Journal of Physics: Condensed Matter

W annier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of W annier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in W annier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

To distinguish between chemical bonding and physical binding is usually simple. They differ, in the normal case, in both interaction strength (binding energy) and interaction length (structure). However, chemical bonding can be weak (e.g. in some metallic bonding) and physical binding can be strong (e.g. due to permanent electrostatic moments, hydrogen binding, etc) making differentiation non-trivial. But since these are shared-electron or unshared-electron interactions, respectively, it is in principle possible to distinguish the type of interaction by analyzing the electron density around the interaction point(s)/interface. After all, the former should be a contact while the latter should be a tunneling barrier. Here, we investigate within the framework of density functional theory typical molecules and crystals to show the behaviour of the electron localization function (ELF) in different shared-electron interactions, such as chemical (covalent) and metallic bonding and compare to unshared-electron interactions typical for physical binding, such as ionic, hydrogen and Keesom, dispersion (van der Waals) binding and attempt to categorise them only by the ELF and the electron population in the interaction region. It is found that the ELF method is not only useful for the characterization of covalent bonds but a lot of information can be extracted also for weaker types of binding. Furthermore, the charge integration over the interaction region(s) and tracing the ELF profile can reveal the strength of the bonding/binding ranging from the triple bonds to weak dispersion.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of ‘active matter’ in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics.

The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green’s-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

In the last two decades, plasmon resonance in gold nanoparticles (Au NPs) has been the subject of intense research efforts. Plasmon physics is intriguing and its precise modelling proved to be challenging. In fact, plasmons are highly responsive to a multitude of factors, either intrinsic to the Au NPs or from the environment, and recently the need emerged for the correction of standard electromagnetic approaches with quantum effects. Applications related to plasmon absorption and scattering in Au NPs are impressively numerous, ranging from sensing to photothermal effects to cell imaging. Also, plasmon-enhanced phenomena are highly interesting for multiple purposes, including, for instance, Raman spectroscopy of nearby analytes, catalysis, or sunlight energy conversion. In addition, plasmon excitation is involved in a series of advanced physical processes such as non-linear optics, optical trapping, magneto-plasmonics, and optical activity. Here, we provide the general overview of the field and the background for appropriate modelling of the physical phenomena. Then, we report on the current state of the art and most recent applications of plasmon resonance in Au NPs.

Atomistic modelling of magnetic materials provides unprecedented detail about the underlying physical processes that govern their macroscopic properties, and allows the simulation of complex effects such as surface anisotropy, ultrafast laser-induced spin dynamics, exchange bias, and microstructural effects. Here we present the key methods used in atomistic spin models which are then applied to a range of magnetic problems. We detail the parallelization strategies used which enable the routine simulation of extended systems with full atomistic resolution.

We report results from visible and UV Raman spectroscopy studies of the phonon spectra of a polycrystalline sample of the prototypical perovskite type oxide BaZrO ₃ and a 500 nm thick film of its Y-doped, proton conducting, counterpart BaZr _0.8Y _0.2O _2.9. Analysis of the Raman spectra measured using different excitation energies (between 3.44 eV and 5.17 eV) reveals the activation of strong resonance Raman effects involving all lattice vibrational modes. Specifically, two characteristic energies were identified for BaZrO ₃, one around 5 eV and one at higher energy, respectively, and one for BaZr _0.8Y _0.2O _2.9, above 5 eV. Apart from the large difference in spectral intensity between the non-resonant and resonant conditions, the spectra are overall similar to each other, suggesting that the vibrational spectra of the perovskites are stable when investigated using an UV laser as excitation source. These results encourage further use of UV Raman spectroscopy as a novel approach for the study of lattice vibrational dynamics and local structure in proton conducting perovskites, and open up for, e.g., time-resolved experiments on thin films targeted at understanding the role of lattice vibrations in proton transport in these kinds of materials.

In quantum technologies, point defects in semiconductors are becoming more significant. Understanding the frequency, intensity, and polarization of the zero phonon line is important. The last two properties are the subject of this paper. I present a method for calculating these properties and show the importance of using wave functions from both the ground and excited state. The validity of this method is demonstrated on the divacancy in 4H-SiC. Here, the calculated polarization and radiative lifetimes are in excellent agreement with experimental measurements. In general, this method can help to identify point defects and estimate suitable applications.

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, ‘skin-effect’, and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

W annier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of W annier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in W annier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green’s-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

yambo is an open source project aimed at studying excited state properties of condensed matter systems from first principles using many-body methods. As input, yambo requires ground state electronic structure data as computed by density functional theory codes such as Quantum ESPRESSO and Abinit. yambo’s capabilities include the calculation of linear response quantities (both independent-particle and including electron–hole interactions), quasi-particle corrections based on the GW formalism, optical absorption, and other spectroscopic quantities. Here we describe recent developments ranging from the inclusion of important but oft-neglected physical effects such as electron–phonon interactions to the implementation of a real-time propagation scheme for simulating linear and non-linear optical properties. Improvements to numerical algorithms and the user interface are outlined. Particular emphasis is given to the new and efficient parallel structure that makes it possible to exploit modern high performance computing architectures. Finally, we demonstrate the possibility to automate workflows by interfacing with the yambopy and AiiDA software tools.

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

In the quest for topological insulators with large band gaps, heterostructures with Rashba spin–orbit interactions come into play. Transition metal oxides with heavy ions are especially interesting in this respect. We discuss the design principles for stacking oxide Rashba layers. Assuming a single layer with a two-dimensional electron gas (2DEG) on both interfaces as a building block, a two-dimensional topological insulating phase is present when negative coupling between the 2DEGs exists. When stacking multiple building blocks, a two-dimensional or three-dimensional topological insulator is artificially created, depending on the intra- and interlayer coupling strengths and the number of building blocks. We show that the three-dimensional topological insulator is protected by reflection symmetry, and can therefore be classified as a topological crystalline insulator. In order to isolate the topological states from bulk states, the intralayer coupling term needs to be quadratic in momentum. It is described how such a quadratic coupling could potentially be realized by taking buckling within the layers into account. The buckling, thereby, brings the idea of stacked Rashba system very close to the alternative approach of realizing the buckled honeycomb lattice in [111]-oriented perovskite oxides.

Non-Hermitian generalizations of the Su–Schrieffer–Heeger (SSH) models with higher periods of the hopping coefficients, called the SSH3 and SSH4 models, are analyzed. The conventional construction of the winding number fails for the Hermitian SSH3 model, but the non-Hermitian generalization leads to a topological system due to a point gap on the complex plane. The non-Hermitian SSH3 model thus has a winding number and exhibits the non-Hermitian skin effect. Moreover, the SSH3 model has two types of localized states and a zero-energy state associated with special symmetries. The total Zak phase of the SSH3 model exhibits quantization, and its finite value indicates coexistence of the two types of localized states. Meanwhile, the SSH4 model resembles the SSH model, and its non-Hermitian generalization also exhibits the non-Hermitian skin effect. A careful analysis of the non-Hermitian SSH4 model with different boundary conditions shows the bulk-boundary correspondence is restored with the help of the generalized Brillouin zone or the real-space winding number. The physics of the non-Hermitian SSH3 and SSH4 models may be tested in various simulators.

Previous work has shown that thermodynamics properties calculated by phonon model with quasi-harmonic approximation (QHA) may differ badly from experiment in some cases. The inaccuracy was examined in the present work by comparing the results of QHA for argon and copper crystal with the ones of molecular dynamics simulations, partition functions obtained by a new method or experiment. It is shown that QHA works well for the systems of atomic volume smaller than 22 ų/atom and the accuracy gets lower and lower gradually with increasing of the atomic volume. Based on this fact, the disagreement (or agreement) between the thermodynamics properties of MgO, Si, CaO, ZrO₂ calculated in previous work by QHA and the experiments can be well understood.

For phonons propagating in a crystal at low temperature, we develop a phonon reflection model and an analysis framework to fully understand reflection peaks from underlying physics principles. Our study shows that the specular reflection structure of peaks contains detailed information about properties of the crystal material, and provides a solid quantitative link between phonon theory and experimental signals. For both kinds of experiments that either use crystal as a particle detector or as a target material for study, this analysis provides a novel and essential method to understand the experimental signatures.

All inorganic layer-by-layer (LbL) thin films composed by TiO₂ nanoparticles and [Al(OH)₄]⁻ anions (TiO₂/AlO_x) as well as Al₂O₃ and Nb₂O₅ nanoparticles (Al₂O₃/Nb₂O₅) have been deposited to fluorine-doped tin-oxide coated glass (FTO) surfaces and applied as blocking layers in dye-sensitized solar cells (DSCs). Structural and morphological characterization of the LbL films by different techniques reveal that in TiO₂/AlO_x assembly, aluminate anions undergo condensation reactions on the TiO₂ surface leading to the formation of highly homogeneous films with unique optical properties. After 25 depositions transmittance losses below 10% in relation to the bare FTO substrate are observed. Electrochemical impedance spectroscopy shows that TiO₂/AlO_x layers impose an effective barrier for the charge recombination at FTO/electrolyte interface with an electron exchange time constant 50-fold higher than that for bare FTO. As a result, an improvement of 85% in the overall conversion efficiency of DSCs was observed with the employment of TiO₂/AlO_x blocking layers. Al₂O₃/Nb₂O₅ LbL films can also work as blocking layers in DSCs but not as efficient, which is associated with the poor homogeneity of the film and its capacitive behavior. The production of cost-effective blocking layers with a low light scattering in the visible region is an important feature toward the application of DSC in other Building-integrated photovoltaic applications.

Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.

Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.

The excitation of magnetically ordered materials with ultrashort laser pulses results in magnetization dynamics on femto- to picosecond timescales. These non-equilibrium spin dynamics have emerged as a rapidly developing research field in recent years. Unraveling the fundamental microscopic processes in the interaction of ultrashort optical pulses with the charge, spin, orbital, and lattice degrees of freedom in magnetic materials shows the potential for controlling spin dynamics on their intrinsic timescales and thereby bring spintronics applications into the femtosecond range. In particular, femtosecond spin currents offer fascinating new possibilities to manipulate magnetization in an ultrafast and non-local manner, via spin injection and spin transfer torque at the interfaces of ferromagnetic layered structures. This topical review covers recent progress on spin dynamics at interfaces on femtosecond time scales. The development of the field of ultrafast spin dynamics in ferromagnetic heterostructures will be reviewed, starting from spin currents propagating on nanometer length scales through layered structures before focusing on femtosecond spin transfer at interfaces. The properties of these ultrafast spin-dependent charge currents will be discussed, as well as the materials dependence of femtosecond spin injection, the role of the interface properties, and competing microscopic processes leading to a loss of spin polarization on sub-picosecond timescales.

Dating back to the late 1980s, bulk metallic glasses (BMGs) are relatively new materials that exhibit exceptional mechanical properties (strength, hardness, fracture toughness, stored elastic energy …), compared to those of most crystalline metallic alloys. Their apparent brittleness under uniaxial loading, however, is still a major obstacle to their industrialization. Moreover, BMGs often contain crystalline defects developed, intentionally or not, during their complex and delicate elaboration. These flaws are known to affect their fracture toughness and their plastic behavior. This paper reviews twenty years of works about this subject on Zr-based BMGs that may contain a low volume fraction of crystalline defects of different natures, e.g. dendrites or spherulites, depending on the synthesis method. Dedicated experimental set-ups, mainly bending tests on notched beams, were developed to create in the specimen a proper pre-crack by fatigue and then load it monotonically up to fracture. The measured fracture toughness and the fractographic observations allow to conclude that these crystalline defects facilitate pre-cracking, but result in an embrittlement that is more or less significant depending on their type. The loading mode of the crack — mode I, II or mixed — as well as the temperature were shown to play a key role in crack initiation and propagation, whether steadily or catastrophically, in the BMG. By means of finite element computations analyses, explanations on how the crystalline flaws presence can affect fracture toughness and perturbate crack growth, under mode I and mode II, were proposed. Finally, the relevance of these experimental techniques as well as the link between crystalline defects, fracture toughness and their consequences on the ductility of a structural component are discussed.

Through coupling optical processes with the scanning tunneling microscope (STM), single-molecule chemistry and physics have been investigated at the ultimate spatial and temporal limit. Electrons and photons can be used to drive interactions and reactions in chemical systems and simultaneously probe their characteristics and consequences. In this review we introduce and review methods to couple optical imaging and spectroscopy with scanning tunneling microscopy. The integration of the STM and optical spectroscopy provides new insights into individual molecular adsorbates, surface-supported molecular assemblies, and two-dimensional materials with subnanoscale resolution, enabling the fundamental study of chemistry at the spatial and temporal limit. The inelastic scattering of photons by molecules and materials, that results in unique and sensitive vibrational fingerprints, will be considered with tip-enhanced Raman spectroscopy. STM-induced luminescence examines the intrinsic luminescence of organic adsorbates and their energy transfer and charge transfer processes with their surroundings. We also provide a survey of recent efforts to probe the dynamics of optical excitation at the molecular level with scanning tunneling microscopy in the context of light-induced photophysical and photochemical transformations.

Comparing quantum oscillation measurements, dc magnetoresistance measurements, and Fermi surfaces obtained from LDA calculations, we argue that the metamagnetic transition of UPt ₃, which occurs at an applied field μ _◦ H _M ∼ 20 T, coincides with a Lifshitz transition at which an open orbit on the band 2 hole-like Fermi surface becomes closed for one spin direction. At low field, proximity of the Fermi energy to this particular van Hove singularity may have implications for the superconducting pairing potential of UPt ₃. In our picture the magnetization comes from non-linear spin-splitting of the heavy fermion bands. In support of this, we show that the non-linear field dependence of a particular quantum oscillation frequency can be fitted by assuming that the corresponding extremal Fermi surface area is proportional to the magnetization. In addition, below H _M , we find in our LDA calculations a new, non-central orbit on band 1, whose non-linear behaviour explains a field-dependent frequency recently observed in magnetoacoustic quantum oscillation measurements.

Topological insulators are characterized by the existence of band inversion and the possibility of the realization of surface states. Doping with a magnetic atom, which is a source of the time-reversal symmetry breaking, can lead to realization of novel magneto-electronic properties of the system. In this paper, we study effects of substitution by the transition metal ions (Mn, Fe, Co and Ni) into Bi ₂Se ₃ on its electric properties. Using the ab inito supercell technique, we investigate the density of states and the projected band structure. Under such substitution the shift of the Fermi level is observed. We find the existence of nearly dispersionless bands around the Fermi level associated with substituted atoms, especially, in the case of the Co and Ni. Additionally, we discuss the modification of the electron localization function as well as charge and spin redistribution in the system. Our study shows a strong influence of the transition metal-Se bond on local modifications of the physical properties. The results are also discussed in the context of the interplay between energy levels of the magnetic impurities and topological surface states.

In this work, we study the extended Falicov–Kimball model at half-filling within the Hartree–Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density–density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2 V for small temperatures as well as correct features of the continuous order–disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal–insulator transitions found within the DMFT.

Entanglement of two different quantum orders is of an interest of the modern condensed matter physics. One of the examples is the dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization. We investigate this effect at finite temperature and demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP). We calculate the magnetic susceptibility of a bulk sample on the paraelectric side of the FE QCP at finite temperature and find enhanced magnetic susceptibility near the FE QCP. We propose quantum paraelectric strontium titanate as a candidate material to search for dynamic multiferroicity. We estimate the magnitude of the magnetic susceptibility for this material and find that it is detectable experimentally.

We show that topology is a very effective tool, to construct classical Hamiltonian time crystals. For this we numerically analyze a general class of time crystalline Hamiltonians that are designed to model the dynamics of molecular closed strings. We demonstrate how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted. The Hamiltonians that we investigate include a generalized Kratky–Porod wormlike chain model in combination with long range Coulomb and Lennard–Jones interactions. Such energy functions are commonplace in coarse grained molecular modeling. Thus we expect that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.

Using a recently developed approach to represent ab initio based force fields by a neural network potential, we perform molecular dynamics simulations of lead telluride and cadmium telluride crystals. In particular, we study the diffusion of a single cation interstitial in these two systems. Our simulations indicate that the interstitials migrate via two distinct mechanisms: through hops between interstitial sites and through exchanges with lattice atoms. We extract activation energies for both of these mechanisms and show how the temperature dependence of the total diffusion coefficient deviates from Arrhenius behaviour. The accuracy of the neural network approach is estimated by comparing the results for three different independently trained potentials.

The magnetocrystalline anisotropy of GdRh ₂Si ₂ is examined in detail via the electron spin resonance (ESR) of its well-localised Gd ³⁺ moments. Below T _N = 107 K, long range magnetic order sets in with ferromagnetic layers in the ( aa)-plane stacked antiferromagnetically along the c-axis of the tetragonal structure. Interestingly, the easy-plane anisotropy allows for the observation of antiferromagnetic resonance at X- and Q-band microwave frequencies. In addition to the easy-plane anisotropy we have also quantified the weaker fourfold anisotropy within the easy plane. The obtained resonance fields are modelled in terms of eigenoscillations of the two antiferromagnetically coupled sublattices. Conversely, this model provides plots of the eigenfrequencies as a function of field and the specific anisotropy constants. Such calculations have rarely been done. Therefore our analysis is prototypical for other systems with fourfold in-plane anisotropy. It is demonstrated that the experimental in-plane ESR data may be crucial for a precise knowledge of the out-of-plane anisotropy.

A polycrystalline sample of Sr ₂ScFeAsO ₃ was studied by ⁵⁷Fe Mössbauer spectroscopy down to 1.7 K. In contrast to the earlier Mössbauer data, the obtained in this work results indicate that Sr ₂ScFeAsO ₃ is in paramagnetic state down to 10 K, while the spectra recorded at 4.6 K and 1.7 K show a weak magnetic order of Fe moments in the Fe ₂As ₂ layers. Temperature dependences of isomer shift and quadrupole splitting/shift are compared with specific heat and electrical resistivity data from earlier investigations revealing different local Debye temperatures for the Fe ₂As ₂ and perovskite-related Sr ₂ScO ₃ layers. Finally, a fast decrease of the carrier density was observed below 80 K and this effect seems to be responsible for the absence of superconductivity in the studied compound.

Broadband dielectric and AC conductivity spectra (1 Hz to 1 THz) of the superprotonic single crystal Rb ₃H(SeO ₄) ₂ (RHSe) along the c axis were studied in a wide temperature range 10 K < T < 475 K that covers the ferroelastic ( T < 453 K) and superprotonic ( T > 453 K) phases. A contribution of the interfacial electrode polarization layers was separated from the bulk electrical properties and the bulk DC conductivity was evaluated above room temperature. The phase transition to the superprotonic phase was shown to be connected with the steep but almost continuous increase in bulk DC conductivity, and with giant permittivity effects due to the enhanced bulk proton hopping and interfacial electrode polarization layers. The AC conductivity scaling analysis confirms validity of the first universality above room temperature. At low temperatures, although the conductivity was low, the frequency dependence of dielectric loss indicates no clear evidence of the nearly constant loss effect, so-called second universality. The bulk (intrinsic) dielectric properties, AC and DC conductivity of the RHSe crystal at frequencies up to 1 GHz are shown to be caused by the thermally activated proton hopping. The increase of the AC conductivity above 100 GHz could be assigned to the low-frequency wing of proton vibrational modes.

A relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Previously, different proper relativistic spin operators have been proposed, such as spin operators of the Foldy–Wouthuysen and Pryce type, that both commute with the free-particle Dirac Hamiltonian and represent constants of motion. Here we consider the dynamics of a relativistic electron spin in an external electromagnetic field. We use two different Hamiltonians to derive the corresponding spin dynamics. These two are: (a) the Dirac Hamiltonian in the presence of an external field, and (b) the semirelativistic expansion of the same. Considering the Foldy–Wouthuysen and Pryce spin operators we show that these lead to different spin dynamics in an external electromagnetic field, which offers possibilities to distinguish their action. We find that the dynamics of both spin operators involve spin-dependent and spin-independent terms, however, the Foldy–Wouthuysen spin dynamics additionally accounts for the relativistic particle-antiparticle coupling. We conclude that the Pryce spin operator provides a suitable description of the relativistic spin dynamics in a weak-to-intermediate external field, whereas the Foldy–Wouthuysen spin operator is more suitable in the strong field regime.