arXiv subjects

Aksel Kobiałka

Publications and source records attributed to Aksel Kobiałka.

At least 19 recordsLinked to original sources

arXiv2026

Nonuniform superconducting states from Majorana flat bands

Zero-energy flat bands within the superconducting gap can give rise to competing ordered phases. We investigate such phases in topological superconductors based on the magnetic adatom platform hosting a flat band of Majorana edge states. Our self-consistent calculations of the superconducting order parameter show the emergence of both a pair density wave with edge-localized amplitude modulations and a phase crystal characterized by edge-localized phase modulations. These two phases lower the free energy of the system by gapping out the Majorana flat band, as dictated by winding numbers, which are primarily tuned by the chemical potential. In fact, at zero temperature the uniform superconducting solution with Majorana flat band never survives and the phase diagram features a pair density wave, while the order parameter transitions into a phase crystal when amplitude modulations are insufficient to hybridize all the Majorana states. A broad intermediate region connects these two phases with comparable modulations in both amplitude and phase. At finite temperatures, the pair density wave survives up to around 80% of the bulk superconducting transition temperature, while the phase crystal only appears at lower temperatures and the intermediate region is strongly suppressed. Our findings establish the ubiquity of emergent nonuniform superconducting phases and their temperature-dependent behavior in topological superconductors.

cond-mat.supr-con↗

arXiv2026

Topology and energy dependence of Majorana bound states in a photonic cavity

Light-matter interaction plays a crucial role in modifying the properties of quantum materials. In this work, we investigate the effect of cavity induced photon fields on a topological superconductor hosting Majorana bound states (MBS). We model the system using a Peierls substitution of the photonic operator in the kinetic and spin-orbit terms, and utilize an exact diagonalization of Hamiltonian for a finite number of photons to investigate the coupled system. We find that the MBS persist even in the presence of a cavity field and notably appear at finite and tunable energy, in contrast to a usual 1D topological superconductor. The MBS energy is shifted by two processes: the cavity photon energy adds a constant energy shift, while the light-matter interaction induces additional parameter dependencies, such that the MBS experience a pseudo-dispersion as a function of both light-matter interaction and magnetic field. Additionally, we find that the MBS energy oscillations are suppressed with increasing light-matter interaction and that disorder stability is not impacted by the light-matter interaction. Combined, these offer additional tunability and stability of the MBS. As a second result, we establish a modified spectral localizer formalism as an essential tool for topological characterization of quantum matter in a cavity. The spectral localizer allows characterization at arbitrary energies, which is needed for probing different photon sectors. However, hybridization between different photon sectors in the low-frequency regime limits a straightforward application of a standard spectral localizer. We fully resolve this issue by judiciously applying an energy shift to the spectral localizer. Our work thus introduces a new avenue for controlling MBS via light-matter coupling and provides a framework for exploring cavity-modified topologies.

cond-mat.mes-hall↗

arXiv2025

Lattice dynamics study of electron-correlation-induced charge density wave in antiferromagnetic kagome metal FeGe

Electron-correlation-driven phonon soft modes have been recently reported in the antiferromagnetic kagome FeGe compound and associated with the observed charge density wave (CDW). In this paper, we present a systematic investigation of the CDW origin in the context of the ab initio lattice dynamics study. Performing the group theory analysis of the mentioned soft mode, we found that the stable structure has the Immm symmetry and can be achieved by shifts of Ge atoms. Additionally, we show that the final structure realizes a distorted honeycomb Ge lattice as well as a non-flat kagome-like Fe net. For completeness, we present the electronic properties calculations. From the theoretical STM topography simulation, we indicate that the observed CDW occurs in the deformed honeycomb Ge sublattice.

cond-mat.mtrl-sci↗

arXiv2024

Topological superconductivity in Fibonacci quasicrystals

We investigate the properties of a Fibonacci quasicrystal (QC) arrangement of a one-dimensional topological superconductor, such as a magnetic atom chain deposited on a superconducting surface. We uncover a general mutually exclusive competition between the QC properties and the topological superconducting phase with Majorana bound states (MBS): there are no MBS inside the QC gaps and the MBS never behaves as QC subgap states, and likewise, no critical, or winding, QC subgap states exist inside the topological superconducting gaps. Surprisingly, despite this competition, we find that the QC is still highly beneficial for realizing topological superconductivity with MBS. It both leads to additional large nontrivial regions with MBS in parameter space, that are topologically trivial in crystalline systems, and increases the topological gap protecting the MBS. We also find that shorter approximants of the Fibonacci QC display the largest benefits. As a consequence, our results promote QCs, and especially their short approximants, as an appealing platform for improved experimental possibilities to realize MBS as well as generally highlights the fundamental interplay between different topologies.

cond-mat.mes-hall↗

arXiv2024

Electronic and dynamical properties of cobalt monogermanide CoGe phases under pressure

We present the pressure dependence of the electronic and dynamical properties of six different CoGe phases: orthorhombic Cmmm, hexagonal P6/mmm and P$\bar{6}$2m, monoclinic C2/m, cubic P2$_{1}$3, and orthorhombic Pnma. Using first-principles DFT calculations and the direct force-constants method, we study the dynamical stability of individual phases under external pressure. We show that the orthorombic Cmmm and hexagonal P6/mmm structures are unstable over a broad pressure range and most pronounced imaginary phonon soft mode in both cases leads to a stable hexagonal P$\bar{6}$2m structure of the lowest ground-state energy of all studied phases at ambient and low (below $\sim 3$ GPa) external pressure. Under these conditions, the cubic P2$_{1}$3 phase has the highest energy, however, together with monoclinic C2/m and orthorombic Pnma it is dynamically stable and all these three structures can potentially coexist as meta-stable phases. Above $\sim 3$ GPa, the cubic P2$_{1}$3 phase becomes the most energetically favorable. Fitting the Birch--Murnaghan equation of state we derive bulk modulus for all mentioned phases, which indicate relatively high resistance of CoGe to compression. Such conclusions are confirmed by band structure calculations. Additionally, we show that electronic bands of the hexagonal P$\bar{6}$2m phase reveal characteristic features of the kagome-like structure, while in the cubic P2$_{1}$3 phase spectrum, one can locate spin-1 and double Weyl fermions. In both cases, the external pressure induces the Lifshitz transition, related to the modification of the Fermi surface topology.

cond-mat.mtrl-sci↗

arXiv2023

Phononic drumhead surface state in distorted kagome compound RhPb

RhPb was initially recognized as one of a CoSn-like compounds with $P6/mmm$ symmetry, containing an ideal kagome lattice of $d$-block atoms. However, theoretical calculations predict the realization of the phonon soft mode which leads to the kagome lattice distortion and stabilization of the structure with $P\bar{6}2m$ symmetry [A. Ptok et al., Phys. Rev. B 104, 054305 (2021)]. Here, we present the single crystal x-ray diffraction results supporting this prediction. Furthermore, we discuss the main dynamical properties of RhPb with $P\bar{6}2m$ symmetry. The bulk phononic dispersion curves contain several flattened bands, Dirac nodal lines, and triple degenerate Dirac points. As a consequence, the phononic drumhead surface state is realized for the (100) surface, terminated by the zigzag-like edge of Pb honeycomb sublattice.

cond-mat.mtrl-sci↗

arXiv2023

$T_{3}$Pb$_{2}Ch_{2}$ ($T$=Pd,Pt and $Ch$=S,Se) with transition metal kagome net: Dynamical properties, phonon nodal line, phonon surface states, and chiral phonons

Shandite with Ni$_{3}$Pb$_{2}$S$_{2}$ chemical formula and R$\bar{3}$m symmetry, contains the kagome sublattice formed by the transition metal atoms. Recent experimental results confirmed the possibility of successfully synthesizing Pd$_{3}$Pb$_{2}Ch_{2}$ ($Ch$=S,Se) with the same structure. In this paper, we theoretically investigate the dynamical properties of such compounds. Furthermore, we study the possibility of realizing Pt$_{3}$Pb$_{2}Ch_{2}$ with the shandite structure. We show that the Pd$_{3}$Pb$_{2}${\it Ch}$_{2}$ and Pt$_{3}$Pb$_{2}$S$_{2}$ are stable with R$\bar{3}$m symmetry. In the case of Pt$_{3}$Pb$_{2}$S$_{2}$, there is a soft mode, which is the source of the structural phase transition from R$\bar{3}$m to R$\bar{3}$c symmetry, related to the distortion within the kagome sublattice. We discuss realized phonon nodal lines in the bulk phonon dispersions in upper frequency modes. We show that the shandite structure can host the phonon surface states, with strong dependence by the surface kind. Additionally, chiral phonons with circular motion of the Pb atoms around the equilibrium position are realized.

cond-mat.mtrl-sci↗

arXiv2022

Dynamical properties of magnetic topological insulator $T$Bi$_{2}$Te$_{4}$ ($T=$Mn, Fe): phonons dispersion, Raman active modes, and chiral phonons study

Recently discovered magnetic topological insulators $T$Bi$_{2}$Te$_{4}$ ($T=$Mn, Fe) crystallize into the $R\bar{3}m$ rhombohedral structure and exhibit the antiferromagnetic order. Here, we discuss the lattice dynamics of these compounds to confirm the stability of these systems. We show that the phonon dispersion does not contain soft modes, so both compounds are dynamically stable in the $R\bar{3}m$ phase. We perform theoretical analyses of the mode activity at $Γ$ point for the discussed compounds. In the case of the Raman active modes, our results are in agreement with the experimentally observed frequencies. Finally, we also discuss the possibility of realization of chiral phonons.

cond-mat.mtrl-sci↗

arXiv2021

Dynamical Study of the Origin of the Charge Density Wave in $A$V$_{3}$Sb$_{5}$ ($A=$K, Rb, Cs) Compounds

Systems containing the ideal kagome lattice can exhibit several distinct and novel exotic states of matter. One example of such systems is a recently discovered $A$V$_{3}$Sb$_{5}$ ($A$ = K, Rb, and Cs) family of compounds. Here, the coexistence of the charge density wave (CDW) and superconductivity is observed. In this paper, we study the dynamic properties of the $A$V$_{3}$Sb$_{5}$ systems in context of origin of the CDW phase. We show and discuss the structural phase transition from $P6/mmm$ to $C2/m$ symmetry that are induced by the presence of phonon soft modes. We conclude that the CDW observed in this family of compounds is a consequence of the atom displacement, from the high symmetry position of the kagome net, in low-temperature phase. Additionally, using the numerical {\it ab initio} methods, we discuss the charge distribution on the $A$V$_{3}$Sb$_{5}$ surface. We show that the observed experimental %$4\times 1$ stripe-like modulation of the surface, can be related to surface reconstruction and manifestation of the three dimensional $2 \times 2 \times 2$ bulk CDW. Finally, the consequence of realization of the $C2/m$ structure on the electronic properties are discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.

cond-mat.mtrl-sci↗

arXiv2021

Unconventional topological transitions in a self-organized magnetic ladder

It is commonly assumed that topological phase transitions in topological superconductors are accompanied by a closing of the topological gap or a change of the symmetry of the system. We demonstrate that an unconventional topological phase transition with neither gap closing nor a change of symmetry is possible. We consider a nanoscopic length ladder of atoms on a superconducting substrate, comprising self-organized magnetic moments coupled to itinerant electrons. For a range of conditions, the ground state of such a system prefers helical magnetic textures, self-sustaining topologically nontrivial phase. Abrupt changes in the magnetic order as a function of induced superconducting pairing or chemical potential can cause topological phase transitions without closing the topological gap. Furthermore, the ground state prefers either parallel or anti-parallel configurations along the rungs, and the anti-parallel configuration causes an emergent time reversal asymmetry protecting Kramer's pair's of Majorana zero modes, but in a BDI topological superconductor. We determine the topological invariant and inspect the boundary Majorana zero modes.

cond-mat.supr-con↗

arXiv2021

Chiral phonons in honeycomb sublattice of layered CoSn-like compounds

Hexagonal and kagome lattices exhibit extraordinary electronic properties. It is a natural consequence of additional discrete degree of freedom associated with a valley or the occurence of electronic flat-bands. Combination of both types of lattices, observed in CoSn-like compounds, leads not only to the topological electronic behavior, but also to the emergence of chiral phonon modes. Here, we study CoSn-like compounds in the context of realization of chiral phonons. Previous theoretical studies demonstrated that the chiral phonons can be found in ideal two-dimensional hexagonal or kagome lattices. However, it turns out that in the case of CoSn-like systems with the $P6/mmm$ symmetry, the kagome lattice formed by $d$-block element is decorated by the additional $p$-block atom. This results in a two dimensional triangular lattice of atoms with non-equal masses and the absence of chiral phonons in the kagome plane. Contrary to this, the interlayer hexagonal lattice of $p$-block atoms is preserved and allows for the realization of chiral phonons. We discuss properties of these chiral phonons in seven CoSn-like compounds and demonstrate that they do not depend on atomic mass ratio or the presence of intrinsic magnetic order. The chiral phonons of $d$-block atoms can be restored by removing the inversion symmetry. The latter is possible in the crystal structure of CoGe and RhPb with the reduced symmetry ($P\bar{6}2m$) and distorted-kagome-like lattice.

cond-mat.mtrl-sci↗

arXiv2021

Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order

Theoretical studies have shown that Majorana bound states can be induced at the ends of a one dimensional wire, a phenomenon possible due to the interplay between s-wave superconductivity, spin-orbit coupling, and an external magnetic field. These states have been observed in superconductor-semiconductor hybrid nanostructures in the presence of a Zeeman field, and in the limit of a low density of particles. In this paper, we demonstrate and discuss the possibility of the emergence of Majorana bound states in a superconducting Rashba nanowire deposited on an antiferromagnetically ordered surface. We calculate the relevant topological invariant in several complementary ways. Studying the topological phase diagram reveals two branches of the non trivial topological phase -- a main branch, which is typical for Rashba nanowires, and an additional branch emerging due to the antiferromagnetic order. In the case of the additional topological branch, Majorana bound states can also exist close to half-filling, obviating the need for either doping or gating the nanowire to reach the low density regime. Moreover, we show the emergence of the Majorana bound states in the absence of the external magnetic field, which is possible due to the antiferromagnetic order. We also discuss the properties of the bound states in the context of real space localization and the spectral function of the system. This allows one to perceive the band inversion within the spin and sublattice subspaces in the additional branch, contrary to the main branch, where the only band inversion reported in previous studies exists in the spin subspace. Finally, we demonstrate how these topological phases can be confirmed experimentally in transport measurements.

cond-mat.mes-hall↗

arXiv2020

Probing the chirality of 1D Majorana edge states around a 2D nanoflake in a superconductor

The interplay between superconductivity, magnetic field and spin-orbit coupling can lead to the realization of non--trivial topological phases. Recent experiments have found signatures of such phases in magnetic nanoflakes formed by nanostructures coupled to a superconducting substrate. These heterostructures comprise a topologically non-trivial region surrounded by a trivial one due to the finite magnetic exchange field induced by the magnetic nanoflake. The analysis of the topological phase diagram of such a system shows that a similar phase separation occurs by tuning the chemical potential of the nanoflake. In this paper, we study such a possibility in detail, analyzing the spatial extent of the edge modes circulating around the nanoflake and discussing some practical implementations. We also show how the chirality of Majorana edge states can be probed using scanning tunneling spectroscopy with a double tip setup.

cond-mat.mes-hall↗

arXiv2020

First principles study of topological phase in chains of $3d$ transition metals

Recent experiments have shown the signatures of Majorana bound states at the ends of magnetic chains deposited on a superconducting substrate. Here, we employ first principles calculations to directly investigate the topological properties of $3d$ transition metal nanochains (i.e., Mn, Cr, Fe and Co). In contrast to the previous studies [Nadj-Perge et al. Science 346, 602 (2014) and Ruby et al. Nano Lett. 17, 4473 (2017)], we found the exact tight binding models in the Wannier orbital basis for the isolated chains as well as for the surface--deposited wires. Based on these models, we calculate topological invariant of $\mathbb{Z}_2$ phase for all systems. Our results for the isolated chains demonstrate the existence of the topological phase only in the Mn and Co systems. We considered also a non-collinear magnetic order as a source of the non--trivial topological phase and found that this type of magnetic order is not a stable ground state in the Fe and Co isolated chains. Further studies showed that a coupling between the chain and substrate leads to strong modification of the band structure. Moreover, the analysis of the topological invariant indicates a possibility of emergence of the topological phase in all studied nanochains deposited on the Pb surface. Therefore, our results demonstrate an important role of the coupling between deposited atoms and a substrate for topological properties of nanosystems.

cond-mat.mtrl-sci↗

arXiv2020

Majorana bound states and zero-bias conductance peaks in superconductor/semiconductor nanowire devices

Theoretical research suggests a emergence of the Majorana bound states at the ends of the nanowires. Experimental verifications of said concept has already been executed, e.g., in superconductor/semiconductor nanowire devices where interplay between superconducting gap, spin-orbit coupling and external magnetic field allows for creation of zero-energy bound states. Recent experiments propose a topological phase diagram by local modification of the effective chemical potential. We discuss this possibility, using a model of experimental system in form of semi-infinite S/N junction. We calculate the zero--bias differential conductance $G$ in the case of the homogeneous system, as well as in the presence of the gate voltage. Relation between conductance and the effective gap in the system is investigated. We show that $G$ can reproduce the topological phase diagram in magnetic field vs. gate voltage space of parameters.

cond-mat.mes-hall↗

arXiv2020

Dimerization-induced topological superconductivity in a Rashba nanowire

We analyze influence of a dimerization on the topological phases of the Rashba nanowire proximitized to a superconducting substrate. We find that periodic alternations of the hopping integral and spin-orbit coupling can lead to band inversion, inducing transition to topologically nontrivial superconducting phase that hosts the Majorana zero-energy modes. This "dimerization-induced topological superconductivity" completely repels the topological phase of the uniform nanowire, whenever they happen to overlap. We provide an analytical justification for this puzzling behavior based on the symmetry/parity considerations and discuss feasible spectroscopic methods for its empirical observation. We also test stability of the topological superconducting phases against electrostatic disorder.

cond-mat.supr-con↗

arXiv2018

Delocalisation of Majorana quasiparticles in plaquette--nanowire hybrid system

Interplay between superconductivity, spin-orbit coupling and magnetic field can lead to realisation of the topologically non--trivial states which in finite one dimensional nanowires are manifested by emergence of a pair of zero-energy Majorana bound states. On the other hand, in two dimensional systems spin current contributed by the edge states might appear. We investigate novel properties of the bound states in a system of mixed dimensionality, composed of one-dimensional nanowire connected with two-dimensional plaquette. This setup could be patterned epitaxially, e.g. using heterostructure analogous to what has been reported recently by F. Nichele et al., Phys. Rev. Lett. 119, 136803 (2017). We study this system, assuming either its part or the entire structure to be in topologically non--trivial superconducting state. Our results predict delocalisation of the Majorana modes, upon leaking from the nanowire to the nanocluster with some tendency towards its corners.

cond-mat.mes-hall↗

arXiv2018

Electrostatical formation of the Majorana quasiparticles in the quantum dot--nanoring structure

Zero--energy Majorana quasiparticles can be induced at the edge of a low dimensional systems. Non--Abelian statistics of this state makes it a good candidate for the realization of quantum computing. From the practical point of view, it is crucial to obtain an intentional creation and manipulation of this type of bound states. Here, we show such a possibility in a setup of quantum nanoring in which we specify a quantum dot region via electrostatic means. States in such quantum dot can lead to the emergence of Andreev and Majorana bound states in investigated system. We study the differences between those bound states and the possibility of their manipulation. Moreover, exact calculation method for spectral function has been proposed, which can be used to discuss the bound states influence on band structure of proposed system. Using this method, it can be shown that the Majorana bound states, induced at the edge of the system, present themselves as a dispersionless zero--energy band.

cond-mat.mes-hall↗