An Erratum to this paper has been published: https://doi.org/10.1134/S0021364025050017

The simulation of the motion of ultracold neutrons is important for estimating their losses, accurately measuring their lifetimes, and describing other experiments. In material traps, it is necessary to take into account not only the specular reflection, but also the diffuse elastic reflection of ultracold neutrons from the walls of a trap. The angular distribution of diffusely reflected neutrons is usually described by Lambert’s cosine law, which does not have a strict theoretical justification and is often violated. In this work, an experiment has been proposed to measure the deviation of the angular distribution of diffusely reflected ultracold neutrons from Lambert’s cosine law. This deviation can be determined by the difference in the number of neutrons leaving a long, narrow trap for ultracold neutrons through its central and end windows. The performed Monte Carlo calculations corresponding to the proposed experiment have shown a significant effect for different shapes of the trap.

Layered van der Waals crystals of topologically non-trivial and trivial semimetals with antiferromagnetic (AFM) ordering of magnetic sublattice are known to exhibit a negative magnetoresistance that is well correlated with AFM magnetization changes in a magnetic field. This effect is reported in several experimental studies with EuFe2As2, EuSn2As2, EuSn2P2, etc., where the resistance decreases quadratically with field by about 5 T̂_2 symmetry. It is almost isotropic to the field and current directions, contrary to the known mechanisms such as giant magnetoresistance and chiral anomaly. The proposed intrinsic mechanism of magnetoresistance is strong in a wide class of the layered AFM-ordered semimetals. The theoretically calculated magnetoresistance is qualitatively consistent with experimental data for crystals of various composition. Layered van der Waals crystals with antiferromagnetic ordering can exhibit magnetoresistance, as observed experimentally in several semimetals. Here, a theoretical mechanism is proposed to describe magnetoresistance in antiferromagnetic metals.

Magnetic quantum oscillations (MQO) of Hall coefficient are measured in rare-earth tritelluride TmTe$_{3}$ and shown to be much stronger and persist to higher temperature than the Shubnikov oscillations. It is general for MQO in strongly anisotropic metals, and the combined measurements of Hall and diagonal magnetoresistance provide useful informations about the electronic structure. The ratio of their MQO amplitudes depends linearly on magnetic field, and its slope gives a simple and accurate measurement tool of the electron mean free time and its temperature dependence.

A film of liquid helium on the surface of material traps for ultracold neutrons protects the neutrons from being absorbed by the trap walls. By using surface roughness and an electrostatic field, it is possible to maintain a helium film of sufficient thickness throughout the height of the trap. The field distribution near the tip of such wall roughness of the trap was calculated, and the effect of this field on holding the helium film was estimated.

We study the scattering of edge states of 2D topological insulator in the uniform external magnetic field due to edge imperfections, common in realistic 2D topological insulator samples. The external magnetic field breaks time-reversal symmetry, opening the possibility of the scattering of otherwise topologically protected fermionic edge states. The scattering happens to be always an over-barrier event, irrespective of the shape of the edge deformation and magnitude of the magnetic field. We use the advanced Pokrovsky–Khalatnikov semiclassical approach, which allows us to obtain analytically both the main exponential and pre- exponential factors of the scattering amplitude for wide classes of analytic deformation profiles.

AbstractThe precise arrangement and nature of atoms drive electronic phase transitions in condensed matter. To explore this tenuous link, we developed a true biaxial mechanical deformation device working at cryogenic temperatures, compatible with x-ray diffraction and transport measurements, well adapted to layered samples. Here we show that a slight deformation of TbTe3 can have a dramatic influence on its Charge Density Wave (CDW), with an orientational transition from c to a driven by the a/c parameter, a tiny coexistence region near a = c, and without space group change. The CDW transition temperature Tc displays a linear dependence with $$\left\vert a/c-1\right\vert$$ a / c − 1 while the gap saturates out of the coexistence region. This behaviour is well accounted for within a tight-binding model. Our results question the relationship between gap and Tc in RTe3 systems. This method opens a new route towards the study of coexisting or competing electronic orders in condensed matter.

Modeling the motion of ultracold neutrons (UCNs) is crucial for assessing their losses, accurately measuring their lifetime, and describing other experiments. In material traps, it is necessary to account not only for specular but also for diffuse elastic reflection of UCNs from the trap walls. Typically, the Lambert cosine law is used to describe the angular distribution of diffusely scattered neutrons. However, this law lacks a rigorous theoretical derivation and is often violated. In our work, we propose an experiment to measure the deviation of the angular distribution of UCNs during diffuse scattering from the Lambert law. This deviation can be determined by the difference in the number of neutrons exiting through the central and end windows of a long narrow UCN trap. Monte Carlo simulations corresponding to a possible experiment have been performed, demonstrating a significant effect for different trap geometries.

We study the effects of imperfect nesting in a simple 2D tight-binding model on the electronic properties in the density-wave (DW) state. The discussed model reflects the main features of quasi-1D metals, where the DW emerges. We show that an imperfect nesting leads to unusual singularities in the quasi-particle density of states, leading to a strong renormalization of the superconducting critical temperature. We also compute the conductivity tensor of the normal state and obtain a satisfactory agreement with the experimental data on rare-earth tritellurides and many other DW materials.

Magnetic quantum oscillations (MQOs) are traditionally applied to investigate the electronic structure of metals. In layered quasi-two-dimensional (Q2D) materials, the MQOs have several qualitative features, offering additional helpful information, provided their theoretical description is developed. Within the framework of the Kubo formula and the self-consistent Born approximation, we reconsider the phase of the beats in the amplitude of the Shubnikov oscillations of the interlayer conductivity in Q2D metals. We show that the phase shift of the beats of the Shubnikov (conductivity) oscillations relative to the de Haas–van Alphen (magnetization) oscillations is larger than woud be expected and, under certain conditions, can reach the value of π/2, as observed experimentally. We explain the phase inversion of the MQOs during the 3D–2D crossover and predict the decrease in the relative MQO amplitude of the interlayer magnetoresistance in a strong magnetic field, larger than the beat frequency.

The most accurate neutron lifetime measurements now use the material or magnetic traps of ultracold neutrons (UCN). The precision of these experiments is determined by the accuracy of estimating the neutron loss rate. In material UCN traps the main source of neutron losses is the absorption by trap walls. In this paper we analyze the standard methods and their approximations for the calculation of UCN absorption rate by the walls of material traps. We emphasize the approximations used both in the standard analytical formulas and in the numerical Monte-Carlo simulations. For the two simplest trap geometries, rectangular and cylindrical, we obtain analytical formulas for this absorption rate provided the UCN velocity distribution is isotropic at trap bottom. Then we perform numerical calculations of UCN velocity distribution and absorption rate taking into account the diffuse elastic UCN reflections by trap walls obeying two different laws: Lambert`s cosine law and isotropic reflection. We compare the results with the standard estimation methods and discuss the differences. We indicate the difference between the UCN number and density velocity distribution. Our results may be useful to resolve the puzzling four-second discrepancy between the magnetic and material-trap measurements of neutron lifetime.

The behavior of the interlayer magnetoresistance Rzz is analyzed in quasi-two-dimensional layered metals in a magnetic field tilted at Yamaji angles at which the minimum of the interlayer conductivity is observed. The cases of the Lorentzian line shape of Landau levels and of the shape corresponding to the self-consistent Born approximation are studied. At high fields, the behavior Rzz ∝ B3/2 is theoretically predicted, which agrees well with experimental data.

Heterogeneous superconductivity onset is a common phenomenon in high-Tc superconductors of both the cuprate and iron-based families. It is manifested by a fairly wide transition from the metallic to zero-resistance states. Usually, in these strongly anisotropic materials, superconductivity (SC) first appears as isolated domains. This leads to anisotropic excess conductivity above Tc, and the transport measurements provide valuable information about the SC domain structure deep within the sample. In bulk samples, this anisotropic SC onset gives an approximate average shape of SC grains, while in thin samples, it also indicates the average size of SC grains. In this work, both interlayer and intralayer resistivity were measured as a function of temperature in FeSe samples of various thicknesses. To measure the interlayer resistivity, FeSe mesa structures oriented across the layers were fabricated using FIB. As the sample thickness decreases, a significant increase in superconducting transition temperature Tc is observed: Tc raises from 8 K in bulk material to 12 K in microbridges of thickness ∼40 nm. We applied analytical and numerical calculations to analyze these and earlier data and find the aspect ratio and size of the SC domains in FeSe consistent with our resistivity and diamagnetic response measurements. We propose a simple and fairly accurate method for estimating the aspect ratio of SC domains from Tc anisotropy in samples of various small thicknesses. The relationship between nematic and superconducting domains in FeSe is discussed. We also generalize the analytical formulas for conductivity in heterogeneous anisotropic superconductors to the case of elongated SC domains of two perpendicular orientations with equal volume fractions, corresponding to the nematic domain structure in various Fe-based superconductors.

The interplay between superconductivity (SC) and spin/charge density wave (DW) in organic metals shows many similarities to high-Tc superconductors. It also contains many puzzles, for example, the anisotropic SC onset observed and the severalfold increase of the upper critical field Hc2 in the coexistence region, as well as the microscopic origin of SC/DW phase separation there. In this paper, by the direct calculation of the Landau expansion for DW free energy, we argue that the phase transition between DW and metallic/SC phase in organic superconductors goes by first order at low-enough temperature, which explains the spatial segregation of DW and SC at large length scale, consistent with experimental observations. This first-order phase transition is not directly related to SC and happens even above the SC transition temperature.

We develop the theory of magnetoresistance oscillations in layered quasi-two-dimensional (quasi-2D) metals. Using the Kubo-Streda formula, we calculate the Hall intralayer conductivity in a magnetic field perpendicular to conducting layers. The analytical expressions for the amplitudes and phases of magnetic quantum oscillations (MQO) and of the difference or the so-called slow oscillations (SO) are derived as a function of several parameters: magnetic field strength, interlayer transfer integral, temperature, and the electron mean-free time. We calculate the quantum oscillations of the magnetoresistance tensor, because the magnetoresistance rather than conductivity is usually measured. We also discuss the averaging of magnetoresistance oscillations over MQO period due to finite temperature and long-range sample inhomogeneities. The results obtained are useful to analyze experimental data on magnetoresistance oscillations in various quasi-2D metals.

A new method is proposed for determining level splitting Δ in a double-well 1D potential. Two “partner” functions (one symmetric Ψ+ and the other antisymmetric Ψ–) are determined. From these functions, potentials V+(x) and V–(x) and energies E_ + ^0 and E_ - ^1 corresponding to them are determined from the Schrödinger equation. A unique property of Ψ+ and Ψ– is identity E_ + ^0 = E_ - ^1 , which makes it possible to determine Δ from the perturbation theory in parameter V+(x) – V–(x). For a double-well oscillator potential, the expression for the level splitting, which connects the instanton and single-well limits, is obtained. These results can be employed in the field theory, for which the possibility of obtaining instanton solutions from perturbation theory has been discussed more than once. A number of potentials are considered, for which the value of Δ can be determined without using the semiclassical approximation. Singular potentials of the funnel type are analyzed. The value of Δ determined in this study is compared with the results of numerical solution of the Schrödinger equation for the instanton potential.

Quantum and difference oscillations of interlayer conductivity in a multilayer system of thin films of topological insulators (TIs) are investigated. Due to the linearity of the carrier spectrum in such a system, new features of quantum oscillations arise. In particular, the frequencies of de Haas–van Alfvén and Shubnikov–de Haas oscillations depend quadratically on the chemical potential, rather than linearly as in systems with parabolic carrier spectrum. For the same reason, the temperature damping factor of oscillations contains the chemical potential. This is due to the nonequidistant character of the Landau levels: the higher the chemical potential, the smaller the distance between Landau levels. However, the beat frequencies, as well as the frequencies of slow oscillations, do not depend on the chemical potential; in this sense, the behavior of these systems is similar to that of conventional non-Dirac systems. Finally, in the Born approximation (in the second order cross-diagram technique), we considered the general case when the interlayer conductivity takes into account both intra- and interband transitions. We have shown that the contribution of intraband transitions is insignificant for the conductivity oscillations in the absence of magnetic impurities. However, in the presence of a Dirac point in the spectrum, a linear (in magnetic field) intraband contribution to conductivity arises from the zero Landau level. At low temperatures, this contribution is exponentially small compared to the intraband contribution and vanishes at zero temperature.

Most high-Tc superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure Pc, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg–Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)2PF6 samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors.

To increase the storage time of ultracold neutrons (UCN) inside the material traps it is promising to cover the trap walls by liquid 4He, the material which does not absorb neutrons at all. A rough side wall of UCN trap holds the required amount of 4He by the capillary effects, but the edges of wall roughness remain insufficiently coated. Here we propose to apply an electric voltage to these rough side walls of UCN traps to increases the thickness of liquid He on the wall edges and to cover the entire wall surface by sufficiently thick helium films. This completely protects UCN from being absorbed inside the trap walls. We estimate the required electric field and voltage for several possible designs of UCN traps. This improvement may give rise to a new generation of ultracold neutron traps with very long storage time. We also estimate the influence of this electric field on the dispersion of ripplons - the quanta surface waves, which give the main contribution to the inelastic UCN scattering at low temperature.

A new method of studying the properties and behavior of microparticles on the surface of liquids is proposed. According to this, the dynamics of polyamide-12 (PA-12) microgranules on the surface of water can be monitored using two techniques. In the first case, a drop of water containing granules is suspended on a glass substrate and viewed from below; the second case, a layer of water with PA-12 microparticles on the surface is observed from above. It is established that the microparticles in both cases are covered with a water film and do not contact with air, similar to glass microspheres with a density several times as low as that of water. As water evaporates, the microparticles remain fully immersed in small puddles. Using an interferometric technique, it was established that the deformation of water surface in suspended drop with PA-12 microgranules under the action of gravity cannot exceed several dozen nanometers. Observations showed that PA-12 microgranules with a density exceeding that of water stick to its surface while being localized beneath. Relationship of the proposed method with the experiment and theory for microparticles at the surface of liquid helium is traced.