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Experimental measurements of photoresistivity under terahertz (THz) radiation in low magnetic fields at conditions of cyclotron resonance (CR) in two-dimensional electron system (2DES) of GaAs/AlGaAs nanostructures are presented and discussed. We report the experimental discovery of "CR-vanishing effect" (CRV) in GaAs/AlGaAs heterostructures with high mobility as a well-defined gap on CR-line that is independent on incident THz power. Our analysis shows that the CRV may appear in systems with well correlated state of 2D electrons such as plasma waves and others. Fundamental nature of these correlated states of electrons in 2DES is discussed. Future THz detectors utilizing the new correlated states in 2DES may expand horizons for supersensitive detection in sub-THz and THz frequencies ranges.

Materials with perovskite structure are known to exhibit fascinating physical properties such as high-temperature superconductivity, negative thermal expansion (NTE) and colossal magnetoresistance. However, transition metal trifluoride perovskites are less well studied compared to their oxide counterparts though they display marked differences such as NTE behavior in ScF3. Doping of such MF3 perovskites has been the focus of the experimental work of Morelock et al. [1] which provides a comprehensive structural study of the material class Sc1$-x$Ti$x$F₃. As shown in Fig. 1, there is a structural phase transition assumed to be tied to tilting of corner sharing octahedrons in this class of crystal structures which is believed to have an electrostatic dipolar origin, seen for example even in AlF₃ [2]. However, the insulating and magnetic properties of TiF₃ are closely related to the transition metal 3d-electrons. The extra valence $d$-electron that Ti carries compared to Sc [1, 3] gives rise to unusual electronic and magnetic properties.

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the influence of the minus sign problem on convergence. Also here in the absence of a minus sign problem we encounter convergence problems for strong interactions.

We report charge dynamics of a quantum spin-1/2 chain (SrCuO₂) over the complete Brillouin zone using the momentum tunability of inelastic X-ray scattering. Excitations at the insulating gap edge are found to be highly dispersive. Observed dispersions are consistent with charge fluctuations involving holons unique to 1-D spin-1/2 quantum systems.

We investigate momentum dependence of charge excitations across the effective Mott gap in a quasi-zero dimensional (q-ZD) model cuprate Li₂CuO₂, using high resolution inelastic X-ray scattering by working near a resonance. In comparison to quasi-one dimensional (q-1D) systems such as Sr₂CuO₃ or SrCuO₂, momentum dependence is much weaker in Li₂CuO₂. Particle-hole pair excitations at the gap edge in these low dimensional Mott systems are found to be strongly dependent on the effective dimensionality (or topology) of the lattice and the strength of electron–electron interaction.

We report momentum dependence of charge excitations across the effective Mott gap in quasi-low dimensional model cuprates with different effective dimensionalities (CuGeO₃ and SrCuO₂), using high resolution inelastic X-ray scattering by working near a resonance. Particle-hole pair excitations at the gap edge in these compounds are found to be strongly dependent on the effective dimensionality of the lattice and the strength of electron–electron Coulomb interaction.

Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high T_c cuprates is discussed.

We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction U_i is site-dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated.

The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in detail. This works as follows: starting from a completely dispersive bare band structure, the interactions quench the kinetic energy, hence the ordered phase is obtained solely by a drastic decrease of the interaction energy. Since U_i are site dependent, this determinative decrease is obtained by a redistribution of the double occupancy d_i such to attain small d_i where the on-site Coulomb repulsion U_i is high, and vice versa. The kinetic energy quench leads to the upper effective flat band, whose role is to enhance by its degeneracy the switching to the ordered phase dictated and stabilized by the interactions present. It is shown that for this phenomenon to occur, a given degree of complexity is needed for the chain, and the mechanism becomes inactive when the U_i interactions are homogeneous, or are missing from the ground state wave function.

In the correlated electron system with the pseudogap, full-gapped domains and Fermi-arced domains coexist. These domains are created by the quantum-fluctuated antiferromagnetic correlation that generates the short-ranged attractive potential to produce the Fermi arcs and the superconductivity. In the full-gapped domains, s-wave or $(d_{x^2-y^2}\pm i{d}_{xy})$-wave symmetry of the electron pairs is favored. In the Fermi-arced domains, only $d_{x^2-y^2}$-wave symmetry of pairs is stable. Superconductivity of different pairing symmetry coexists in different domains as well. Different from the Cooper pairs, the correlated electrons pair up in the real space with an energy gap. Gapless states, on the contrary, hinder the development of superconductivity.

The ground state of rare earth intermediate valence (IV) metals is that of a heavy mass Fermi liquid. The transport, optical conductivity, dHvA signals, and Q-resolved neutron spectra reflect the existence of a Fermi surface with strongly renormalized masses and a hybridization gap. On the other hand, properties such as the susceptibility, specific heat, valence and spin dynamics that are dominated by the spin fluctuations, which are highly localized, can be understood qualitatively (and sometimes quantitatively) as those of a collection of non-interacting Anderson/Kondo impurities. Anomalies exist in some compounds both in the low temperature behavior and in the rate of crossover from Fermi liquid to local moment behavior which may reflect non-universal behavior of the Anderson lattice.

Materials with perovskite structure are known to exhibit fascinating physical properties such as high-temperature superconductivity, negative thermal expansion (NTE) and colossal magnetoresistance. However, transition metal trifluoride perovskites are less well studied compared to their oxide counterparts though they display marked differences such as NTE behavior in ScF3. Doping of such MF3 perovskites has been the focus of the experimental work of Morelock et al. [1] which provides a comprehensive structural study of the material class Sc1−xTixF₃. As shown in Fig. 1, there is a structural phase transition assumed to be tied to tilting of corner sharing octahedrons in this class of crystal structures which is believed to have an electrostatic dipolar origin, seen for example even in AlF₃ [2]. However, the insulating and magnetic properties of TiF₃ are closely related to the transition metal 3d-electrons. The extra valence d-electron that Ti carries compared to Sc [1, 3] gives rise to unusual electronic and magnetic properties.

Experimental measurements of photoresistivity under terahertz (THz) radiation in low magnetic fields at conditions of cyclotron resonance (CR) in two-dimensional electron system (2DES) of GaAs/AlGaAs nanostructures are presented and discussed. We report the experimental discovery of “CR-vanishing effect” (CRV) in GaAs/AlGaAs heterostructures with high mobility as a well-defined gap on CR-line that is independent on incident THz power. Our analysis shows that the CRV may appear in systems with well correlated state of 2D electrons such as plasma waves and others. Fundamental nature of these correlated states of electrons in 2DES is discussed. Future THz detectors utilizing the new correlated states in 2DES may expand horizons for supersensitive detection in sub-THz and THz frequencies ranges.