Complexity in correlated electron materials

In a much cited paper, Dagotto [22] discusses the concept of complexity in connection with correlated electron materials. The essential point is that the competition between the charge-spin-orbital-lattice degrees of freedom can lead to the coexistence of different phases which are vir tually degenerate in energy, and hence to inhomogeneities and glassy dynamics on a wide range of length and time scales.
A hallmark of such “complex matter”, which exists “at the edge of chaos”, is a non-linear “giant” response to a small per turbation. For example, charge transpor t in manganite TMOs is different from that in simple metals: an isolated charge may strongly perturb its local environment, inducing the creation of a polaron, which may then attract other polarons to form larger, long-range structures. The manganite phase diagram was shown in Figure V.4 a, with the close juxtaposition of ferromagnetic metal (FM) and antiferromagnetic insulator (AFI) phases. The complexity view of the magnetic-field-induced metal-insulator transition in this material is that a ground state exists with quenched disorder, arising perhaps from lattice distor tion accompanying chemical doping (see Fig. V.19 a), with a glassy intermixture of FM and AFI phases (see Fig. V.19 b). A small applied magnetic field is then sufficient to tip the energy balance in favor of the FM phase, causing a giant, percolative change in the bulk conductivity. Also the cuprate superconductors show a variety of nanoscale inhomogenieties (see Fig. V.20), including the charge-spin stripes mentioned at the beginning of this Chapter (see Fig. V.5 b). Although the impor tance of stripes to the mechanism of high-temperature superconductivity is in question, also these materials appear to exhibit a giant response: A S–N–S (superconductor – normal conductor – superconductor) junction made of cuprate materials, whose N-layer thickness exceeds 100 coherence lengths, behaves as if it were a S-S Josephson junction, implying that the presence of neighboring superconducting material tips the balance in the thick Nlayer to superconducting behavior [22]. In his paper, Dagotto draws parallels between correlatedelectron materials and other forms of complex matter, such as polymers, liquid crystals and even bio-material. Just as groups of atoms in these soft materials form local solid patterns (i.e., molecules), which, when considered globally, exhibit complex, fluid behavior, so can, for example, Jahn-Teller-ordered regions in manganites lead to a complex electron liquid-crystal behavior, intermediate between an electron solid and an electron liquid. The analogy with biochemical systems (see Chapter IV) is striking: a large number of nearly degenerate states, with the corresponding entropic barriers, move on a rugged energy landscape. But a peculiarity of the electron- based complexity is that it is inherently quantummechanical [22]. The impor tance of the SwissFEL for investigating the spatial and temporal characteristics of such complex electron matter is twofold. Despite decades of work by a generation of scientists, a theoretical understanding of these materials is lacking. Fundamental approaches, like the Hubbard model (see Infobox), may be close to explaining microscopic features, such as the superconducting pairing mechanism, but they reach their limits when considering long-range interactions such as Coulomb and electron-lattice effects. Time-resolved structural and spectroscopic information from the SwissFEL may provide the experimental foundation for a new level of description of these materials, connecting microscospic mechanisms with macroscopic phenomenology, in the form of large-scale, numerical simulations. The second major SwissFEL contribution could be the development of practical applications of these fascinating materials: particularly relevant are dynamic effects such as non-linear switching between states of high and low conductivity, the coupling of magnetic and electric effects in the so-called “multiferroics” (see Infobox), dielectric effects in relaxor ferroelectrics and the development of oxide electronics, including TMO field-effect transistors and novel spintronic devices.