arXiv subjects

M. Zegrodnik

Publications and source records attributed to M. Zegrodnik.

At least 19 recordsLinked to original sources

arXiv2025

Scanning gate microscopy probing of anisotropic electron flow in a two dimensional electron gas at the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface: A theoretical investigation

We theoretically investigate the anisotropic dispersion features of a two dimensional electron gas at the (110) oriented $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interfaces, as revealed by scanning gate microscopy of electronic flow from a quantum point contact. The dispersion relation of the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface is characterized by a highly non-circular Fermi surface. Here, we develop an efficient tight-binding model for the electron gas at the interface. We show that the anisotropy of the Fermi surface causes both the direction of the electron flux from the quantum point contact and the periodicity of the self-interference conductance fringes to depend strongly on the orientation of the constriction relative to the crystal lattice. We show that the radially non-uniform distribution of the Fermi velocity on the Fermi surface results in skewing of electron trajectories when the quantum point contact gates are not aligned with the in-plane primitive vectors. We show that this effect results in the separation of electrons belonging to different orbitals for wide (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ quantum wells.

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arXiv2025

Superconducting gap symmetry of 2DEG at (111)-oriented LaAlO$_3$/SrTiO$_3$ interface

We investigate the superconducting properties of the two-dimensional electron gas at the (111) LaAlO$_3$/SrTiO$_3$ interface. Using a multiorbital tight-binding model defined on a hexagonal lattice, we analyze the emergence of superconductivity driven by both interlayer (nearest-neighbor) and intralayer (next-nearest-neighbor) pairing interactions, with a particular focus on the symmetry of the superconducting gap. We demonstrate that, in both pairing scenarios, the superconducting gap transforms according to the $A_1$ irreducible representation of the $C_{6v}$ point group. Within the interlayer pairing scenario, the superconducting phase is characterized by a fully gapped quasiparticle excitation spectrum exhibiting extended $s$-wave symmetry, accompanied by an enhancement of the superconducting gap magnitude in the vicinity of the van Hove singularity. Conversely, the intralayer pairing channel produces a distinctive double-dome structure in the superconducting phase diagram, with the gap symmetry evolving from a fully gapped, extended $s$-wave at low carrier densities to a nodal extended $s$-wave state at higher electron concentrations. The qualitative agreement with experimentally observed nonmonotonic behavior of the critical temperature $T_c(V_g)$ suggests that intralayer next-nearest-neighbor pairing may play a dominant role in the superconductivity of the (111) LAO/STO interface.

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arXiv2024

Electrical spin manipulation in double SrTiO$_3$/LaAlO$_3$ quantum dots

The spin dynamics in two electron double quantum dots embedded in two dimensional electron gas at the interface between SrTiO$_3$ and LaAlO$_3$ is studied by an exact numerical solution of the time-dependent Schrödinger equation, in the context of the electric dipole spin resonance experiment. Based on the three band model of $3d$-electrons localized at Ti ions on the square lattice we analyze in details the singlet-triplet transition induced by the AC electric field, in the magnetic field range close to the avoided crossing which appears as a result of the spin-orbit coupling. Our calculations show that for symmetric double quantum dots the single photon spin-flip transitions is prohibited due to the parity symmetry and the transition can occur only by the higher order two-photon processes. For a weakly asymmetric system, when the first order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. Interestingly, for a sufficiently high magnetic field and high AC field amplitude the electric field drives the system across the avoided crossing inducing the spin-flip by the Landau-Zener-Stueckelberg-Majorana transitions with 100\% spin flip probability for a slow sweep. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin-flip of its fidelity is also presented.

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arXiv2023

Mixed singlet-triplet superconducting state within the moiré $t$-$J$-$U$ model as applied to the description of twisted WSe$_2$ bilayer

We analyze an analog of the $t$-$J$-$U$ model as applied to the description of a single moiré flat band of twisted WSe$_2$ bilayer. To take into account the correlation effects induced by a significant strength of the Coulomb repulsion, we use the Gutzwiller approach and compare it with the results obtained by the Hartree-Fock method. We discuss in detail the graduate appearance of a two dome structure of the superconducting state in the phase diagram by systematically increasing the Coulomb repulsion integral, $U$. The two superconducting domes residing on both sides of a Mott insulating state can be reproduced for a realistic parameter range in agreement with the available experimental data. According to our analysis the paired state has a highly unconventional character with a mixed $d+id$ (singlet) and $p-ip$ (triplet) symmetry. Both components of the mixed paired state are of comparable amplitudes. However, as shown here, a transition between pure singlet and pure triplet pairing should be possible in the considered system by tuning the gate voltage, which controls the magnitude of the valley-dependent spin-splitting in the system.

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arXiv2022

Interplay between the extended s-wave symmetry of the gap and the spin-orbit coupling in the low-electron concentration regime of quasi-two-dimensional superconductors

We analyze the real-space paired state with the $\mathbf{k}$-dependent superconducting gap in the presence of Rashba type spin-orbit coupling and external magnetic field. We show that the $extended$ $s$-$wave$ pairing symmetry is the most probable scenario to appear in the low-electron concentration regime. According to our study, the van Hove singularity induced by the spin-orbit coupling may lead to a significant enhancement of the superconducting gap, critical temperature and critical magnetic field. Moreover, the combined effect of the spin-orbit coupling and the external magnetic field results in a non-zero total momentum of the Cooper pairs, which is a characteristic feature of the so-called helical state. In such situation, due to the C$_4$ symmetry breaking, a small $d$-$wave$ and $p$-$wave$ contributions to the pairing appear, which significantly change the character of the helical state. The obtained results are discussed in the context of the experimental data related with the unconventional superconducting features of the transition metal oxide interfaces as well as the recently reported supercurrent diode effect.

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arXiv2022

Correlation induced $d$-wave pairing in quantum dot square lattice

We consider an electrostatically induced square lattice of quantum dots and study the role of electron-electron correlations in the resulting electronic features of the system. We utilize the Wannier functions methodology in order to construct Hamiltonian for interacting fermions and find that the change of the depth of the quantum dot confining potential results in a transition from a moderately-, to strong-correlated regime of the system. We obtain the approximate ground state by means of Variational Monte-Carlo method for a wide range of dopings. The values of microscopic parameters, charge gap as well as spin- and pair-correlation functions obtained in the strongly-correlated regime signify the presence of antiferromagnetic spin-ordering and the realization of the Mott insulator phase. Moreover, we report on a two dome structure of the emerging $d$-wave paired state residing on both sides of the half filled case. The obtained results are discussed in view of the well known families of unconventional superconducting materials such as copper based compounds.

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arXiv2021

Impact of the spin-orbit interaction on the phase diagram and anisotropy of the in-plane critical magnetic field in superconducting LaAlO$_3$/SrTiO$_3$ interface

The two-dimensional electron gas at the interface between LaAlO$_3$ and SrTiO$_3$ (LAO/STO) exhibits gate tunable superconductivity with a characteristic dome-like shape of the critical temperature ($T_c$) in the phase diagram. As shown recently [Phys. Rev. B 102, 085420 (2020)], such an effect can be explained as a consequence of the extended $s-$wave symmetry of the gap within an intersite real space pairing scenario, leading to a good agreement between the experiment and theory. In this work, we turn to a detailed analysis of the influence of spin-orbit coupling on the LAO/STO phase diagram by considering the atomic and the Rashba components. In particular, we analyze the optimal carrier concentration for which the maximal $T_c$ is reached relative to the Lifshitz transition point. We find that the a misalignment between the two can be significantly enhanced by the spin-orbit splitting of the bands, combined with the fact that superconductivity sets in when the Fermi level passes the anticrossing induced by the spin-orbital hybridization. In the presence of the external in-plane magnetic field, our calculations show four-fold anisotropy with the paramagnetic limit largely exceeded for $B_{||}$ directed along the high symmetry points [01] and [01]. The obtained electron concentration dependence of $B_{c||}$ reproduces the characteristic dome-like shape reported in experiments and the estimated value of $B_{c||}$ corresponds to that measured experimentally.

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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

Superconducting dome in the LaAlO$_3$/SrTiO$_3$ interfaces as a direct effect of the extended s-wave symmetry of the gap

The two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interface exhibits gate tunable superconductivity with a domelike shape of $T_{\rm{C}}$ as a function of electron concentration. Here, we propose that the experimentally observed behavior can be explained as a direct effect of the dominant $extended$ $s$-$wave$ symmetry of the superconducting gap. Our results agree very well with the experimental data. As shown, neither the correlation effects nor the spin-orbit coupling influence significantly the physical picture of the paired state steaming out from our analysis.

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arXiv2020

Superconducting properties of the hole-doped three-band \emph{d-p} model studied with minimal-size real-space \emph{d}-wave pairing operators

The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to $d$-$wave$ superconducting state with a characteristic dome-like shape of the order parameter for hole doping $δ\lesssim 0.4$, in a good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method (DE-GWF) [cf. Phys. Rev. B \textbf{99}, 104511 (2019)]. Subsequently, the nature of the $d$-$wave$ pairing is investigated by means of recently proposed \emph{minimal-size real-space d-wave pairing operators} [Phys. Rev. B \textbf{100}, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analysing the corresponding off-diagonal pair-pair correlation functions. The dominant character of \emph{d-wave} pairing on $d$ orbitals is confirmed. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(π,π)$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value $Δ_{CG}\approx1.78\pm0.51\text{ eV}$, and agrees with values reported experimentally for the cuprates.

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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

Superconducting dome in doped 2D superconductors with broken inversion symmetry

We analyze an unconventional inter-subband paired phase in a 2D doped superconductor considering both systems with the inversion symmetry and with the inversion symmetry broken. We find that for a centro-symmetric system the inter-subband pairing can appear in the high concentration regime when the repulsive Coulomb interaction leads to the nearly degenerate symmetric and antisymmetric state. We discuss in detail the mutual competition between the intra- and inter-subband paired phase. For systems with broken inversion symmetry, we find that the critical temperature has a characteristic domelike shape as a function of the asymmetry parameter, which is explained as resulting form the inter-subbband pairing. This results is discussed in the context of the domelike shape of $T_c$ in the LaAlO$_3$/SrTiO$_3$ interface.

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arXiv2019

Intersubband pairing induced Fulde-Ferrell phase in metallic nanofilms

We consider a free-standing metallic nanofilm with a predominant intersubband paring which emerges as a result of the confinement in the growth direction. We show that the Fermi wave vector mismatch between the subbands, detrimental to the intersubband pairing, can be compensated by the non-zero center of mass momentum of the Cooper pairs. This leads to the spontaneous appearance of the intersubband Fulde-Ferrell (IFF) state, even in the absence of an external magnetic field. Our study of the intrasubband pairing channel on the stability of the IFF phase shows that the former strongly competes with the intersubband pairing, which prohibits the coexistence of the two superconducting phases. Interestingly, upon application of the magnetic field we find a transition to an exotic mixed spin-singlet subband-triplet and spin-triplet subband-singlet paired state. Finally, we discuss the possibility of existence of the IFF pairing in novel superconducting materials.

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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

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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arXiv2015

Tunneling conductance in half-metal/conical magnet/superconductor junctions in the adiabatic and non-adiabatic regime: self-consistent calculations

The tunneling conductance in the half-metal/conical magnet/superconductor (HM/CM/SC) is investigated by the use of the combined Blonder-Tinkham-Klapwijk (BTK) formalism and the Bogoliubov-de Gennes (BdG) equations. We show that the conductance calculated self-consistently differs significantly from the one calculated in the non-self-consistent framework. The use of the self-consistent procedure ensures that the charge conservation is satisfied. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection the probability of which strongly depends on the spin transmission in the CM layer. We show that the spin of electron injected from the HM can be transmitted through the CM to the SC adiabatically or non-adiabatically depending on the period of the exchange field modulation. We find that the conductance in the subgap region oscillates as a function of the CM layer thickness wherein the oscillations transform from irregular, in the non-adiabatic regime, to regular in the adiabatic case. In the non-adiabatic regime the decrease of the exchange field amplitude in the CM leads to the emergence of the conductance peak for one particular CM thickness in agreement with experiment [J.W.A Robinson, J. D. S Witt and M. G. Blamire, Science 329, 5987]. For both transport regimes the conductance is analyzed over a broad range of parameters determining the spiral magnetization in the CM.

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arXiv2015

Orbital effect on the in-plane critical field in free-standing superconducting nanofilms

The superconductor to normal metal phase transition induced by the in-plane magnetic field is studied in free-standing Pb(111) nanofilms. In the considered structures the energy quantization induced by the confinement leads to the thickness-dependent oscillations of the critical field (the so-called 'shape resonances'). In this paper we examine the influence of the orbital effect on the in-plane critical magnetic field in nanofilms. We demonstrate that the orbital term suppresses the critical field and reduces the amplitude of the thickness-dependent critical field oscillations. Moreover, due to the orbital effect, the slope $H_{c,||}-T_c$ at $T_c(0)$ becomes finite and decreases with increasing film thickness in agreement with recent experiments. The temperature $t^*$ at which the superconductor to normal metal phase transition becomes of the first order is also analyzed.

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