arXiv subjects

P. Wójcik

Publications and source records attributed to P. Wójcik.

At least 19 recordsLinked to original sources

arXiv2026

Spin SWAP operation in double quantum dots at the LaAlO3/SrTiO3 interface

Progress in the fabrication of nanoscale transition-metal-oxide heterostructures makes these platforms promising candidates for the realization of spin qubits, mainly due to the $d$-character of their electronic structures, which could potentially result in a reduction of hyperfine interactions and spin decoherence. Here, we present a systematic study of spin control within the SWAP operation in double quantum dots embedded in a two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ interface. Our analysis starts with a study of single-electron spin dynamics, focusing on the influence of spin-orbit and interorbital coupling on the spin evolution. In this case, our findings are supported by semiclassical calculations based on the Bloch equations, which show good agreement with full quantum mechanical simulations. We then simulate the SWAP operation by analyzing the crossover between two regimes: (i) large quantum dots, where the electronic structure is dominated by the $d_{xy}$ orbitals and the spin dynamics is affected primarily by Rashba-type spin-orbit interaction; and (ii) small quantum dots, where higher-energy orbitals $d_{xz/yz}$ contribute to the electronic structure, leading to a significant reduction in the SWAP fidelity. In the first regime, particularly relevant from the application point of view, we analyze in detail the anisotropy of the SWAP operation induced by the spin-orbit coupling.

cond-mat.mes-hall↗

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.

cond-mat.supr-con↗

arXiv2025

Enhancement of the topological regime in elongated Josephson junctions

We theoretically study topological superconductivity in elongated planar Josephson junctions. In the presence of spin-orbit coupling and an in-plane magnetic field, the Josephson junction can enter the topological phase and host zero-energy Majorana bound states over a range of the superconducting phase difference centered around $π$, with the span of this range determined by the strength of the magnetic field. We demonstrate that the topological superconducting phase range can be greatly increased by elongation of the junction, which causes an amplification of the Zeeman-induced phase shift of Andreev bound states. We show that the appearance of trivial in-gap states that occurs in elongated junctions can prohibit the creation of Majorana modes, but it can be mitigated by further proximitization of the junction with additional superconducting contacts. The topological transition in this system can be probed by measurements of the critical current and we show that the elongation of the junction leads to a linear decrease of the transition critical magnetic field beneficial for experimental studies.

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arXiv2024

Scaled tight binding model for a two dimensional electron gas at the (001) LaAlO$_3$/SrTiO$_3$ interface

The progress in the fabrication of nanoscale systems based on the two-dimensional electron gas at the interface between LaAlO$_3$ and SrTiO$_3$ (LAO/STO) has created an increased demand for simulations of these nanostructures, which typically range in size from tens to hundreds of nanometers. Due to the low lattice constant of LAO/STO, approximately 0.394 nm, these calculations become extremely time-consuming. Here, we present a scaled tight-binding approximation defined on a mesh with size that can be several times larger than in the ordinary approach. The scaled model is analyzed within the context of quantum transport simulations and electronic structure calculations. Our findings demonstrate that the scaled model closely aligns with the ordinary one up to a scaling factor of 8. These results pave the way for more efficient simulations of LAO/STO nanostructures with realistic sizes relevant to experimental applications.

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arXiv2024

Electric dipole spin resonance in single and two electron quantum dot defined in two-dimensional electron gas at the SrTiO$_3$/LaAlO$_3$ interface

We investigate the energy spectrum of a single and two electron quantum dot (QD) embedded in two dimensional electron gas at the interface between SrTiO$_3$ and LaAlO$_3$, in the presence of the external magnetic field. For this purpose the three band model of $3d$-electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one $d_{xy}$ orbital with the spin-orbit interaction originating from the coupling to the $d_{xz}$, $d_{yz}$ bands. This is not the case for stronger confinement where contribution of the states related to the $d_{xz/yz}$ orbital is relevant. Based on the time depended calculations we discuss in details the manipulation of the electron spin in QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in details with respect to the parity selection rule. Our calculations show that for a single electron QD the spin-flip in the ground-state has a character of a Rabi resonance while for two electrons the singlet-triplet transition is forbidden by the parity symmetry. For the two electrons QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.

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arXiv2024

Enhancement and anisotropy of electron Lande factor due to spin-orbit interaction in semiconductor nanowires

We investigate the effective Lande factor in semiconductor nanowires with strong Rashba spin-orbit coupling. Using the $\mathbf{k}\cdot\mathbf{p}$ theory and the envelope function approach we derive a conduction band Hamiltonian where the tensor $g^*$ is explicitly related to the spin-orbit coupling constant $α_R$. Our model includes orbital effects from the Rashba spin-orbit term, leading to a significant enhancement of the effective Lande factor which is naturally anisotropic. For nanowires based on the low-gap, high spin-orbit coupled material InSb, we investigate the anisotropy of the effective Lande factor with respect to the magnetic field direction, exposing a twofold symmetry for the bottom gate architecture. The anisotropy results from the competition between the localization of the envelope function and the spin polarization of the electronic state, both determined by the magnetic field direction.

cond-mat.mes-hall↗

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.

cond-mat.supr-con↗

arXiv2022

Theory of scanning gate microscopy imaging of the supercurrent distribution in a planar Josephson junction

We theoretically investigate the mapping of the supercurrent distribution in a planar superconductor-normal-superconductor junction in the presence of a perpendicular magnetic field via the scanning gate microscopy technique. We find that the distribution of counter-propagating supercurrents aligned in Josephson vortices can be mapped by the change of the critical current induced by the tip of the scanning probe, if the flux in the junction is set close to maxima of the Fraunhofer pattern. Instead, when the magnetic field drives the junction to a supercurrent minimum in the Fraunhofer pattern, the superconducting phase adapts, and the tip always increases the supercurrent. The perpendicular magnetic field leads to the formation of Josephson vortices, whose extension for highly transparent junctions depends on the current circulation direction. We show that this leads to an asymmetric supercurrent distribution in the junction and that this can be revealed by scanning gate microscopy. We explain our findings on the basis of numerical calculations for both short- and long-junction limits and provide a phenomenological model for the observed phenomena.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

arXiv2021

Helical and topological phase detection based on nonlocal conductance measurements in a three terminal junction

The helical state is a fundamental prerequisite for many spintronics applications and Majorana zero mode engineering in nanoscopic semiconductors. Its existence in quasi-one-dimensional nanowires was predicted to be detectable as a characteristic reentrant behavior in the conductance, which in a typical two-terminal architecture may be difficult to distinguish from other possible phenomena such as Fabry-Perot oscillations. Here we present an alternative method of helical gap detection free of the mentioned ambiguity, and based on the nonlocal conductance measurements in a three-terminal junction. We find that the interplay between the spin-orbit coupling and the perpendicular magnetic field leads to a spin-dependent trajectory of electrons and as a consequence a preferential injection of electrons in one of the arms. This causes a remarkable enhancement of nonlocal conductance in the helical gap regime. We show that this phenomenon can be also used to detect the topological superconducting phase when the junction is partially proximitized by an s-wave superconductor.

cond-mat.mes-hall↗

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.

cond-mat.supr-con↗

arXiv2020

Anisotropy of the spin-orbit coupling driven by a magnetic field in InAs nanowires

We use the $\mathbf{k} \cdot \mathbf{p}$ theory and the envelope function approach to evaluate the Rashba spin-orbit coupling induced in a semiconductor nanowire by a magnetic field at different orientations, taking explicitely into account the prismatic symmetry of typical nano-crystals. We make the case for the strongly spin-orbit-coupled InAs semiconductor nanowires and investigate the anisotropy of the spin-orbit constant with respect to the field direction. At sufficiently high magnetic fields perpendicular to the nanowire, a 6-fold anisotropy results from the interplay between the orbital effect of field and the prismatic symmetry of the nanowire. A back-gate potential, breaking the native symmetry of the nano-crystal, couples to the magnetic field inducing a 2-fold anisotropy, with the spin-orbit coupling being maximized or minimized depending on the relative orientation of the two fields. We also investigate in-wire field configurations, which shows a trivial 2-fold symmetry when the field is rotated off the axis. However, isotropic spin-orbit coupling is restored if a sufficiently high gate potential is applied. Our calculations are shown to agree with recent experimental analysis of the vectorial character of the spin-orbit coupling for the same nanomaterial, providing a microscopic interpretation of the latter.

cond-mat.mes-hall↗

arXiv2020

SQUID pattern disruption in transition metal dichalcogenide Josephson junctions due to non-parabolic dispersion of the edge states

We theoretically study Josephson junctions with a transition metal dichalcogenide zigzag ribbon as a weak link. We demonstrate that the spatial profile of the supercurrent carried by the edge modes determines the critical current dependence on the perpendicular magnetic field. We explore this finding and analyze the impact of Zeeman interaction and the orbital effects of the magnetic field on the Andreev bound states energies. We show that the unequal Fermi velocities of the spin-opposite edge modes lead to an anomalous shift of the Andreev bound states in the presence of the magnetic field. This is manifested in a pronounced modification of the SQUID critical current oscillations when two opposite edges of the ribbon are conducting and can be exploited in order to reveal the anomalous phase shift of the Andreev bound states in a single Josephson junction device.

cond-mat.mes-hall↗

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.

cond-mat.supr-con↗

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.

cond-mat.mes-hall↗

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.

cond-mat.mes-hall↗

arXiv2019

Probing Andreev reflection reach in semiconductor-superconductor hybrids by Aharonov-Bohm effect

Recent development in fabrication of hybrid nanostructures allows for creation of quantum interferometers that combine semiconductor and superconductor materials. We show that in those nanostructures the joint phenomena of Aharonov-Bohm effect and Andreev reflections can be used to determine the length on which the electron is retro-reflected as a hole. We propose to exploit this feature for probing of the quasiparticle coherence length in semiconductor-superconductor hybrids by a magnetoconductance measurement.

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