons (the breakdown of the Migdel approximation) in cuprate superconductors, the role of electron-phonon coupling in the pairing mechanism of high-temperature superconductivity has been generally ignored. Only after 2001, have three Nature papers by a Stanford group [12], a UC-Berkeley group [13], and a Cornell group [14] also shown evidence for strong electron-phonon coupling in cuprates from angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). These experiments show strong coupling to the high-energy phonon modes. The recent optical experiments by a UCSB group [15] also disprove magnetic origin of a bosonic mode mediating the pairing and they thus attribute this mode to a phonon mode. My recent theoretical studies of the pairing interactions and gap symmetry in cuprates have provided compelling evidence for predominantly phonon-mediated pairing (see Fig. 2) [16] and extended s-wave gap symmetry with eight line nodes (see Fig. 3) [17]. In particular, I show that low-energy phonon modes couple very strongly to doped holes and may play a dominant role in the electron pairing. I have also shown that high-temperature superconductivity in both cuprates and bismuthates arises from Cooper pairing of polaronic charge carriers [9-11,18].

Fig. 3 The high-resolution spectra of the second derivative -d²ReS/dw² of the real part of electron self-energy S along the diagonal direction (right scale) and the -d²/dV²-like tunneling spectrum for a slightly over-doped Bi₂Sr₂CaCu₂O_8+y (BSCCO) crystal (left scale), Here w = E_F−E−D_D and D_D is the diagonal superconducting gap. If we assign D_D =7.0 meV for the superconducting BSCCO, the peak features in -d²ReS/dw² match precisely with in the tunneling spectrum and those in the phonon density of states. This result rules out seemingly well accepted d-wave gap symmetry and strongly supports an extended s-wave gap symmetry with eight line nodes. After [17].

For manganites, the CMR mechanism is still not clear although it is generally accepted that the electron-phonon interaction plays an essential role in the physics of this system. Further, the very nature of charge carriers in the ferromagnetic state has not been clarified. Recently, we have shown theoretically and experimentally that the low temperature metallic state of doped manganites is not a conventional Fermi-liquid but has polaronic nature. Even in the paramagnetic state, the nature of charge carriers is still under intensive debate. Some theorists believe small polarons are the charge carriers in the paramagnetic state and the others favor small bipolarons. There are few experiments that can clearly distinguish between small polarons and bipolarons because they behave similarly in most physical properties. Studies of the oxygen-isotope effects on electrical and magnetic properties may provide essential constraints on the nature of charge carriers in the paramagnetic state. Another important issue to be clarified is the microscopic origin of the intrinsic electronic inhomogeneity in some doped manganites. The electronic inhomogeneity may be one of the key ingredients to understand the microscopic mechanism of CMR.