arXiv subjects

Michał Zegrodnik

Publications and source records attributed to Michał Zegrodnik.

At least 19 recordsLinked to original sources

arXiv2026

Topological properties and gap structure of the paired state in twisted TMD bilayers within a two-band effective model

We present a theoretical study motivated by the recent experimental results which demonstrate superconductivity emerging from flat topological bands of twisted transition metal dichalcogenide (TMD) bilayers. To capture the non-trivial band topology of the system, we employ an effective two-band Kane-Mele-like model and substitute it with Coulomb repulsion and inter-site pairing interactions treated at the Hartree-Fock mean-field level. Assuming a real-space pairing scenario, we analyze the resulting superconducting gap symmetry and the stability of the paired state as a function of band filling and applied displacement field. Finally, we highlight the interplay between superconductivity and non-trivial topology, detailing how interaction-induced effects and the evolution of the density of states shape the resulting superconducting phase diagram.

cond-mat.supr-con↗

arXiv2026

Superconductivity in moiré transition metal dichalcogenide bilayers: comparison of two distinct theoretical approaches

Superconductivity has recently been observed in moiré transition-metal dichalcogenide bilayers. Here, we investigate the superconducting state in twisted WSe$_2$ using two complementary theoretical approaches. The first is based on the negative $U$-Hubbard model and represents a relatively conventional pairing scenario, in which strong electron-electron repulsion does not directly affect the paired state and an isotropic $s$-$wave$ gap emerges. The second approach employs the $t$-$J$-$U$ model, allowing for unconventional gap symmetries and incorporating strong correlation effects via substantial renormalization induced by Coulomb repulsion. We compare the key properties of the superconducting states obtained within these two frameworks and discuss their implications in light of available experimental observations.

cond-mat.supr-con↗

arXiv2026

Emergent Quantum Valley Hall Insulator from Electron Interactions in Transition-Metal Dichalcogenide Heterobilayers

We explore the emergence of topological phases in moiré MoTe$_2$/WSe$_2$ bilayer, highlighting the crucial role of spin-orbit coupling and Coulomb interactions at two holes per moiré unit cell $v = 2$. Our analysis uncovers robust Quantum Valley Hall Insulating (QVHI) phase and reveals that long-range interactions alone can mediate the interlayer electron tunneling, generating topologically nontrivial bands even in the absence of the corresponding single-particle hopping. Additionally, we show that in the case of band mixing terms originating both from the interaction and single particle physics a competition between topological states realizing $s$-$wave$ and $p\pm ip$-$wave$ symmetries can appear. Moreover, within the considered theoretical framework, we present that by introducing a small Zeeman field, one can lift the band inversion in one of the valleys. This leads to a Quantum Anomalous Hall Insulating (QAHI) state with the topological gap opening in a single valley and the other being topologically trivial.

cond-mat.mes-hall↗

arXiv2025

Interplay between altermagnetism and superconductivity in two dimensions: intertwined symmetries and singlet-triplet mixing

We study the interplay between altermagnetism and unconventional superconductivity for the case of two-dimensional square- and triangular-lattice systems. Our approach is based on an effective single particle Hamiltonian which mimics the alternating spin splitting characteristic for the $d$-$wave$ and $i$-$wave$ altermagnetic state. By supplementing the model with intersite pairing term we characterize the principal features of the coexistent altermagnetic-superconducting state as well as the possibility of inducing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Our calculations show that the subtle interplay between the symmetries of the superconducting and altermagnetic order parameters as well as the shape/size of the Fermi surface lead to various types of anisotropic behaviors of the resultant non-zero momentum pairing, which has not been possible in the originally proposed FFLO state. Moreover, in the considered systems additional pairing symmetries appear leading to an exotic multi-component order parameter with singlet-triplet mixing. To interpret the obtained data we analyze the Cooper pair density in the momentum space and the corresponding Fermi wave vector mismatch resulting from the altermagnetic spin splitting. We discuss our result in the context of possible applications like, e.g., the superconducting diode.

cond-mat.supr-con↗

arXiv2025

Signatures of superconducting pairing driven by electron-electron interactions in moiré WSe$_2$/WSe$_2$ homobilayer modelled by Hubbard Hamiltonian

Strong evidence of unconventional superconductivity has been very recently reported experimentally in twisted transition metal dichalcogenide bilayer and gathered a significant amount of interest. Here we consider the Hubbard model on a triangular lattice describing the hole-doped moiré superlattice emerging in WSe$_{2}$/WSe$_{2}$ twisted homobilayer in the moderately correlated regime. By applying the Density Matrix Renormalization Group, we diagonalize the spin-valley-polarized Hamiltonian and show signatures of coexisting singlet and triplet pairings in the range of hole dopings and displacement fields reported in the experiments. In this view, we show that the superconductivity in the WSe$_{2}$/WSe$_{2}$ twisted homobilayer is likely to be induced by electronic correlations and has a mixed-symmetry character. These predictions can shed light on the nature of the superconducting state observed in the twisted homobilayer of WSe$_{2}$/WSe$_{2}$. We also identify the emerging superconducting orders, which are $d_{xy}(d_{x^2-y^2} \pm id_{xy} )$ and $p_y(p_{x}\mp ip_{y})$ for the singlet and triplet channels in the cylinder of width three(four), respectively.

cond-mat.supr-con↗

arXiv2025

Optimal superconductivity in twisted bilayer WSe$_2$ where the Van Hove singularity crosses half-filling

The recent discovery of unconventional superconductivity has pointed to twisted WSe$_2$ bilayer as a versatile platform for studying the correlated and topological phases of matter. Here we analyze the effect of the displacement field and electron interactions on the formation of a topological paired state in twisted WSe$_2$. Our approach is based on the effective single band $t$-$J$-$U$ model supplemented with intersite Coulomb interaction term and treated within the Gutzwiller approximation. We show that the superconducting phase is stabilized in a small range of displacement fields where the Van Hove singularity crosses half-filling, which is in qualitative agreement with recent experimental data. According to our analysis, such a circumstance comes as a result of a subtle interplay between the large density of states of the Van Hove singularity, in combination with the renormalization effects that appear in the weak-to-moderate correlations regime. The two factors create favorable conditions for the SC pairing only in a small area of the phase diagram.

cond-mat.supr-con↗

arXiv2025

Interplay between topology and electron-electron interactions in the moiré MoTe$_{\mathrm{2}}$/WSe$_{\mathrm{2}}$ heterobilayer

We study, the interplay between topology and electron-electron interactions in the moiré MoTe$_2$/WSe$_2$ heterobilayer. In our analysis we apply an effective two-band model with complex hoppings that incorporates the Ising-type spin-orbit coupling and lead to a non-trivial topology after the application of perpendicular electric field (displacement field). The model is supplemented by on-site and inter-site Coulomb repulsion terms and treated by both Hartree-Fock and Gutzwiller methods. According to our analysis, for the case of one hole per moiré unit cell, the system undergoes two phase transitions with increasing displacement field. The first one is from an in-plane 120$^\circ$ antiferromagnetic charge transfer insulator to a topological insulator. At the second transition, the system becomes topologically trivial and an out-of-plane ferrimagnetic metallic phase becomes stable. In the topological region a spontaneous spin-polarization appears and the holes are distributed in both layers. Additionally, we analyze the influence of the intersite Coulomb repulsion terms on the appearance of the topological phase as well as on the formation of the charge density wave state. We discuss the obtained results in the context of available experimental data.

cond-mat.str-el↗

arXiv2025

Charge and spin properties of a generalized Wigner crystal realized in the moiré WSe$_2$/WS$_2$ heterobilayer

We examine the charge and spin properties of an effective single-band model representing a moiré superlattice of the WSe$_{2}$/WS$_{2}$ heterobilayer. We focus on the $2/3$ electron filling, which refers to the formation of a generalized Wigner crystal, as evidenced experimentally. Our approach is based on the extended-Hubbard model on a triangular lattice with non-interacting part effectively describing a spin-split band due to Ising-type spin-orbit coupling. We investigate the system in the regime of strong on-site Coulomb repulsion and the ground state of the Hamiltonian is obtained with the use of the Density Matrix Renormalization Group formulated within the Matrix Product State approach. According to our analysis, based on the density-density correlation functions resolved in the momentum space, a transition from the metallic to the insulating state appears with increasing intersite electron-electron interactions. This transition is identified as being concomitant with the emergence of a generalized Wigner crystal that realizes the honeycomb lattice pattern. We investigate the magnetic properties of such a Wigner crystal state and find that the presence of spin-valley polarization and the increased intersite repulsion induce spin canting of the out-of-plane antiferromagnetic ordering.

cond-mat.str-el↗

arXiv2024

Topological superconductivity with mixed singlet-triplet pairing in moiré transition-metal-dichalcogenide bilayers

We investigate strong coupling topological superconductivity in twisted moiré bilayer WSe$_2$. Our approach is based on an effective $t$-$J$ model with displacement-field-dependent complex hoppings, which is treated with the variational Gutzwiller projection method. The calculated phase diagram contains domes of topologically nontrivial superconducting phases, with Chern numbers $C=\pm 2,\;\pm 4$. The order parameter is characterized by a mixed $d$+$id$-wave (singlet) and $p$-$ip$-wave (triplet) gap symmetry. We also report on the appearance of an additional topologically trivial extended $s$-wave and $f$-wave paired phase. As we show, by changing the electron density and displacement field, one can tune the singlet and triplet contributions to the pairing, as well as induce topological phase transitions between superconducting states characterized by different values of the Chern number. We analyze the physical origin of the reported effects and discuss it briefly in the view of new possibilities for designing unconventional superconductivity in moiré systems.

cond-mat.supr-con↗

arXiv2024

Variational Monte-Carlo Approach for Hubbard Model Applied to Twisted Bilayer WSe$_2$ at Half-Filling

We consider an effective Hubbard model with spin- and direction-dependent complex hoppings $t$, applied to twisted homobilayer WSe$_2$ using a variational Monte Carlo approach. The electronic correlations are taken into account by applying the Gutzwiller on-site correlator as well as long-range Jastrow correlators subjected to noninteracting part being of Pfaffian form. Our analysis shows the emergence of Mott insulating state at critical value of Hubbard interaction $U_{c1}\approx 6.5|t|\div7|t|$ estimated by extrapolating the density-density equal-time two-particle Green's functions. The signatures of an intermediate insulating phase between $U_{c1}$ and $U_{c2}\approx9.5|t|\div10|t|$ are also discussed. Furthermore, we report the formation of the $120^{\circ}$ in-plane Néel state indicated by the detailed analysis of the spin-spin correlation functions. As shown, switching between antiferromagnetic phases characterized by opposite chirality could be experimentally realized by the change of perpendicular electric field. In proper range of electric fields also a transition to in-plane ferromagnetic state appears.

cond-mat.str-el↗

arXiv2023

Honeycomb anti-dot artificial lattice as a prototypical correlated Dirac fermions system

We study theoretically the electronic properties of the artificial quantum dot honeycomb lattice defined in a two-dimensional electron gas, focusing on the possibility of achieving a regime in which electronic correlations play a dominant role. At first we establish a non-interacting model compatible with recently studied experimentally devices. According to the values of the obtained electron-electron interaction integrals, we postulate that the inclusion of inherent electron-gas self-screening is indispensable to reconstruct the experimental observations. Applying the Thomas-Fermi type of screening, we show that the radius of the anti-dot is crucial to achieve a correlated state in which phenomena like antiferromagentic ordering and interaction-induced insulating state appear. We estimate the conditions for which the electronically correlated state in an artificial honeycomb lattice can be realized.

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↗

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↗

arXiv2018

Antiferromagnetism, charge density wave, and d-wave superconductivity in the extended $t$--$J$--$U$ model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory

In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the $t$-$J$-$U$-$V$ model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term $V$ in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of $V$ in a limited hole-doping range $δ$. The effect of the $V$ term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. In the Appendices we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end we overview briefly the possible extensions of the current models to make description of the SC, AF, and CDW states on equal footing.

cond-mat.str-el↗

arXiv2017

Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions

We analyze the effect of intersite-interaction terms on the stability of the coexisting superconucting-nematic phase (SC+N) within the extended Hubbard and $t$-$J$-$U$ models on the square lattice. In order to take into account the correlation effects with a proper precision, we use the approach based on the \textit{diagrammatic expansion of the Gutzwiller wave function} (DE-GWF), which goes beyond the renormalized mean field theory (RMFT) in a systematic manner. As a starting point of our analysis we discuss the stability region of the SC+N phase on the intrasite Coulomb repulsion-hole doping plane for the case of the Hubbard model. Next, we show that the exchange interaction term enhances superconductivity while suppresses the nematicity, whereas the intersite Coulomb repulsion term acts in the opposite manner. The competing character of the SC and N phases interplay is clearly visible throughout the analysis. A universal conclusion is that the nematic phase does not survive within the $t$-$J$-$U$ model with the value of $J$ integral typical for the high-T$_C$ cuprates ($J\approx 0.1$eV). For the sake of completeness, the effect of the correlated hopping term is also analyzed. Thus the present discussion contains all relevant two-site interaction terms which appear in the parametrized one-band model within the second quantization scheme. At the end, the influence of the higher-order terms of the diagrammatic expansion on the rotational symmetry breaking is also shown by comparing the DE-GWF results with those corresponding to the RMFT.

cond-mat.str-el↗

arXiv2017

Universal properties of high-temperature superconductors from real-space pairing III: The role of correlated hopping and intersite Coulomb interaction within the t-J-U model

We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the $d$-$wave$ superconducting (SC) state, in both the electron and hole doped regimes within the t-J-U model. In our analysis we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF) which allows us to go beyond the renormalized mean field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping $\sim K$. Also, the doping dependences of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter $K$. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in the Appendix for reference.

cond-mat.supr-con↗

arXiv2017

Effect of interlayer processes on the superconducting state within t-J-U model: Full Gutzwiller wave-function solution and relation to experiment

The Gutzwiller wave function solution of the $t$-$J$-$U$ model is considered for the bilayer high-T$_C$ superconductor by using the so-called diagrammatic expansion method. The focus is on the influence of the interlayer effects on the superconducting state. The chosen pairing symmetry is a mixture of $d_{x^2-y^2}$ symmetry within the layers and the so-called $s^{\pm}$ symmetry for the interlayer contribution. The analyzed interlayer terms reflect the interlayer electron hopping, the interlayer exchange coupling, and the interlayer pair hopping. The obtained results are compared with selected experimental data corresponding to the copper-based compound Bi-2212 with two Cu-O planes in the unit cell. For the sake of comparison, selected results for the case of the bilayer Hubbard model are also provided. This paper complements our recent results obtained for the single-plane high temperature cuprates [cf. J. Spałek, M. Zegrodnik, and J. Kaczmarczyk, Phys. Rev. B {\bf 95}, 024506 (2017)]

cond-mat.supr-con↗

arXiv2016

Universal properties of high temperature superconductors from real space pairing: t-J-U model and its quantitative comparison with experiment

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 ($δ$) 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 $δ$-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.

cond-mat.supr-con↗