No Arabic abstract
The idea of exciton condensation in solids was introduced in 1960s with the analogy to superconductivity in mind. While exciton supercurrents have been realized only in artificial quantum-well structures so far, the application of the concept of excitonic condensation to bulk solids leads to a rich spectrum of thermodynamic phases with diverse physical properties. In this review we discuss recent developments in the theory of exciton condensation in systems described by Hubbard-type models. In particular, we focus on the connections to their various strong-coupling limits that have been studied in other contexts, e.g., cold atoms physics. One of our goals is to provide a dictionary which would allow the reader to efficiently combine results obtained in these different fields.
We use a combination of dynamical mean-field model calculations and LDA+U material specific calculations to investigate the low temperature phase transition in the compounds from the (Pr$_{1-y}$R$_y$)$_x$Ca$_{1-x}$CoO$_3$ (R=Nd, Sm, Eu, Gd, Tb, Y) family (PCCO). The transition, marked by a sharp peak in the specific heat, leads to an exponential increase of dc resistivity and a drop of the magnetic susceptibility, but no order parameter has been identified yet. We show that condensation of spin-triplet, atomic-size excitons provides a consistent explanation of the observed physics. In particular, it explains the exchange splitting on the Pr sites and the simultaneous Pr valence transition. The excitonic condensation in PCCO is an example of a general behavior expected in certain systems in the proximity of a spin-state transition.
Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we show how the fermion sign problem can be solved completely with meron-cluster methods in a large class of models of strongly correlated electron systems, some of which are in the extended Hubbard model family and show s-wave superconductivity. In these models we also find that on-site repulsion can even coexist with a weak chemical potential without introducing sign problems. We argue that since these models can be simulated efficiently using cluster algorithms they are ideal for studying many of the interesting phenomena in strongly correlated electron systems.
The properties of condensed matter are determined by single-particle and collective excitations and their interactions. These quantum-mechanical excitations are characterized by an energy E and a momentum hbar k which are related through their dispersion E_k. The coupling of two excitations may lead to abrupt changes (kinks) in the slope of the dispersion. Such kinks thus carry important information about interactions in a many-body system. For example, kinks detected at 40-70 meV below the Fermi level in the electronic dispersion of high-temperature superconductors are taken as evidence for phonon or spin-fluctuation based pairing mechanisms. Kinks in the electronic dispersion at binding energies ranging from 30 to 800 meV are also found in various other metals posing questions about their origins. Here we report a novel, purely electronic mechanism yielding kinks in the electron dispersions. It applies to strongly correlated metals whose spectral function shows well separated Hubbard subbands and central peak as, for example, in transition metal-oxides. The position of the kinks and the energy range of validity of Fermi-liquid (FL) theory is determined solely by the FL renormalization factor and the bare, uncorrelated band structure. Angle-resolved photoemission spectroscopy (ARPES) experiments at binding energies outside the FL regime can thus provide new, previously unexpected information about strongly correlated electronic systems.
Excitonic insulator is a coherent electronic phase that results from the formation of a macroscopic population of bound particle-hole pairs - excitons. With only a few candidate materials known, the collective excitonic behavior is challenging to observe, being obscured by crystalline lattice effects. Here we use polarization-resolved Raman spectroscopy to reveal the quadrupolar excitonic mode in the candidate zero-gap semiconductor Ta$_2$NiSe$_5$ disentangling it from the lattice phonons. The excitonic mode pronouncedly softens close to the phase transition, showing its electronic character, while its coupling to non-critical lattice modes is shown to enhance the transition temperature. On cooling, we observe the gradual emergence of coherent superpositions of band states at the correlated insulator gap edge, with strong departures from mean-field theory predictions. Our results demonstrate the realization of a strongly correlated excitonic state in an equilibrium bulk material.
We discuss the problem of a possible violation of the optical sum rule in the normal (non superconducting) state of strongly correlated electronic systems, using our recently proposed DMFT+Sigma approach, applied to two typical models: the hot - spot model of the pseudogap state and disordered Anderson - Hubbard model. We explicitly demonstrate that the general Kubo single band sum rule is satisfied for both models. However, the optical integral itself is in general dependent on temperature and characteristic parameters, such as pseudogap width, correlation strength and disorder scattering, leading to effective violation of the optical sum rule, which may be observed in the experiments.