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Despite several theoretical predictions regarding the physics and application of quantum wells (QWs) of topological crystalline insulators (TCI), no quantized charge transport via helical or chiral edge states has been experimentally demonstrated for such a class of systems. In this study, we report here on a successful growth by molecular beam epitaxy of high crystalline quality Pb$_{1-x}$Sn$_{x}$Se:Bi/Pb$_{1-y}$Eu$_{y}$Se QWs with $x = 0.25$ and $y = 0.1$, and on their magnetotransport characterization as a function of the QW thickness between 10 and 50 nm, temperatures down to 300 mK, perpendicular and tilted magnetic fields up to 36 T. The character of weak antilocalization magnetoresistance and universal conductance fluctuations points to a notably long phase coherence length. It is argued that a relatively large magnitude of the dielectric constant of IV-VI compounds suppresses the decoherence by electron-electron scattering. The observation of Shubnikov-de-Haas oscillations and the quantum Hall effect, together with multiband $k\cdot p$ modelling, have enabled us to assess valley degeneracies, the magnitude of strain, subbands effective masses, the Berry phases, and the topological phase diagram as a function of the QW thickness. Our results demonstrate that further progress in controlling Sn content, carrier densities, and magnetism in Pb$_{1-x}$Sn$_{x}$Se/Pb$_{1-y}$Eu$_{y}$Se QWs will allow for the exploration of the topologically protected quantized edge transport even in the absence of an external magnetic field. Furthermore, a reduced strength of electron-electron interactions will result in the absence of unpaired localized spins in the topological gap and, thus, in a substantially longer topological protection length compared to the quantum spin Hall materials explored so far., Comment: 19 pages, 20 figures in the main text and appendices; comments are welcome; data is available at https://doi.org/10.5281/zenodo.14593670

The quantum spin Hall effect in non-magnetic and Mn-doped HgTe quantum well is strongly affected by Kondo scattering of edge electrons by holes localized on acceptors. A generalized eigenvalue method is usually employed for determining impurity binding energies from the multiband Kohn-Luttinger Hamiltonians in bulk samples and semiconductor quantum structures. Such an approach provides accurate values of the level positions but its applicability for determining the impurity localization radius can be questioned. As an alternative method we propose here the Gram-Schmidt ortogonalization procedure allowing to employ the standard eigenvalue algorithms and, thus, to determine both impurity level energies and the set of normalized eigenvectors. We apply this approach to singly-ionized acceptor states in HgTe quantum wells and obtain impurity level energies and localization radiuses even for states degenerate with the continuum of band states. Such information allows us to assess the energy of bound magnetic polarons in quantum wells doped with magnetic ions. We determine the polaron energies and discuss consequences of the resonant polaron formation on band transport in the bulk samples and quantum wells in the regimes of quantum Hall effects., Comment: 7 pages, 3 figures

We report magnetization changes generated by an electric field in ferromagnetic Ga$_{1-x}$Mn$_x$N grown by molecular beam epitaxy. Two classes of phenomena have been revealed. First, over a wide range of magnetic fields, the magnetoelectric signal is odd in the electric field and reversible. Employing a macroscopic spin model and atomistic Landau-Lifshitz-Gilbert theory with Langevin dynamics, we demonstrate that the magnetoelectric response results from the inverse piezoelectric effect that changes the trigonal single-ion magnetocrystalline anisotropy. Second, in the metastable regime of ferromagnetic hystereses, the magnetoelectric effect becomes non-linear and irreversible in response to a time-dependent electric field, which can reorient the magnetization direction. Interestingly, our observations are similar to those reported for another dilute ferromagnetic semiconductor Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{1-x}$Te$_3$, in which magnetization was monitored as a function of the gate electric field. Those results constitute experimental support for theories describing the effects of time-dependent perturbation upon glasses far from thermal equilibrium in terms of an enhanced effective temperature., Comment: 18 pages, 10 Figures

A major hurdle for building a large-scale quantum computer is to scale up the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be provided by physically moving subregisters consisting of a few ions across the processor. The topology of the connectivity is given by the layout of the ion trap where one-dimensional and two-dimensional arrangements are possible. Here, we focus on an architecture based on a rectangular two-dimensional lattice, where each lattice site contains a subregister with a linear string of ions. We refer to this architecture as the Quantum Spring Array (QSA). Subregisters placed in neighboring lattice sites can be coupled by bringing the respective ion strings close to each other while avoiding merging them into a single trapping potential. Control of the separation of subregisters along one axis of the lattice, known as the axial direction, uses quasi-static voltages, while the second axis, the radial, requires control of radio frequency signals. In this work, we investigate key elements of the 2D lattice quantum computation architecture along both axes: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to noise. The coherence of the coupling is assessed, and an entangled state of qubits in separate trapping regions along the radial axis is demonstrated. Moreover, we demonstrate control over radio frequency signals to adjust radial separation between strings, and thus tune their coupling rate. We further map the 2D lattice architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale fault-tolerant operation., Comment: 23 pages, 19 figures (15 in main text, 4 in appendices)

In this report, we introduce a novel approach to visualize extremely large graphs efficiently. Our method combines two force-directed algorithms, Kamada-Kawai and ForceAtlas2, to handle different graph components based on their node count. Additionally, we suggest utilizing the Fast Multipole method to enhance the speed of ForceAtlas2. Although initially designed for analyzing bitcoin transaction graphs, for which we present results here, this algorithm can also be applied to other crypto currency transaction graphs or graphs from diverse domains.

The new Spectrum Roentgen Gamma (SRG) eROSITA X-ray telescope has a superior response to extended soft X-rays, which makes it ideal for studying low X-ray surface brightness emission of cosmic filaments. We search for extended X-ray emission between the two nearby galaxy clusters Abell~3667 and Abell~3651, which are separated by a projected transverse distance of ${\sim}13\,\mathrm{Mpc}$, using data from the SRG/eROSITA All-Sky Survey. We performed a detailed X-ray image analysis of the region between the two galaxy clusters and conducted a redshift analysis of the sources between them. We carried out a thorough surface brightness and spectral analysis between the clusters. The analysis was complemented with an X-ray pointed observation from XMM-Newton, infrared 2MASS data, and redshift information from NED. We discover an emission filament beyond the known radio relic northwest of A3667 and even beyond three times its virial radius. It is smoothly connected to A3651. The X-ray emission in the direction of the filament shows an enhancement of $30\pm3\,\%$ with a significance of $11\,\sigma$. The 2MASS map and redshift analysis show an alignment of galaxies along the filament and make a projection effect unlikely. Taking the redshift progression of galaxies within the filament into account, we estimate its three-dimensional length to be in the range of $25\,\mathrm{Mpc} - 32\,\mathrm{Mpc}$. The surface brightness analysis in combination with the temperature $T=({0.91}_{-0.11}^{+0.07})\,\mathrm{keV}$ and metallicity $Z=({0.10}_{-0.08}^{+0.05})\,\mathrm{Z_{\odot}}$ from the spectral analysis leads to estimates of a total flux, gas mass, and central baryon overdensity of $F_\mathrm{X}= (7.4\pm1.2)\times 10^{-12}\,\mathrm{erg\,s^{-1}\,cm^{-2}}$, $M_\mathrm{g}=(2.7^{+1.4}_{-0.8})\times 10^{14}\,\mathrm{M_\odot}$ and $\delta_0=215^{+86}_{-50}$., Comment: 12 pages and 13 figures in the main text plus 3 pages and 3 figures as appendix. Astronomy & Astrophysics, accepted on September 25, 2024. Now with included spectral analysis

The eROSITA telescope array aboard the Spektrum Roentgen Gamma (SRG) satellite began surveying the sky in December 2019, with the aim of producing all-sky X-ray source lists and sky maps of an unprecedented depth. Here we present catalogues of both point-like and extended sources using the data acquired in the first six months of survey operations (eRASS1; completed June 2020) over the half sky whose proprietary data rights lie with the German eROSITA Consortium. We describe the observation process, the data analysis pipelines, and the characteristics of the X-ray sources. With nearly 930000 entries detected in the most sensitive 0.2-2.3 keV energy range, the eRASS1 main catalogue presented here increases the number of known X-ray sources in the published literature by more than 60%, and provides a comprehensive inventory of all classes of X-ray celestial objects, covering a wide range of physical processes. A smaller catalogue of 5466 sources detected in the less sensitive but harder 2.3-5 keV band is the result of the first true imaging survey of the entire sky above 2 keV. We show that the number counts of X-ray sources in eRASS1 are consistent with those derived over narrower fields by past X-ray surveys of a similar depth, and we explore the number counts variation as a function of the location in the sky. Adopting a uniform all-sky flux limit (at 50% completeness) of F_{0.5-2 keV} > 5 \times 10^{-14}$ erg\,s$^{-1}$\,cm$^{-2}$, we estimate that the eROSITA all-sky survey resolves into individual sources about 20% of the cosmic X-ray background in the 1-2 keV range. The catalogues presented here form part of the first data release (DR1) of the SRG/eROSITA all-sky survey. Beyond the X-ray catalogues, DR1 contains all detected and calibrated event files, source products (light curves and spectra), and all-sky maps. Illustrative examples of these are provided., Comment: 39 pages, 23 figures. Accepted for publication in A&A. Accompanying eROSITA-DE Data Release 1

Decentralized exchanges are widely used platforms for trading crypto assets. The most common types work with automated market makers (AMM), allowing traders to exchange assets without needing to find matching counterparties. Thereby, traders exchange against asset reserves managed by smart contracts. These assets are provided by liquidity providers in exchange for a fee. Static analysis shows that small price changes in one of the assets can result in losses for liquidity providers. Despite the success of AMMs, it is claimed that liquidity providers often suffer losses. However, the literature does not adequately consider the dynamic effects of fees over time. Therefore, we investigate the impermanent loss problem in a dynamic setting using Monte Carlo simulations. Our findings indicate that price changes do not necessarily lead to losses. Fees paid by traders and arbitrageurs are equally important. In this respect, we can show that an arbitrage-friendly environment benefits the liquidity provider. Thus, we suggest that AMM developers should promote an arbitrage-friendly environment rather than trying to prevent arbitrage., Comment: This paper was presented at the CfC 2024 Academic Track Conference

Using first principle calculations we examine properties of (Cd,V)Te, (Cd,Cr)Te, (Hg,V)Te, and (Hg,Cr)Te relevant to the quantum anomalous Hall effect (QAHE), such as the position of V- and Cr- derived energy levels and the exchange interactions between magnetic ions. We consider CdTe and HgTe, containing 12.5% of cation-substitutional V or Cr ions in comparison to the well-known case of (Cd,Mn)Te and (Hg,Mn)Te, and examine their suitability for the fabrication of ferromagnetic barriers or ferromagnetic topological quantum wells, respectively. To account for the strong correlation of transition metal d electrons we employ hybrid functionals with different mixing parameters aHSE focusing on aHSE = 0.32, which better reproduces the experimental band gaps in HgTe, CdTe, Hg0.875Mn0.125Te, and Cd0.875Mn0.125Te. We find that Cr, like Mn, acts as an isoelectronic dopant but V can be an in-gap donor in CdTe and a resonant donor in HgTe, similar to the case of Fe in HgSe. From the magnetic point of view, Cr-doping results in a ferromagnetic phase within the general gradient approximation (GGA) but interactions become antiferromagnetic within hybrid functionals. However, (Hg,V)Te is a ferromagnet within both exchange-correlation functionals in a stark contrast to (Hg,Mn)Te for which robust antiferromagnetic coupling is found theoretically and experimentally. Furthermore, we establish that the Jahn-Teller effect is relevant only in the case of Cr-doping. Considering lower defect concentrations in HgTe-based quantum wells compared to (Bi,Sb)3Te2 layers, our results imply that HgTe quantum wells or (Cd,Hg)Te barriers containing either V or Cr show advantages over (Bi,Sb,Cr,V)3Te2-based QAHE systems but whether (i) ferromagnetic coupling will dominate in the Cr case and (ii) V will not introduce too many electrons to the quantum well is to be checked experimentally, Comment: 12 pages, 10 figures. Accepted in Phys. Rev. B

Earlier theoretical results on $p$-$d$ and $d$-$d$ exchange interactions for zinc-blende semiconductors with $\mathrm{Cr}^{2{+}}$ and $\mathrm{Mn}^{3{+}}$ ions are revisited and extended by including contributions beyond the dominating ferromagnetic (FM) superexchange term [i.e., the interband Bloembergen-Rowland-Van Vleck contribution and antiferromagnetic (AFM) two-electron term], and applied to topological Cr-doped HgTe and non-topological (Zn,Cr)Te and (Ga,Mn)N in zinc-blende and wurtzite crystallographic structures. From the obtained values of the $d$-$d$ exchange integrals $J_{ij}$, and by combining the Monte-Carlo simulations with the percolation theory for randomly distributed magnetic ions, we determine magnitudes of Curie temperatures $T_{\text{C}}(x)$ for $\mathrm{Zn}_{1-x}\mathrm{Cr}_x\mathrm{Te}$ and $\mathrm{Ga}_{1-x}\mathrm{Mn}_x\mathrm{N}$ and compare to available experimental data. Furthermore, we find that competition between FM and AFM $d$-$d$ interactions can lead to a spin-glass phase in the case of $\mathrm{Hg}_{1-x}\mathrm{Cr}_x\mathrm{Te}$. This competition, along with a relatively large magnitude of the AF $p$-$d$ exchange energy $N_0\beta$ can stabilize the quantum spin Hall effect, but may require the application of tilted magnetic field to observe the quantum anomalous Hall effect in HgTe quantum wells doped with Cr, as confirmed by the Chern number determination., Comment: 19 pages, 11 figures

Stablecoins have gained significant popularity recently, with their market cap rising to over $180 billion. However, recent events have raised concerns about their stability. In this paper, we classify stablecoins into four types based on the source and management of collateral and investigate the stability of each type under different conditions. We highlight each type's potential instabilities and underlying tradeoffs using agent-based simulations. The results emphasize the importance of carefully evaluating the origin of a stablecoin's collateral and its collateral management mechanism to ensure stability and minimize risks. Enhanced understanding of stablecoins should be informative to regulators, policymakers, and investors alike.

In low-temperature resonant Raman experiments on MoSe$_2$-WSe$_2$ heterobilayers, we identify a hybrid interlayer shear mode (HSM) with an energy, close to the interlayer shear mode (SM) of the heterobilayers, but with a much broader, asymmetric lineshape. The HSM shows a pronounced resonance with the intralayer hybrid trions (HX$^-$) of the MoSe$_2$ and WSe$_2$ layers, only. No resonance with the neutral intralayer excitons is found. First-principles calculations reveal a strong coupling of Q-valley states, which are delocalized over both layers and participate in the HX$^-$, with the SM. This emerging trion-phonon coupling may be relevant for experiments on gate-controlled heterobilayers., Comment: 6 pages, 4 figures

An underestimation of the fundamental band gap values by the density functional theory within the local density approximation and associated approaches is a well-known challenge of ab-initio electronic structure computations. Motivated by recent optical experiments [D. Santos-Cottin et al., arXiv:2301.08014], we have revisited first-principle results obtained earlier for EuCd2As2 and extended the computational studies to the whole class of systems EuCd2X2 (X = P, As, Sb, Bi), to EuIn2X2 (X = P, As, Sb), and to nonmagnetic AEIn2As2 (AE= Ca, Sr, Ba) employing a hybrid functional method. We find that our approach provides the magnitude of the energy gap for EuCd2As2 in agreement with the experimental value. Actually, our results indicate that EuSn2As2, BaIn2As2, EuCd2Bi2 and EuCd2SbBi are robust topological insulators, while all other compounds are topologically trivial semiconductors. The trivial band gaps of EuCd2P2, EuCd2As2 and EuCd2Sb2 are in the range of 1.38-1.48 eV, 0.72-0.79 eV and 0.46-0.49 eV, respectively. The topologically trivial Eu-based systems are antiferromagnetic semiconductors with a strong red shift of the energy gap in a magnetic field caused by the exchange coupling of the band states to spins localized on the 4f-shell of Eu ions. Additionally, the EuIn2X2 (X = P, As) compounds show altermagnetic exchange-induced band spin-splitting, particularly noticeable in the case of states derived from 5d-Eu orbitals., Comment: 16 pages, 18 figures, 1 table

EuCd$_2$As$_2$ is now widely accepted as a topological semimetal in which a Weyl phase is induced by an external magnetic field. We challenge this view through firm experimental evidence using a combination of electronic transport, optical spectroscopy and excited-state photoemission spectroscopy. We show that the EuCd$_2$As$_2$ is in fact a semiconductor with a gap of 0.77 eV. We show that the externally applied magnetic field has a profound impact on the electronic band structure of this system. This is manifested by a huge decrease of the observed band gap, as large as 125~meV at 2~T, and consequently, by a giant redshift of the interband absorption edge. However, the semiconductor nature of the material remains preserved. EuCd$_2$As$_2$ is therefore a magnetic semiconductor rather than a Dirac or Weyl semimetal, as suggested by {\em ab initio} computations carried out within the local spin-density approximation., Comment: Accepted for publication in Physical Review Letters

We study theoretically the interplay between magnetism and topology in three-dimensional HgTe/MnTe superlattices stacked along the (001) axis. Our results show the evolution of the magnetic topological phases with respect to the magnetic configurations. An axion insulator phase is observed for the antiferromagnetic order with the out-of-plane N\'eel vector direction below a critical thickness of MnTe, which is the ground state amongst all magnetic configurations. Defining $T$ as the time-reversal symmetry, this axion insulator phase is protected by a magnetic two-fold rotational symmetry $C_2{\cdot}T$. The axion insulator phase evolves into a trivial insulator as we increase the thickness of the magnetic layers. By switching the N\'eel vector direction into the $ab$ plane, the system realizes different antiferromagnetic topological insulators depending on the thickness of MnTe. These phases feature gapless surface Dirac cones shifted away from high-symmetry points on surfaces perpendicular to the N\'eel vector direction of the magnetic layers. In the presence of ferromagnetism, the system realizes a magnetic Weyl semimetal and a ferromagnetic semimetal for out-of-plane and in-plane magnetization directions, respectively. We observe large anomalous Hall conductivity in the presence of ferromagnetism in the three-dimensional superlattice., Comment: 14 pages, 13 figures

We present the theory and numerical evaluations of the backscattering rate determined by acceptor holes or Mn spins in HgTe and (Hg,Mn)Te quantum wells in the quantum spin Hall regime. The role of anisotropic s-p and sp-d exchange interactions, Kondo coupling, Luttinger liquid effects, precessional dephasing, and bound magnetic polarons is quantified. The determined magnitude and temperature dependence of conductance are in accord with experimental results for HgTe and (Hg,Mn)Te quantum wells., Comment: 12 pages, 8 figures, companion paper to arXiv:2206.01613, Phys. Rev. Lett. 130, 086202 (2023).; v2 contains modifications resulting from the review process

Semiconductors' sensitivity to electrostatic gating and doping accounts for their widespread use in information communication and new energy technologies. It is demonstrated quantitatively and with no adjustable parameters that the presence of paramagnetic acceptor dopants elucidates a variety of hitherto puzzling properties of two-dimensional topological semiconductors at the topological phase transition and in the regime of the quantum spin Hall effect. The concepts of charge correlation, Coulomb gap, exchange interaction between conducting electrons and holes localized on acceptors, strong coupling limit of the Kondo effect, and bound magnetic polaron explain a short topological protection length, high hole mobilities compared with electron mobilities, and different temperature dependence of the spin Hall resistance in HgTe and (Hg,Mn)Te quantum wells., Comment: 5 pages, 3 figures; companion paper to arXiv:2209.03283, Phys. Rev. B 107, 085421 (2023), v3 contains modifications resulting from the review process

We calculate the electronic and optical properties of InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattices within relativistic density functional theory. To have a good description of the electronic and optical properties, the modified Becke-Johnson exchange-correlation functional is pondered to correctly approximate the band gap. First, we analyze electronic and optical characteristics of bulk InAs and InSb, and then we investigate the InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattice. The optical gaps deduced from the imaginary part of the dielectric function are associated with the characteristic interband transitions. We investigate the electronic and optical properties of the InAs/InAs$_{0.625}$Sb$_{0.375}$ superlattice with three lattice constants of the bulk InAs, GaSb and AlSb, respectively. It is observed that the electronic and optical properties strongly depend on the lattice constant. Our results support the presence of two heavy-hole bands with increasing in-plane effective mass as we go far from the Fermi level. We notice a considerable decrease in the energy gaps and the effective masses of the heavy-holes in the k$_x$-k$_y$ plane compared to the bulk phases of the parent compounds. We demonstrate that the electrons are s-orbitals delocalized in the entire superlattice, while the holes have mainly 5p-Sb character localized in the In(As,Sb) side of the superlattice. In the superlattice, the low-frequency absorption spectra greatly increase when the electric field is polarized orthogonal to the growth axis allowing the applicability of III-V compounds for the long-wavelength infrared detectors., Comment: 11 figures, 13 pages

We present a physics show musical with live physics experiments and live performed songs with live orchestral accompaniment. The musical was first put on stage in German at the Physikalische Institut, University of Bonn, on the 24th of March, 2019. Here we present the original German script as well as an English translation, including a translation of the songs. We also give brief descriptions of all the experiments employed, with photos as well as how we present the experiments. The musical tells the story of a couple, Life and Death, nicknamed Vita and Mortis, who want to buy a planet where they can settle down and raise a family. They arrive at the store Planetamos, run by the manager Luna Callisto and the scientist Jupi Mercury. The latter two present to Vita and Mortis what is required for life on a planet, as well as all of the extra features for sale, to make it that very special place for their family. Through Vita and Mortis the audience learns about the physical requirements for life on a planet orbiting a star. The show involves 14 live physics experiments. The four actors sing 7 songs, which are to well-known tunes with new lyrics, in German. During the show the singers are accompanied by a small live orchestra, consisting of a flute, an oboe, a piano, a violin, a cello, a harp and percussion. The show was developed by the University of Bonn physics students, who have all been very active in the University of Bonn Physics Show (Physikshow der Universitaet Bonn) the past few years. To the best of our knowledge this is the first physics show musical with live experiments and live song and orchestra., Comment: 86 pages, 18 figures

In search of materials with three-dimensional flat band dispersions, using {\em ab-initio} computations, we investigate how topological phases evolve as a function of hydrostatic pressure and uniaxial strain in two types of superlattices: HgTe/CdTe and HgTe/HgSe. In short-period HgTe/CdTe superlattices, our analysis unveils the presence of isoenergetic nodal lines, which could host strain-induced three-dimensional flat bands at the Fermi level without requiring doping, when fabricated, for instance, as core-shell nanowires. In contrast, HgTe/HgSe short-period superlattices are found to harbor a rich phase diagram with a plethora of topological phases. Notably, the unstrained superlattice realizes an ideal Weyl semimetal with Weyl points situated at the Fermi level. A small-gap topological insulator with multiple band inversions can be obtained by tuning the volume: under compressive uniaxial strain, the material transitions sequentially into a Dirac semimetal to a nodal-line semimetal, and finally into a topological insulator with a single band inversion., Comment: 19 pages, 16 figures. Paper accepted in Physical Review Research

HgTe quantum wells with a thickness of ${\sim}$7 nm may have a graphene-like band structure and have been recently proposed to be potential candidates for quantum Hall effect (QHE) resistance standards under the condition of operation in the fields above certain critical field $B_c$, above which the topological phase (with parasitic edge conduction) disappears. We present experimental studies of the magnetoresistance of different of HgTe quantum wells as a function temperature and magnetic field, determining the critical magnetic field $B_c$. We demonstrate that for QWs of specific width $B_c$ becomes low enough to grant observation of remarkably wide QHE plateaus at the filling factor ${v=-1}$ (holes) in relaxed cryomagnetic conditions: while using commercial 0.82 T Neodymium permanent magnets and temperature of a few Kelvin provided by ${^4He}$ liquid system only. Band structure calculations allow us to explain qualitatively observed phenomena due to the interplay between light holes and heavy holes energy sub-bands (side maxima of the valence band). Our work clearly shows that the peculiar band structure properties of HgTe QWs with massless Dirac fermions make them an ideal platform for developing metrological devices with relaxed cryomagnetic conditions.

It has been suggested that the enlarged spin susceptibility in topological insulators, described by Van Vleck's formalism, accounts for the ferromagnetism of bismuth-antimony topological chalcogenides doped with transition metal impurities. In contrast, earlier studies of HgTe and related topological systems pointed out that the interband analog of the Ruderman-Kittel-Kasuya-Yosida interaction (the Bloembergen-Rowland mechanism) leads to antiferromagnetic coupling between pairs of localized spins. Here, we critically revisit these two approaches, show their shortcomings, and elucidate why the magnitude of the interband contribution is small even in topological systems. From the proposed theoretical approach and our computational studies of magnetism in Mn-doped HgTe and CdTe, we conclude that, in the absence of band carriers, the superexchange dominates, and its sign depends on the coordination and charge state of magnetic impurities rather than on the topological class of the host material., Comment: 12 pages, 4 figures; new version contains extended Supplemental Material

The abundance of semiconductors in our smartphones, computers, fiber optic junctions, cars, light sources, photovoltaic and thermoelectric cells results from the possibilities of controlling their properties through doping, lighting, and applying various fields. This paper, a part of the volume celebrating 100 years of the Polish Physical Society, presents a biased selection of worthwhile results obtained by researchers at the Institute of Physics, Polish Academy of Sciences relevant, as seen today, to topological matter and spintronics. Comprehensive studies, combining materials development, experimental investigations, and theoretical description of narrow-gap and dilute-magnetic semiconductors have been especially significant in this context. This survey also emphasizes, in an autobiographical tone, a half of a century of the author's intellectual emotions accompanying the rise of ideas and quantitative theories, allowing identifying the physics behind ongoing and future observations., Comment: version 3 is updated by recent results

Breaking time-reversal symmetry in three-dimensional topological insulator thin films can lead to different topological quantum phases, such as the Chern insulator (CI) phase, and the axion insulator (AI) phase. Using first-principles density functional theory methods, we investigate the onset of these two topological phases in a tri-layer heterostructure consisting of a Bi$_2$Se$_3$ (Bi$_2$Te$_3$) TI thin film sandwiched between two antiferromagnetic MnTe layers. We find that an orthogonal exchange field from the MnTe layers, stabilized by a small anisotropy barrier, opens an energy gap of the order of 10 meV at the Dirac point of the TI film. A topological analysis demonstrates that, depending on the relative orientation of the exchange field at the two interfaces, the total Chern number of the system is either ${\cal C} = 1$ or ${\cal C} = 0$, characteristic of the CI and the AI phase, respectively. Non-topological surface states inside the energy-gap region, caused by the interface potential, complicate this identification. Remarkably though, the calculation of the anomalous Hall conductivity shows that such non-topological surface states do not affect the topology-induced transport properties. Given the size of the exchange gap, we estimate that gapless chiral edge states, leading to the quantum anomalous Hall effect, should emerge on the sidewalls of these heterostructures in the CI phase for widths $\ge 200$ nm. We also discuss the possibility of inducing transitions between the CI and the AI phases by means of the spin-orbit torque caused by the spin Hall effect in an adjacent conducting layer., Comment: 13 pages, 8 figures

Exchange coupling between localized spins and band or topological states accounts for giant magnetotransport and magnetooptical effects as well as determines spin-spin interactions in magnetic insulators and semiconductors. However, even in archetypical dilute magnetic semiconductors such as Cd$_{1-x}$Mn$_x$Te and Hg$_{1-x}$Mn$_x$Te the evolution of this coupling with the wave vector is not understood. A series of experiments have demonstrated that exchange-induced splitting of magnetooptical spectra of Cd$_{1-x}$Mn$_x$Te and Zn$_{1-x}$Mn$_x$Te at the L points of the Brillouin zone is, in contradiction to the existing theories, more than one order of magnitude smaller compared to its value at the zone center and can show an unexpected sign of the effective Land\'e factors. The origin of these findings we elucidate quantitatively by combining: (i) relativistic first-principles density functional calculations; (ii) a tight-binding approach that takes carefully into account k-dependence of the potential and kinetic sp-d exchange interactions; (iii) a theory of magnetic circular dichroism (MCD) for $E_1$ and $E_1$ + $\Delta_1$ optical transitions, developed here within the envelope function $kp$ formalism for the L point of the Brillouin zone in zinc-blende crystals. This combination of methods leads to the conclusion that the physics of MCD at the boundary of the Brillouin zone is strongly affected by the strength of two relativistic effects in particular compounds: (i) the mass-velocity term that controls the distance of the conduction band at the L point to the upper Hubbard band of Mn ions and, thus, a relative magnitude and sign of the exchange splittings in the conduction and valence bands; (ii) the spin-momentum locking by spin-orbit coupling that reduces exchange splitting depending on the orientation of particular L valleys with respect to the magnetization direction., Comment: 20 pages, 6 figures

Three-dimensional topological insulators (3D-TIs) possess a specific topological order of electronic bands, resulting in gapless surface states via bulk-edge correspondence. Exotic phenomena have been realized in ferromagnetic TIs, such as the quantum anomalous Hall (QAH) effect with a chiral edge conduction and a quantized value of the Hall resistance ${R_{yx}}$. Here, we report on the emergence of distinct topological phases in paramagnetic Fe-doped (Bi,Sb)${_2}$Se${_3}$ heterostructures with varying structure architecture, doping, and magnetic and electric fields. Starting from a 3D-TI, a two-dimensional insulator appears at layer thicknesses below a critical value, which turns into an Anderson insulator for Fe concentrations sufficiently large to produce localization by magnetic disorder. With applying a magnetic field, a topological transition from the Anderson insulator to the QAH state occurs, which is driven by the formation of an exchange gap owing to a giant Zeeman splitting and reduced magnetic disorder. Topological phase diagram of (Bi,Sb)${_2}$Se${_3}$ allows exploration of intricate interplay of topological protection, magnetic disorder, and exchange splitting., Comment: 31 pages, 4 figures and supplementary 30 pages, 11 figures

Many conductors, including recently studied Dirac materials, show saturation of coherence length on decreasing temperature. This surprising phenomenon is assigned to external noise, residual magnetic impurities or two-level systems specific to non-crystalline solids. Here, by considering the SnTe-class of compounds as an example, we show theoretically that breaking of mirror symmetry deteriorates Berry's phase quantization, leading to additional dephasing in weak-antilocalization magnetoresistance (WAL-MR). Our experimental studies of WAL-MR corroborate these theoretical expectations in (111) Pb$_{1-x}$Sn$_x$Se thin film with Sn contents $x$ corresponding to both topological crystalline insulator and topologically trivial phases. In particular, we find the shortening of the phase coherence length in samples with intentionally broken mirror symmetry. Our results indicate that the classification of quantum transport phenomena into universality classes should encompass, in addition to time-reversal and spin-rotation invariances, spatial symmetries in specific systems., Comment: Accepted version

The synthesis of stoichiometric Sr$_2$RuO$_4$ thin films has been a challenge because of the high volatility of ruthenium oxide precursors, which gives rise to ruthenium vacancies in the films. Ru vacancies greatly affect the transport properties and electronic phase behavior of Sr$_2$RuO$_4$, but their direct detection is difficult due to their atomic dimensions and low concentration. We applied polarized X-ray absorption spectroscopy at the oxygen K-edge and confocal Raman spectroscopy to Sr$_2$RuO$_4$ thin films synthesized under different conditions. The results show that these methods can serve as sensitive probes of the electronic and vibrational properties of Ru vacancies, respectively. The intensities of the vacancy-related spectroscopic features extracted from these measurements are well correlated with the transport properties of the films. The methodology introduced here can thus help to understand and control the stoichiometry and transport properties in films of Sr$_2$RuO$_4$ and other ruthenates.

The exchange bias effect is an essential component of magnetic memory and spintronic devices. Whereas recent research has shown that anisotropies perpendicular to the device plane provide superior stability against thermal noise, it has proven remarkably difficult to realize perpendicular exchange bias in thin-film structures. Here we demonstrate a strong perpendicular exchange bias effect in heterostructures of the quasi-two-dimensional canted antiferromagnet La$_2$CuO$_4$ and ferromagnetic (La,Sr)MnO$_3$ synthesized by ozone-assisted molecular beam epitaxy. The magnitude of this effect can be controlled via the doping level of the cuprate layers. Canted antiferromagnetism of layered oxides is thus a new and potentially powerful source of uniaxial anisotropy in magnetic devices., Comment: 7 pages, 5 figures

The interplay of magnetic and semiconducting properties has been in the focus since more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers., Comment: 7 pages, 87 references

Antiferromagnets (AFs) attract much attention due to potential applications in spintronics. Both the electric current and the electric field are considered as tools suitable to control properties and the N\'eel vector direction of AFs. Among AFs, CuMnAs has been shown to exhibit specific properties that result in the existence of the current-induced spin-orbit torques commensurate with spin directions and topological Dirac quasiparticles. Here, we report on the observation of a reversible effect of an electric field on the resistivity of CuMnAs thin films, employing ionic liquid as a gate insulator. The data allow to determine the carrier type, concentration, and mobility independently of the Hall effect that may be affected by an anomalous component.

We report the studies of high-quality HgTe/(Cd,Hg)Te quantum wells (QWs) with a width close to the critical one $d_c$, corresponding to the topological phase transition and graphene like band structure in view of their applications for Quantum Hall Effect (QHE) resistance standards. We show that in the case of inverted band ordering, the coexistence of conducting topological helical edge states together with QHE chiral states degrades the precision of the resistance quantization. By experimental and theoretical studies we demonstrate how one may reach very favorable conditions for the QHE resistance standards: low magnetic fields allowing to use permanent magnets ( B $\leq$ 1.4T) and simultaneously realtively high teperatures (liquid helium, T $\geq$ 1.3K). This way we show that HgTe QW based QHE resistance standards may replace their graphene and GaAs counterparts and pave the way towards large scale fabrication and applications of QHE metrology devices., Comment: 8 pages, 10 figures

The origin of nematicity, i.e., in-plane rotational symmetry breaking, and in particular the relative role played by spontaneous unidirectional ordering of spin, orbital, or charge degrees of freedom, is a challenging issue of magnetism, unconventional superconductivity, and quantum Hall effect systems, discussed in the context of doped semiconductor systems, such as Ga$_{1-x}$Mn$_x$As, Cu$_x$Bi$_2$Se$_3$, and Ga(Al)As/Al$_x$Ga$_{1-x}$As quantum wells, respectively. Here, guided by our experimental and theoretical results for In$_{1-x}$Fe$_x$As, we demonstrate that spinodal phase separation at the growth surface (that has a lower symmetry than the bulk) can lead to a quenched nematic order of alloy components, which then governs low temperature magnetic and magnetotransport properties, in particular the magnetoresistance anisotropy whose theory for the $C_{2v}$ symmetry group is advanced here. These findings, together with earlier data for Ga$_{1-x}$Mn$_x$As, show under which conditions anisotropic chemical phase separation accounts for the magnitude of transition temperature to a collective phase or merely breaks its rotational symmetry. We address the question to what extent the directional distribution of impurities or alloy components setting in during the growth may account for the observed nematicity in other classes of correlated systems., Comment: 16 pages and 11 figures

The determination of the Landau free energy (the grand thermodynamic potential) by a perturbation theory is advanced to arbitrary order for the specific case of non-interacting fermionic systems perturbed by a one-particle potential. Peculiar features of the formalism are highlighted, and its applicability for bosons is indicated. The results are employed to develop a more explicit approach describing exchange interactions between spins of Anderson's magnetic impurities in metals, semiconductors, and insulators. Within the fourth order our theory provides on the equal footing formulae for the Ruderman-Kittel-Kasuya-Yosida, Bloembergen-Rowland, superexchange, and two-electron exchange integrals at non-zero temperature., Comment: 11 pages

Historically, comprehensive studies of dilute ferromagnetic semiconductors, e.g., $p$-type (Cd,Mn)Te and (Ga,Mn)As, paved the way for a quantitative theoretical description of effects associated with spin-orbit interactions in solids, such as crystalline magnetic anisotropy. In particular, the theory was successful in explaining {\em uniaxial} magnetic anisotropies associated with biaxial strain and non-random formation of magnetic dimers in epitaxial (Ga,Mn)As layers. However, the situation appears much less settled in the case of the {\em cubic} term: the theory predicts switchings of the easy axis between in-plane $\langle 100\rangle$ and $\langle 110\rangle$ directions as a function of the hole concentration, whereas only the $\langle 100\rangle$ orientation has been found experimentally. Here, we report on the observation of such switchings by magnetization and ferromagnetic resonance studies on a series of high-crystalline quality (Ga,Mn)As films. We describe our findings by the mean-field $p$-$d$ Zener model augmented with three new ingredients. The first one is a scattering broadening of the hole density of states, which reduces significantly the amplitude of the alternating carrier-induced contribution. This opens the way for the two other ingredients, namely the so-far disregarded single-ion magnetic anisotropy and disorder-driven non-uniformities of the carrier density, both favoring the $\langle 100\rangle$ direction of the apparent easy axis. However, according to our results, when the disorder gets reduced a switching to the $\langle 110\rangle$ orientation is possible in a certain temperature and hole concentration range., Comment: 12 pages, 9 figures

We report the synthesis of Ca$_2$RuO$_4$ thin films on NdCaAlO$_{4}$ (110), LaAlO$_3$ (100) and LaSrAlO$_4$ (001) substrates and show that epitaxial strain induces a transition from the Mott-insulating phase of bulk Ca$_2$RuO$_4$ into a metallic phase. Magnetometry and spin-polarized neutron reflectometry reveal a low-temperature, small-moment ferromagnetic state in metallic Ca$_2$RuO$_4$ films.

Using the theory of imaging with partially coherent light, we derive general expressions for different kinds of interferometric setups like double slit, shift and mirror interference. We show that in all cases the interference patterns depend not only on the point spread function of the imaging setup but also strongly on the spatial emission pattern of the sample. Taking typical experimentally observed spatial emission patterns into account, we can reproduce at least qualitatively all the observed interference structures, which have been interpreted as signatures for spontaneous long range coherence of excitons, already for incoherent emitters. This requires a critical reexamination of the previous work.

Ion implantation of Mn combined with pulsed laser melting is employed to obtain two representative compounds of dilute ferromagnetic semiconductors (DFSs): Ga1-xMnxAs and In1-xMnxAs. In contrast to films deposited by the widely used molecular beam epitaxy, neither Mn interstitials nor As antisites are present in samples prepared by the method employed here. Under these conditions the influence of localization on the hole-mediated ferromagnetism is examined in two DFSs with a differing strength of p-d coupling. On the insulating side of the transition, ferromagnetic signatures persist to higher temperatures in In1-xMnxAs compared to Ga1-xMnxAs with the same Mn concentration x. This substantiates theoretical suggestions that stronger p-d coupling results in an enhanced contribution to localization, which reduces hole-mediated ferromagnetism. Furthermore, the findings support strongly the heterogeneous model of electronic states at the localization boundary and point to the crucial role of weakly localized holes in mediating efficient spin-spin interactions even on the insulator side of the metal-insulator transition., Comment: 23 pages, 10 figures, to appear at Phys. Rev. Mater

Point-contact spectroscopy of several non-superconducting topological materials reveals a low temperature phase transition that is characterized by a Bardeen-Cooper-Schrieffer-type of criticality. We find such a behavior of differential conductance for topological surfaces of non-magnetic and magnetic Pb$_{1-y-x}$Sn$_y$Mn$_x$Te. We examine a possible contribution from superconducting nanoparticles, and show to what extent our data are consistent with Brzezicki's et al. theory [arXiv:1812.02168], assigning the observations to a collective state adjacent to atomic steps at topological surfaces., Comment: 15 pages, 27 figures (with Supplemental Material)

Transition metal oxides are promising candidates for thermoelectric applications, because they are stable at high temperature and because strong electronic correlations can generate large Seebeck coefficients, but their thermoelectric power factors are limited by the low electrical conductivity. We report transport measurements on Ca3Co4O9 films on various perovskite substrates and show that reversible incorporation of oxygen into SrTiO3 and LaAlO3 substrates activates a parallel conduction channel for p-type carriers, greatly enhancing the thermoelectric performance of the film-substrate system at temperatures above 450 {\deg}C. Thin-film structures that take advantage of both electronic correlations and the high oxygen mobility of transition metal oxides thus open up new perspectives for thermopower generation at high temperature.