arXiv subjects

J. Spałek

Publications and source records attributed to J. Spałek.

18 recordsLinked to original sources

arXiv2022

Many-particle covalency, ionicity, and atomicity revisited for a few simple example molecules

We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab intio (EDABI) approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding.

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arXiv2021

Photoemission signature of momentum-dependent hybridization in CeCoIn$_5$

Hybridization between $f$ electrons and conduction bands ($c$-$f$ hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn$_5$ heavy fermion superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of $T=6$ K. The used photon energy of 122 eV corresponds to Ce $4d$-$4f$ resonance. Calculations carried out with relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining $f$-electron character when approaching Fermi energy. We have also observed a considerable variation of $f$-electron spectral weight at $E_F$, which is normally determined by both matrix element effects and wave vector dependent $c$-$f$ hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of $4f$-electron enhanced spectral intensity at $E_F$ around $\barΓ$ and $\bar{M}$ points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of $4f$-electron density for a range of values of the parameters used in the model.

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arXiv2021

A unified theory of spin and charge excitations in high-$T_c$ cuprates: Quantitative comparison with experiment and interpretation

We provide a unified interpretation of both paramagnon and plasmon modes in high-$T_c$ copper-oxides, and verify it quantitatively against available resonant inelastic $x$-ray scattering (RIXS) data across the hole-doped phase diagram. Three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+$1/\mathcal{N}_f$ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors ($1/\mathcal{N}_f$). We show that intense paramagnons persist along the anti-nodal line from the underdoped to overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to anti-phase oscillations on neighboring $\mathrm{CuO_2}$ planes. The theoretical spin- and charge excitation energies reproduce semi-quantitatively RIXS data for $\mathrm{(Bi, Pb)_2 (Sr, La)_2 CuO_{6+δ}}$. The present VWF+$1/\mathcal{N}_f$ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-$T_c$ cuprates as strongly correlated systems.

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arXiv2021

Superconducting dome with $extended$ $s$-$wave$ pairing symmetry in the heavily hole-overdoped copper-oxide planes

We analyze the two-orbital (with $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals) analogue of the $t$-$J$-$U$ model as applied to the description of the copper-oxide monolayer deposited on the Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ substrate (CuO$_2$/BSCCO). We show, that an $extended$ $s$-$wave$ superconducting dome appears in the heavily hole overdoped regime of the model, with dominant contribution to the pairing coming from the $d_{3z^2-r^2}$ orbitals. Also, the lower critical doping for the appearance of the SC state concurs with the Lifshitz Transition after which the hole-like Fermi pockets are created around the $M$ points in the Brillouin zone. The obtained results are in accord with the recent experimental result [cf. Y. Zhong et al., Sci. Bull. 61, 1239 (2016)]. An analogous two-band description is also analyzed in the context of the Ba$_2$CuO$_{4-y}$ bulk compound, where the heavily hole-overdoped situation is believed to be reached [cf. W. M. Li et al. PNAS 116, 12156 (2019)]. As we show, a two dome structure can be realized in such system with the $d$- and $s$-$wave$ symmetries of the gap corresponding to the low hole-doping and heavily hole overdoped cases, respectively.

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arXiv2020

Realistic estimates of superconducting properties for the cuprates: reciprocal-space diagrammatic expansion combined with variational approach

We propose a systematic approach to the systems of correlated electrons, the so-called $\mathbf{k}$-DE-GWF method, based on reciprocal-space ($\mathbf{k}$-resolved) diagrammatic expansion of the variational Gutzwiller-type wave function for parametrized models of correlated fermions. The present approach, in contrast to either variational Monte-Carlo (VMC), or the recently developed real-space diagrammatic expansion of the Gutzwiller-type wave function (direct-space DE-GWF technique), is applicable directly in the thermodynamic limit and thus is suitable for describing selected singular features of the wave-vector-dependent quantities. We employ the $\mathbf{k}$-DE-GWF method to extract the non-analytic part of the two leading moments of the fermion spectral-density function across the (two-dimensional) Brillouin zone for the Hubbard model and away from the half-filling. Those moments are used to evaluate the nodal quasiparticle velocities and their spectral weights in the correlated superconducting state. The two velocities determined in that manner exhibit scaling with the electron concentration qualitatively different from that obtained earlier for the excited states of the high-$T_c$ cuprates within the projected quasi-particle ansatz, and the results are in a very good quantitative agreement with experimental data if interpreted as those characterizing the spectrum below and above the observed kink. We provide a detailed discussion of the two gaps and two excitation branches (two velocities) appearing naturally within our DE-GWF approach. The two separate sets of characteristics distinguish the renormalized quasiparticle states very close to the Fermi surface from the deeper correlated-state properties. Also, an enhancement of the $\mathbf{k}$-dependent magnetic susceptibility is shown to contain a spin-fluctuation contribution within our language.

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arXiv2020

Robust spin and charge excitations throughout high-$T_c$-cuprate phase diagram from incipient Mottness

The generic phase diagram of lightly hole-doped high-$T_c$-cuprates hosts antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong-coupling, using a modified $1/N$ expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-$U$ energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semi-quantitatively with recent resonant $X$-ray and neutron scattering data for $\mathrm{La_{2-\mathit{x}}Sr_\mathit{x}CuO_4}$ and $\mathrm{(Bi,Pb)_2(Sr,La)_2CuO_{6+δ}}$ at all available doping levels. The weak-coupling random-phase-approximation fails already for underdoped samples, pointing to the non-trivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.

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arXiv2019

Superconductivity and intra-unit-cell electronic nematic phase in the three-band model of cuprates

The intra-unit-cell nematic phase is studied within the three-band Emery model of the cuprates with the use of the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF). According to our analysis the spontaneous $C_4$ symmetry breaking of the electronic wave function, leading to the nematic behavior, can appear due to electron correlations induced mainly by the onsite Coulomb repulsion, even in the absence of the corresponding intersite oxygen-oxygen repulsion term. The latter has been considered as the triggering factor of the nematic state formation in a number of previous studies. Also, we show that, at the transition to the nematic phase electron concentration transfer from $d$- to $p$- orbitals takes place, apart from the usually discussed $p_x/p_y$ polarization. The determined stability regime of the nematic phase appears in the doping range similar to that of the paired phase, showing that both phases have a common origin, even though they compete. Also, we show that in a significant doping range a coexistence region of superconductivity and nematicity appears. The results are discussed in the view of the experimental findings considering the relation between nematicity and pseudogap behavior.

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arXiv2019

Coexistent spin-triplet superconducting and ferromagnetic phases induced by the Hund's rule coupling and electronic correlations II: Effect of applied magnetic field

Recently proposed local-correlation-driven pairing mechanism, describing ferromagnetic phases (FM1 and FM2) coexisting with spin-triplet superconductivity (SC) within a single orbitally degenerate Anderson lattice model, is extended to the situation with applied Zeeman field. The model provides and rationalizes in a semiquantitative manner the principal features of the phase diagram observed for $\mathrm{UGe_2}$ in the field absence [cf. Phys. Rev. B $\mathbf{97}$, 224519 (2018)]. As spin-dependent effects play a crucial role for both the ferromagnetic and SC states, the role of the Zeeman field is to single out different stable spin-triplet SC phases. This analysis should thus be helpful in testing the proposed real-space pairing mechanism, which may be regarded as complementary to spin-fluctuation theory suitable for $\mathrm{^3He}$. Specifically, we demonstrate that the presence of the two distinct phases, FM1 and FM2, and associated field-driven metamagnetic transition between them, induce respective metasuperconducting phase transformation. At the end, we discuss briefly how the spin fluctuations might be incorporated as a next step into the considered here renormalized quasiparticle picture.

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arXiv2018

Superconductivity in the three-band model of cuprates: Variational wave function study and relation to the single-band case

The $d$-$wave$ superconductivity is analyzed within the three-band $d$-$p$ model with the use of the diagrammatic expansion of the Guztwiller wave function method (DE-GWF). The determined stability regime of the superconducting state appears in the range of hole doping $δ\lesssim 0.35$, with the optimal doping close to $δ\approx 0.19$. The pairing amplitudes between the $d$-orbitals due to copper and $p_x/p_y$ orbitals due to oxygen are analyzed together with the hybrid $d$-$p$ pairing. The $d$-$d$ pairing between the nearest neighboring atomic sites leads to the dominant contribution to the SC phase. Moreover, it is shown that the decrease of both the Coulomb repulsion on the copper atomic sites ($U_d$) and the charge transfer energy between the oxygen and copper atomic sites ($ε_{dp}$) increases the pairing strength as it moves the system from the strong to the intermediate-correlation regime, where the pairing is maximized. Such a result is consistent with our analysis of the ratio of changes in the hole content at the $d$ and $p$ orbitals due to doping, which, according to experimental study, increases with the increasing maximal critical temperature [cf. Nat. Commun. 7, 11413 (2016)]. Furthermore, the results for the three-band model are compared to those for the effective single-band picture and similarities between the two approaches are discussed. For the sake of completeness, the normal-state characteristics determined from the DE-GWF approach are compared with those resulting from the Variational Quantum Monte Carlo method with inter-site correlations included through the appropriate Jastrow factors.

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arXiv2018

Spin-triplet paired phases inside ferromagnet induced by Hund's rule coupling and electronic correlations: Application to $\mathrm{UGe}_2$

We discuss a mechanism of real-space spin-triplet pairing, alternative to that due to quantum paramagnon excitations, and demonstrate its applicability to $\mathrm{UGe_2}$. Both the Hund's rule ferromagnetic exchange and inter-electronic correlations contribute to the same extent to the equal-spin pairing, particularly in the regime in which the weak-coupling solution does not provide any. The theoretical results, obtained within the orbitally-degenerate Anderson lattice model, match excellently the observed phase diagram for $\mathrm{UGe_2}$ with the coexistent ferromagnetic (FM1) and superconducting ($A_1$-type) phase. Additionally, weak $A_2$- and $A$-type paired phases appear in very narrow regions near the metamaganetic (FM2 $\rightarrow$ FM1) and FM1 $\rightarrow$ paramagnetic first-order phase-transition borders, respectively. The values of magnetic moments in the FM2 and FM1 states are also reproduced correctly in a semiquantitative manner. The Hund's metal regime is also singled out as appearing near FM1-FM2 boundary.

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arXiv2018

Incorporation of charge- and pair-density-wave states into the one-band model of d-wave superconductivity

We study the coexistence of pair- (PDW) and charge-density-wave (CDW) states within the single-band $t$-$J$-$U$ and Hubbard models of $d$-$wave$ superconductivity and discuss our results in the context of the experimental observations for the copper-based compounds. In order to take into account the correlation effects with a proper precision, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), that goes beyond the renormalized mean field theory (RMFT) in a systematic manner. According to our analysis of the $t$-$J$-$U$ model, the transition between the pure $d$-$wave$ superconducting phase (SC) and the coexistent CDW+PDW phase takes place at $δ\approx 0.18$ (close to the optimal doping), with the modulated phase located in the underdoped regime. The situation is slightly different for the case of the Hubbard model, where a narrow stability regime of a precursor nematic phase sets in preceding the formation of the modulated CDW+PDW state, with the decreasing hole doping. The results complete our discussion of the standard phase diagram for high-T$_C$ superconducting compounds within the DE-GWF variational approach in the single narrow-band case.

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arXiv2017

Stable high-temperature paramagnons in a three-dimensional antiferromagnet near quantum criticality: Application to TlCuCl$_3$

The complete set of hallmarks of the three-dimensional antiferromagnet near the quantum critical point has been recently observed in the spin dimer compound TlCuCl$_3$. Nonetheless, the mechanism, responsible for several distinct features of the experimental data, has remained a puzzle, namely: (i) the paramagnons exhibit remarkable robustness to thermal damping and are stable up to high temperatures, where $k_B T$ is comparable with the excitation energy, (ii) the width to mass ratios of the high-temperature paramagnons are, within the error bars, equal to that of the low-temperature amplitude (or Higgs) mode. We propose such a mechanism and identify two principal factors, contributing to the scaling between width to mass ratios of the paramagnon and the amplitude mode: (i) the emergence of the thermal mass scale reorganizing the paramagnon decay processes, and (ii) substantial renormalization of the multi-magnon interactions by thermal fluctuations. The study is carried out for the general case of a $D= 3 + 1$ quantum antiferromagnet within the framework of the $φ^4$ model using the hybrid Callan-Symanzik + Wilson thermal renormalization group method. Our approach is tested by demonstrating a good quantitative agreement with available experimental data across the phase diagram of TlCuCl$_3$.

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arXiv2015

Correlation-driven multigap d-wave superconductivity in Anderson lattice model

We present the full Gutzwiller-wave-function solution of the Anderson lattice model in two dimensions that leads to the correlation-driven multigap superconducting (SC) ground state with the dominant $d_{x^2-y^2}$-wave symmetry. The results are consistent with the principal properties of the heavy-fermion superconductor CeCoIn$_5$. We regard the pairing mechanism as universal and thus applicable to other Ce-based heavy-fermion compounds. Additionally, a gain in kinetic energy in the SC state takes place, as is also the case for high-temperature superconductors.

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arXiv2014

High temperature superconductivity in the two-dimensional $t$-$J$ model: Gutzwiller wave function solution

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) proposed very recently is used for the description of superconducting (SC) ground state in the two-dimensional square-lattice $t$-$J$ model with the hopping electron amplitudes $t$ (and $t'$) between nearest (and next-nearest) neighbors. On the example of the SC state analysis we provide a detailed comparison of the method results with other approaches. Namely: (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results; (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed "grand-canonical Gutzwiller approximation" (GCGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a $d_{x^2-y^2}$-wave only for optimally- and overdoped system, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the $\mathbf{k}$-space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly-correlated systems, as: (i) it works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to GA (i.e., it provides the results much faster than the VMC approach).

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arXiv2013

High-temperature superconductivity in the Hubbard model: Gutzwiller wave-function solution

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes t (and t') between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (U, δ, t') and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, U/t > 3, and for not too large hole doping, δ< 0.32 for t' = 0.25 t; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles $d_{x^2-y^2}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.

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arXiv2012

From magnetic and Kondo-compensated states to unconventional superconductivity in heavy fermions: a unified approach

Inspired by the recent experimental evidence of antiferromagnetism and superconductivity coexistence in heavy fermion CeRhIn$_5$, we propose a fully microscopic approach based on the idea of real space pairing within the Anderson-Kondo lattice model. We present an overall phase diagram incorporating the emergence of a quantum critical point, where Kondo insulating (KI), antiferromagnetic (AF) and superconducting (SC) phases meet. We also obtain the Kondo insulating state with totally compensated magnetic moments as the parental state for the emerging SC phases. Furthermore, the coexistent (AF+SC) phase may contain also a non-trivial spin-triplet gap component within the essentially spin-singlet pairing mechanism

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arXiv2010

Andreev reflection between a normal metal and the FFLO superconductor II: a self-consistent approach

We consider Andreev reflection in a two dimensional junction between a normal metal and a heavy fermion superconductor in the Fulde-Ferrell (FF) type of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We assume s-wave symmetry of the superconducting gap. The parameters of the superconductor: the gap magnitude, the chemical potential, and the Cooper pair center-of-mass momentum Q, are all determined self-consistently within a mean-field (BCS) scheme. The Cooper pair momentum Q is chosen as perpendicular to the junction interface. We calculate the junction conductance for a series of barrier strengths. In the case of incoming electron with spin σ= 1 only for magnetic fields close to the upper critical field H_{c2}, we obtain the so-called Andreev window i.e. the energy interval in which the reflection probability is maximal, which in turn is indicated by a peak in the conductance. The last result differs with other non-self-consistent calculations existing in the literature.

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arXiv2008

Verwey transition in Fe$_{3}$O$_{4}$ at high pressure: quantum critical behavior at the onset of metallization

We provide evidence for the existence of a {\em quantum critical point} at the metallization of magnetite Fe$_{3}$O$_{4}$ at an applied pressure of $p_{c} \approx 8$ GPa. We show that the present ac magnetic susceptibility data support earlier resistivity data. The Verwey temperature scales with pressure $T_{V}\sim (1-p/p_{c})^ν$, with $ν\sim 1/3$. The resistivity data shows a temperature dependence $ρ(T)=ρ_{0}+AT^{n}$, with $n\simeq 3$ above and 2.5 at the critical pressure, respectively. This difference in $n$ with pressure is a sign of critical behavior at $p_{c}$. The magnetic susceptibility is smooth near the critical pressure, both at the Verwey transition and near the ferroelectric anomaly. A comparison with the critical behavior observed in the Mott-Hubbard and related systems is made.

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