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Józef Spałek

Publications and source records attributed to Józef Spałek.

At least 19 recordsLinked to original sources
arXiv2026

Correlation-assisted topological and metamagnetic transitions in Rashba-coupled superconductors: $t$-$J$-$U$ model study

Unconventional superconductivity commonly emerges in systems characterized by strong electronic correlations, with layered copper-oxides serving as a canonical example. Observation of spin-momentum locking within Bi-family of the cuprates, compatible with the presence of non-negligible Rashba-type spin-orbit coupling (RSOC), calls for an investigation of the joint effects of electronic correlations and RSOC on pairing in copper-oxide and related superconductors. Employing statistically-consistent variational approximation (SGA), we carry out such an analysis by constructing the phase diagram for the case of square-lattice \textit{t-J-U} model incorporating RSOC. We also investigate the effects of time-reversal-symmetry breaking by Zeeman field, as well as characterize emergent topological superconducting (TSC) states. Chern number $C = \pm 4$ TSC is found in a broad regime of on-site Coulomb repulsion close to half-filling. The latter is not governed by correlations and emerges also within the weak-coupling Bogoliubov-de Gennes (BdG) scheme. Yet, we identify a distinct $C = \pm 2$ TSC state that is driven specifically by electronic correlations via a topological transition occurring with no bulk quasiparticle gap closure, and is accompanied by discontinuous metamagnetic and Lifshitz transitions. Moreover, a qualitatively distinct doping evolution of the $d$- and $p$-wave components of the underlying mixed-parity SC order parameter above the metal-to-insulator transition is demonstrated. Our work points toward the relevance of joint correlation and RSOC effects beyond BdG scheme to phase diagrams of RSOC-coupled superconductors.

cond-mat.str-el↗
arXiv2026

t-J model at 50

I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three--orbital situation. The main purpose is to list some basic features of the physics associated with t--J model.

cond-mat.str-el↗
arXiv2026

Strongly correlated quantum matter: t--J model, real-space pairing, spin-dependent masses, and atomicity in chemical bond and nanosystems

I critically overview my research on strongly correlated fermion systems for almost five decades. It concentrated on: (i) the first derivation of what is now called the t--J model, comprising both the limit of Anderson kinetic exchange of spin--spin interaction in the Mott--Hubbard insulator and taking into account real-space pairing, subsequently applied to high-temperature superconductivity; (ii) the concept of spin-dependent heavy mass of quasiparticles in heavy-fermion systems, and (iii) the first nontrivial model of statistical thermodynamics of the Mott--Hubbard transition. Those three features, together with the specific quantum critical phenomena provide, in my view, fundamental components of the theory of strongly correlated fermions established in the 1960s. Some related questions such as introduction of atomicity in the chemical bonding (iv), and specific properties of correlated nanosystems within the rigorous EDABI (v) approach are also briefly elaborated at the end.

cond-mat.str-el↗
arXiv2026

A nonstandard statistics for strongly correlated systems: Two simple examples

We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, $i.e.$, that of fermions with exclusion of doubly occupancy of quasimomentum states $\{\bf k\}$ with opposite spins ($\uparrow\downarrow$). The second is that of statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_B T/|t|$, where $t<0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ($n\to1$). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.

cond-mat.str-el↗
arXiv2024

Tuning topological superconductivity within the $t$-$J$-$U$ model of twisted bilayer cuprates

We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBC) as a function of electron density and layer twist angle. The bilayer $t$-$J$-$U$ model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically-consistent Gutzwiller formulation. The constructed phase diagram encompasses both gapless $d$-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped $d+\mathrm{e}^{iφ}d$ phase that breaks spontaneously time-reversal-symmetry (TRS) and is characterized by nontrivial Chern number. We find that $d+\mathrm{e}^{iφ}d$ state occupies a non-convex butterfly-shaped region in the doping vs. twist-angle plane, and demonstrate the presence of previously unreported reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from $45^\circ$. Our analysis of the microscopically derived Landau free energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.

cond-mat.supr-con↗
arXiv2024

Role of Kinetic Exchange and Coulomb Interaction in Bonding of Hydrogen Molecular Systems and Excited States

We present a detailed investigation of the electronic structure and bonding characteristics of hydrogen-based molecular systems (\ch{H2+}, \ch{H2}, \ch{H2-}) using the Exact Diagonalization Ab Initio (EDABI) approach within the framework of combined first- and second-quantization. By analyzing the relative contributions of kinetic exchange and effective Coulomb interactions, we provide a comprehensive understanding of covalency, atomicity, and ionicity as a function of interatomic distances. Our approach leverages exact solutions of the extended Heitler-London model to quantify these interactions, extending the analysis to the discussion of properties of excited states and the dissociation limit to these molecules. The findings reveal significant differences in bonding characteristics, particularly highlighting the stability and bonding nature of the neutral \ch{H2} molecule compared to its ionic counterparts. This study not only enhances an understanding of molecular interactions in hydrogen systems but also demonstrates the potential of the EDABI approach in developing more accurate computational models in quantum chemistry.

physics.chem-ph↗
arXiv2024

Exact Entanglement correlation complements the chemical bond description

We analyze the properties of the exact solution obtained by us recently for the extended Hetiler-London model for chemical bonding which has an analytic form. The emphasis is put on defining two-particle entanglement correlation as the complementary characterization of the chemical bond and relating it to the partial atomicity and the so-called true covalency. The newly introduced characteristics remove the deficiency of the standard definition of covalency which now vanishes in the limit of the separated atoms. In effect, a gradual evolution of the system of two indistinguishable electrons in a bound state into their distinguishable correspondents can be traced systematically. The present analysis has a universal meaning and may also be applied to more complex systems.

cond-mat.str-el↗
arXiv2023

High Temperature Superconductivity with Strong Correlations and Disorder: Possible Relevance to Cu-doped Apatite

We examine the properties of topological strongly correlated superconductor with bond disorder on triangular lattice and demonstrate that our theoretical ($t$-$J$-$U$) model exhibits some unique features of the Cu-doped apatite $\mathrm{Pb_{10-\mathit{x}}Cu_\mathit{x}(PO_4)_{6}O}$. Namely, the paired state appears only for carrier concentration $0.8 \lesssim n < 1$ per Cu and is followed by a close-by phase separation into the superconducting and Mott insulating parts. Furthermore, a moderate amount of the bond disorder ($Δt / t \lesssim 20 \%$) does not alter essentially the topology with robust Chern number $C=2$ which diminishes beyond that limit. A room-temperature superconductivity is attainable only for the exchange to hopping ratio $J/|t| \ge 1$ if one takes the bare bandwidth suggested by current DFT calculations. The admixture of $s$-wave pairing component is induced by the disorder. The results have been obtained within statistically consistent variational approximation (SGA).

cond-mat.supr-con↗
arXiv2023

Non-Fermi liquid behavior of doped Kondo insulator: The unique properties of CeRhSb$_{1-x}$Te$_x$

It follows from our analysis of CeRhSb that the formation of Kondo insulator state due to the presence of the collective spin singlet state is strongly reduced by its doping with various dopants when their amount exceeds 8--10\%, regardless of whether they are substituted for Ce, Rh or Sb. A wide variety of experimental results (electrical resistivity $ρ$, magnetic susceptibility $χ$, specific heat $C$, x-ray photoelectron spectroscopy) and theoretical investigations have convincingly demonstrated the proposed earlier scaling law $χ\timesρ=const.$ in the Kondo insulator regime, which is universal for all known Kondo insulators. We also analyze the properties of the Griffiths--phase for CeRhSb when Pd substitutes Rh, or Sb is fractionally replaced by Te and Sn, whereas doping of Ce with La leads to the formation of magnetic cluster structure as a result of the Kondo hole effect. Magnetoresistance of CeRhSb and CeRhSb$_{0.98}$Te$_{0.02}$ as a function of the field $B$ shows a $-B^2$ behavior, which provides evidence for the topologically nontrivial nature of these compounds, as was previously predicted theoretically for CeRhSb on the basis on the band structure calculations.

cond-mat.str-el↗
arXiv2023

Interparticle correlations and chemical bonding from physical side: Covalency $\textit{versus}$ atomicity and ionicity

In this Chapter we reexamine the concept of $\textit{covalency}$ and $\textit{ionicity}$ on example of the simplest molecules. First, starting from the exact expression for the two-particle wave function in the case of $H_2$ molecule within the Heitler-London model, we demonstrate an unphysical behavior of the covalency at large interatomic distance which, within standard definition, reaches the maximal value in the limit of separated atoms. Second, we correct this deficiency by introducing the concept of $\textit{atomicity}$, with the help of which, we define the $\textit{true}$ (intrinsic) $\textit{covalency}$, as well as retain the precise concept of $\textit{ionicity}$. We connect the introduced atomicity to the onset of Mott-Hubbard localization, adopted here from the well established notion in the condensed matter. The evolution from the molecular to atomic states develops rapidly with interatomic distance beyond the localization threshold. This brief overview is intented as pedagogical in nature, nonetheless is analyzed quantitatively for the case of $H_2$ molecule. At the end, we outline a similar-type of model for the related case of the hydrogen bond on example of adenine-tymine pair. Methodologically, the approach is based on combining the first- (wave mechanics) and second-quantization into a single scheme of formal description.

physics.chem-ph↗
arXiv2022

A brief perspective of high temperature superconductivity in the cuprates: Strong correlations combined with superexchange match experiment

High temperature superconductivity encompasses the cuprates, nickelates, iron pnictides, and LaH$_x$ compounds. The first three groups of compounds involve in the pairing electrons, which are strongly to moderately correlated, whereas in the last class of systems specific phonon excitations. In this overview we concentrate first on the (semi)quantitative theory of high T$_{C}$ superconductivity in the cuprates based on our original vibrational approach beyond the renormalized mean field theory. The model we explore mainly is $t$-$J$-$U$ model containing both the superexchange (kinetic energy) combined with strong interelectronic correlations. Selected equilibrium and dynamic-excitation properties are analyzed briefly. General questions regarding the pseudogap and two--dimensional character of those systems are raised.

cond-mat.str-el↗
arXiv2022

Degree of atomicity in the chemical bonding: Why to return to the H2 molecule?

We analyze two-particle binding factors for the case of \ch{H2} molecule with the help of our original Exact Diagonalization \textit{Ab Intio} (EDABI) approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed and the concept of \textit{atomicity} is introduced and corresponds to the Mott and Hubbard criteria concerning the localization in many-particle systems. This additional characteristic introduces atomic ingredient into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, as well as provides a physical reinterpretation of the chemical bond's nature.

physics.atm-clus↗
arXiv2022

Towards Complementary Characterization of the Chemical Bond

A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of \ch{H2} molecule. This is achieved by starting from analytic form for the two--particle wave function for electrons forming the bond, in which we single out the atomic contribution (\textit{atomicity}) in an unequivocal manner. The presence the of atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atomic correspondant is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (\textit{Mottness}) to the intrinsic covalency and ionicity is established. This goal is achieved by combining the single--particle wave function readjustment with a simultaneous determination of two--particle states in the particle (second--quantization) representation.

cond-mat.str-el↗
arXiv2022

Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory

In this review, we single out selected universal features of high-$T_c$ and related systems, which can be compared with experiment. We start with the concept of real-space pairing, combined with strong correlations. The discussion of concrete properties relies on variational approach, based on renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and Diagrammatic Expansion of the Variational Wave Function (DE-GWF). Two energy scales appear, one involving quasiparticles close to the Fermi energy, and the other reflecting the correlated state. Those two regimes are separated by a kink in the dispersion relation, observed in photoemission. One obtains both the doping dependent properties and renormalized quasiparticles. The reviewed ground-state characteristics for high-$T_c$ systems encompass superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state, all in quantitative manner. Calculated dynamic properties are: universal Fermi velocity, Fermi wave-vector, effective mass enhancement, pseudogap, and $d$-wave gap magnitude. The minimal realistic model is represented by the $t$-$J$-$U$ Hamiltonian. Inadequacy of the $t$-$J$ and Hubbard models is discussed. For heavy fermion systems we summarize superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. We overview also coexistent ferromagnetic (spin-triplet) superconducting phases observed for $\mathrm{UGe_2}$. Finally, we extend our scheme to collective spin and charge fluctuations in high-$T_c$ systems, starting from variational approach, combined with $1/N$ expansion (beyond random phase approximation). Spectrum of collective spin and charge excitations is determined for the Hubbard and $t$-$J$-$U$ models, and compared quantitatively with recent experiments.

cond-mat.str-el↗
arXiv2021

Collective spin and charge excitations in the $t$-$J$-$U$ model of high-$T_c$ cuprates

The $t$-$J$-$U$ model of high-$T_c$ copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the $t$-$J$-$U$ model. We employ VWF+$1/\mathcal{N}_f$ approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors ($1/\mathcal{N}_f$). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and $t$-$J$-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, $t$-$J$, and $t$-$J$-$U$ models. The results are discussed in the context of recent resonant inelastic $x$-ray scattering experiments for the high-$T_c$ cuprates.

cond-mat.str-el↗
arXiv2021

Universal collective modes from strong electronic correlations: Modified $1/\mathcal{N}_f$ theory with application to high-$T_c$ cuprates

A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors ($1/\mathcal{N}_f$), is developed. The departure point, VWF method, goes beyond the renormalized mean-field theory and provides semi-quantitative description of principal equilibrium properties of high-$T_c$ superconducting cuprates. The developed here scheme of VWF+$1/\mathcal{N}_f$, in the leading order provides dynamical spin and charge responses around the VWF solution, generalizing the weak-coupling spin-fluctuation theory to the regime of strong correlations. Thermodynamic corrections to the correlated saddle-point state arise systematically at consecutive orders. Explicitly, VWF+$1/\mathcal{N}_f$ is applied to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum-Monte-Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. The emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated and a non-monotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge-mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the $t$-$J$-model approach to the charge dynamics in favor of more general $t$-$J$-$U$ and $t$-$J$-$U$-$V$ models. The results are also related to recent inelastic resonant $X$-ray and neutron scattering experiments for the high-$T_c$ cuprates.

cond-mat.str-el↗
arXiv2018

Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene

We consider the superconducting and Mott-insulating states for the twisted bilayer graphene, modeled as two narrow-band system of electrons with appreciable intraatomic Coulomb interactions. The interaction induces kinetic exchange which leads to real-space, either triplet- or singlet-spin pairing, in direct analogy to heavy-fermions and high-temperature superconductors. By employing the statistically-consistent Gutzwiller method, we construct explicitly the phase diagram as a function of electron concentration for the spin-triplet $d_{x^2 - y^2}+id_{xy}$ paired case, as well as determine the topological edge states. The model reproduces principal features observed experimentally in a semi-quantitative manner. The essential role of electronic correlations in driving both the Mott-insulating and superconducting transitions is emphasized. The transformation of the spin-triplet state into its spin-singlet analogue is also analyzed, as well as the appearance of the phase separated superconducting+Mott-insulating state close to the half filling.

cond-mat.supr-con↗