Jozef Spałek

Selected universal experimental properties of high temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single band of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called $t$-$J$-$U$ model). The model rationale is provided by estimating its macroscopic parameters on the basis of the 3-band approach for the Cu-O plane. We use our original full Gutzwiller-wave-function solution by going beyond the renormalized mean field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping ($\delta$) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically $\delta$-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave-vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in the experiment and reproduced within our approach. An assessment of the currently used models is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of introduced higher order contributions.

Superconductivity in heavy-fermion systems has an unconventional nature and is considered to originate from the universal features of the electronic structure. Here, the Anderson lattice model is studied by means of the full variational Gutzwiller wave function incorporating nonlocal effects of the on-site interaction. We show that the $d$-wave superconducting ground state can be driven solely by interelectronic correlations. The proposed microscopic mechanism leads to a multigap superconductivity with the dominant contribution due to $f$ electrons and in the $d_{x^2-y^2}$-wave channel. Our results rationalize several important observations for ${\mathrm{CeCoIn}}_5$.

We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the~interelectronic interactions can be evaluated exactly. The system has been selected due to its tunability, i.e., its electron wave functions can be modified much easier than in, e.g., quantum dots. We determine many-particle states for $N_e=2$ and $3$ electrons and calculate the 3- and 4-state interaction parameters, and discuss their importance. For that purpose, we combine the first- and second-quantization schemes and hence are able to single out the component single-particle contributions to the resultant many-particle state. The method provides both the ground- and the first-excited-state energies, as the exact diagonalization of the many-particle Hamiltonian is carried out. DRN provides one of the few examples for which one can determine theoretically all interaction microscopic parameters to a high accuracy. Thus the evolution of the single-particle vs. many-particle contributions to each state and its energy can be determined and tested with the increasing system size. In this manner, we contribute to the wave-function engineering with the~interactions included for those few-electron systems.

We obtain in a direct and rigorous manner a transition from a stable molecular hydrogen $nH_2$ single chain to the quasiatomic two-chain $2nH$ state. We devise an original method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double-counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains possible to tackle, $n=3\div6$. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio $U/W$ reflects the Mott--Hubbard-transition aspect of the atomization. Universal feature of the transition relation to the Mott criterion for the insulator--metal transition is also noted. The role of the electron correlations is thus shown to be of fundamental significance.

We obtain in a direct and rigorous manner a transition from a stable molecular-hydrogen $n{\text{H}}_2$ single chain to the quasiatomic two-chain $2n\text{H}$ state. We devise a method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains that are possible to tackle, $n=3–6$. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio $U/W$ reflects the Mott-Hubbard transition aspect of atomization. A universal feature of the transition relation to the Mott criterion for the insulator-metal transition is also noted. The role of electron correlations is thus shown to be of fundamental significance in this case. The long-range nature of Coulomb interactions is included.

The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow $f$ band originating from atomic $f$-electron states and subsequently interpret this behavior as a direct itineracy of $f$ electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow $f$ band rationalizes the common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of ${\mathrm{CeCoIn}}_5$. Moreover, it is shown that the emerging $f$-electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for $4f$- or $5f$-electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$-state half filling, $\langle {\widehat{n}}_f\rangle \to 1$. The nonstandard features of the emerging correlated quantum liquid state are stressed.

The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM). This approach allows for a systematic evaluation of the expectation values with GWF in the finite dimensional systems. It introduces results extending in an essential manner those obtained by means of standard Gutzwiller Approximation (GA) scheme which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss principal paramagnetic properties of ALM and their relevance to heavy fermion systems. We demonstrate the formation of an effective, narrow $f$-band originating from atomic $f$-electron states and subsequently interpret this behavior as a mutual intersite $f$-electron coherence; a combined effect of both the hybridization and the Coulomb repulsion. Such feature is absent on the level of GA which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow effective $f$-band rationalizes common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of CeCoIn$_5$. Moreover, we show that the emerging $f$-electron coherence leads in a natural manner to three physically distinct regimes within a single model, that are frequently discussed for 4$f$- or 5$f$- electron compounds as separate model situations. We identify these regimes as: (i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii) Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$ electrons half-filling, $\langle\hat n_{f}\rangle\rightarrow1$. The non-Landau features of emerging correlated quantum liquid state are stressed.

An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, $(H_{2})_{n}$ chain is considered with the long-range electron-electron interactions taken into account. The implemented procedure covers: (i) single-particle Wannier wave-function basis construction in the correlated state, (ii) microscopic parameters calculation, and (iii) ground state energy optimization. The optimization loop is based on highly effective process-pool solution - specific root-workers approach. The hierarchical, two-level parallelism was applied: both shared (by use of Open Multi-Processing) and distributed (by use of Message Passing Interface) memory models were utilized. We discuss in detail the feature that such approach results in a substantial increase of the calculation speed reaching factor of $300$ for the fully parallelized solution.

We show that the Fulde-Ferrell (FF) phase may appear as a sole result of the orbital effect in a cylindrical metallic nanowire. Namely, in the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number $m$ is lifted, which leads to a Fermi wave vector mismatch between the subbands with opposite orbital momenta in the paired state. This mismatch can be compensated by the nonzero total momentum of the Cooper pairs created by electrons from the split subbands which results in the formation of the FF phase. In this manner, a transformation of the orbital motion into a linear supercurrent parallel to the applied field is taking place. With the increasing magnetic field a series of FF stability regions appear, in between which the standard BCS superconducting phase is stable. For the sake of completeness, we show, that the inclusion of the Zeeman term in the model does not change the picture qualitatively, particularly if larger $m$ states contribute essentially to the Fermi-surface splitting. A brief but important note concerning the possibility of steering the supercurrent by an applied magnetic field parallel to it, is also provided.