Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical and that do not have a simple description in terms of weakly interacting quasiparticles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by 19 orders of magnitude in temperature, but were shown to exhibit very similar hydrodynamic flows. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio, which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection

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Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality

Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands give rise to strongly correlated phenomena and are associated with unconventio...

Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes

Explicit and implicit experimental evidence for charge density wave (CDW) presence in high- superconducting oxides is analyzed. The theory of CDW superconductors is presented. It is shown
that the observed pseudogaps and dip-hump structures in tunnel and photoemission spectra are
manifestations of the same CDW gapping of the quasiparticle density of states. Huge pseudogaps
are transformed into modest dip-hump structures at low temperatures, , when the electron spectrum superconducting gapping dominates. Heat capacity jumps at the superconducting critical temperature and the paramagnetic limit are calculated for CDW superconductors. For a certain
range of parameters, the CDW state in a -wave superconductor becomes reentrant with , the main control quantity being a portion of dielectrcally gapped Fermi surface. It is shown that in
the weak-coupling approximation, the ratio between the superconducting gap at zero temperature
 and has the Bardeen-Cooper-Schrieffer value for -wave Cooper pairing and exceeds
the corresponding value for -wave pairing of CDW superconductors. Thus, large experimentally
found values are easily reproduced with reasonable input parameter values of
the model. The conclusion is made that CDWs play a significant role in cuprate superconductivity.

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Competition of Superconductivity and Charge Density Waves in Cuprates: Recent Evidence and Interpretation

The spectral function of a one-dimensional Holstein polaron

Being a giant bulk Rashba semiconductor, the ambient-pressure phase of BiTeI was predicted to transform into a topological insulator under pressure at 1.7-4.1 GPa [Nat. Commun. 2012, 3, 679]. Because the structure governs the new quantum state of matter, it is essential to establish the high-pressure phase transitions and structures of BiTeI for better understanding its topological nature. Here, we report a joint theoretical and experimental study up to 30 GPa to uncover two orthorhombic high-pressure phases of Pnma and P4/nmm structures named phases II and III, respectively. Phases II (stable at 8.8-18.9 GPa) and III (stable at >18.9 GPa) were first predicted by our first-principles structure prediction calculations based on the calypso method and subsequently confirmed by our high-pressure powder X-ray diffraction experiment. Phase II can be regarded as a partially ionic structure, consisting of positively charged (BiTe)(+) ladders and negatively charged I- ions. Phase III is a typical ionic structure characterized by interconnected cubic building blocks of Te-Bi-I stacking. Application of pressures up to 30 GPa tuned effectively the electronic properties of BiTeI from a topological insulator to a normal semiconductor and eventually a metal having a potential of superconductivity.

High-Pressure Phase Transitions and Structures of Topological Insulator BiTel

On the basis of well established experimental results we propose a picture for high- T c superconductivity in which two types of charge carriers play a role: (1) localized bosons in the form of tightly bound electron pairs of polaronic origin and (2) fermions in the form of itinerant valence electrons. The level of the bosons is supposed to fall inside the band of fermions and due to a boson a-fermion pair-exchange coupling the intrinsically localized bosons can condense and simultaneously induce a BCS-like superconductivity in the fermionic subsystem. We study the doping dependence for this model for such quantities as the critical temperature, the BCS-like gap in the single-particle excitation spectrum of the fermions, the penetration depth and the plasma frequency and compare these results with experiment.

The boson-fermion model of high-Tc superconductivity. Doping dependence

The normal and anomalous one-particle Green's functions are derived for a system with strong electron-phonon coupling. The collapse of the electron band and the phonon vacuum is studied within the mean-field approximation. We derive the angle-resolved photoemission spectrum for such a system of small polarons in the normal and in a BCS-like superconducting state. The polaronic features of the charge carriers are manifest in a superposition of (1) a rather well-defined peak corresponding to the coherent part of the heavily dressed electron in a polaronic state and (2) a broad featureless spectrum which is practically momentum independent. In the limit of strong coupling, such that the polaronic band width is smaller than the characteristic phonon frequency, an oscillatory structure is superposed onto this featureless incoherent background. Upon going from the normal to the superconducting state we predict a shift downwards of the coherent part of the spectrum accompanied by a change in intensity. The shape of the incoherent part is roughly the same in the normal and superconducting states but its intensity is increased in the latter. We compare these predictions with the experimental results of certain high- T c superconducting materials.

Photoemission spectroscopu of the superconducting and normal state for polaronic systems

In high T c materials electrons on the whole are only weakly coupled to the phonons except for a few specific local modes. The latter gives rise to the formation of polaronic charge carriers on specific molecular centers in those materials. There is considerable experimental evidence for their existence in form of localized states and we conjecture that localized bi-polaronic states lie inside the valence band of itinerant electrons. With increased doping this valence band is gradually being emptied out, eventually resulting in a situation where the chemical potential coincides with the level of the bi-polaronic state. At this point an insulator→metal transition is triggered off and due to hybridization between the localized bi-polarons and the itinerant electrons the initially localized bi-polaronic states acquire itinerant upon lowering the temperature; eventually undergoing a transition to a superfluid state at a critical temperature T c . A characteristic feature of this scenario of an hybridized Boson-Fermion mixture is the pinning of the chemical potential at the Bosonic (bi-polaronic) level which only weakly depends on doping in the fully developed metallic regime. T c is then essentially controlled by the number of Bosons which does depend on doping and leads to the known universal behaviour of T c as a function of Boson concentration and mass.

The polaron scenario for high Tc superconductivity

The spin as well as charge pseudogap features in the high T c cuprate can be traced back to the dynamical properties on small clusters (consisting of Cu ions together with their ligand O ions environments) which make up the overall structure of these materials. These ligand complexes being deformable, causes the itinerant electrons on the Cu ions to enter into resonating bipolaron states via binary collision processes, similar to the Feshbach resonance in ultra-cold fermionic gases. We illustrate such resonant pairing on an isolated cluster and discuss how, upon coupling together such clusters, the local physics evolves into global macroscopic features, such as lattice mediated driven superconducting, respectively insulating, states of such resonating bipolarons.

Resonating bipolaron driven pseudogap phase

In the framework of a scenario consisting of a mixture of itinerant electrons and localized bipolarons, hybridized with each other via a charge exchange term, we discuss the evolution of certain physical features of the pseudogap phase as the temperature decreases from T ∗ to T c . This evolution can be characterized by the presence of purely diffusive electron-pairs just below T ∗ , their becoming itinerant below a certain temperature T B ∗ and their ultimate condensation into a superconducting state at T c . An onset of a Drude component in the optical conductivity and imperfect Meissner screening in the temperature interval [ T c , T B ∗ ] are manifestations of that.

J. Ranninger

Papers

The boson-fermion model of high-Tc superconductivity. Doping dependence

Photoemission spectroscopu of the superconducting and normal state for polaronic systems

The polaron scenario for high Tc superconductivity

Resonating bipolaron driven pseudogap phase

Theory of normal state single particle and transport properties