Interplay of fluctuations, ordering phenomena, and emergent phases

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Superconductors with high transition temperature became finally relevant for applications. Yet, they are still among the top subjects hosting open scientific problems. They exhibit a variety of additional ordered states and instabilities which are similarly interesting as superconductivity itself. The major open question concerns the interrelation of these phases among each other and with superconductivity. In many cases the phase transitions are preceded by fluctuations. The concomitantly enhanced susceptibility is considered one of the potential driving forces behind the high transition temperatures to superconductivity. Yet, not even the origin and nature of the fluctuations are clear. It is the purpose of this proposal to study and understand spin, orbital, charge, and order parameter fluctuations in selected systems. The focus will be placed on the identification of the type of fluctuations and their interrelation among each other and with new phases. The basic experimental method will be inelastic (Raman) scattering of visible light as a function of photon polarization and energy, magnetic field, hydrostatic and uniaxial pressure and temperature. For identifying the physical origin of the fluctuations their symmetry properties, variation with excitation energy, temperature, pressure and field, and the spectral shape of the response will be analyzed quantitatively. The exchange of isotopes will be used to analyze the coupling of fluctuations with the lattice. It is intended to look at systems in which the fluctuations can be influenced by tuning a control parameter such as doping and pressure. Then one phase, for example magnetism, can usually be suppressed and yields to another phase. If the fluctuations of the suppressed phase survive they may be intertwined with the new phase emerging upon changing the control parameter. Materials prototypical for this interrelation are the cuprates, organic metals, heavy fermion systems or the ferro-pnictides and -chalcogenides. In all cases competing phases were observed but the existence, role and origin of fluctuations are controversial. In addition to critical fluctuations, there exist also amplitude fluctuations of the order parameter in phases with long-ranged order which are equivalent to the Higgs modes in field theory. These amplitude fluctuations may have a strong influence on the spectral properties of spin and superconducting gap excitations. It is planned to study the line shapes of spin excitations for various incident photon energies. This enables one to disentangle the influence of amplitude fluctuations and multi-magnon excitations and derive the generic line shape and the coupling parameters. Similarly, the amplitude mode in a superconductor leaves a fingerprint of Cooper pairing. It is expected that important open questions such as the origin and interrelation of critical fluctuations with other phases and the derivation of the microscopic parameters can be addressed and answered.