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Consider a polynomial F such that each variable appears in exactly one monomial. The hypersurface defined by the polynomial F is called a hypersurface with separable variables. A variety is called rigid if there are no nontrivial actions of the additive group of the ground field on it. If a variety is rigid, then it is known that in the automorphism group there exists a unique maximal torus. We describe the automorphism group of a rigid hypersurface with separable variables, in particular we show that it is a finite extension of the maximal torus.

Influence of the prolonged irradiation by fission products of 252Cf radionuclide on the operational parameters of silicon-lithium Si(Li) p-i-n detectors, Si surface barrier detectors and Si planar p+n detector was investigated. The obtained results revealed a linear shift of the fission fragment peaks positions towards the lower energies with increase of the irradiation dose for all investigated detectors. The rate of the peaks shift was found to depend strongly on the detector type and the strength of the electric field in the detectors active region, but not on the temperature of irradiation (room or liquid nitrogen temperature). Based on the obtained results, the possibility of integration of the investigated types of Si semiconductor detectors in a radionuclide neutron calibration source is considered., Comment: 6 pages, 2 figures, 1 table

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero. An affine algebraic variety $X$ over $\mathbb{K}$ is toral if it is isomorphic to a closed subvariety of a torus $(\mathbb{K}^*)^d$. We study the group $\mathrm{Aut}(X)$ of regular automorpshims of a toral variety $X$. We prove that if $T$ is a maximal torus in $\mathrm{Aut}(X)$, then $X$ is a direct product $Y\times T$, where $Y$ is a toral variety with a trivial maximal torus in the automorphism group. We show that knowing $\mathrm{Aut}(Y)$, one can compute $\mathrm{Aut}(X)$. In the case when the rank of the group $\mathbb{K}[Y]^*/\mathbb{K}^*$ is $\dim Y + 1$, the group $\mathrm{Aut}(Y)$ can be described explicitly.

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.

We present a description of the originally developed $\beta$-spectrometer consisting of two Si(Li)-detectors with sensitive area thickness above 8~mm and $4\pi$-geometry. The full absorption spectrometer allows for direct measurements of $\beta$-spectra, disregarding the corrections to the response function induced by the electron backscattering from the crystal surface. In case of $\beta$-spectra of transitions to the excited state of the daughter isotope additional 3" BGO-detector is used in order to detect the $\gamma$-quanta in coincidence with the pair of Si(Li)-spectrometers., Comment: 9 pages, 7 figures

The paper presents results of laboratory experiment modeling the interaction between Lunar magnetic anomalies and Solar wind. To model the LMA we use quadrupole magnetic field. The main dimentionless parameter of the problem, the ion inertia length relative to the mini-magnetosphere size, well corresponds between experiment and LMA conditions. The main result is measurement of the magnetically reflected proton fluxes, which show qualitative agreement to available satellite data.

Electrons in condensed matter may transition into a variety of broken-symmetry phase states due to electron-electron interactions. Applying diverse mean-field approximations to the interaction term is arguably the simplest way to identify the phase states theoretically possible in a given setting. Here, we explore electron-electron attraction in a two-band system comprising symmetric conduction and valence bands touching each other at a single point. We assume a mean-field pairing between the electrons having opposite spins, momenta, and, in contrast to the conventional superconducting pairing, residing in opposite bands, i.e., having opposite energies. We show that electrons transition into a novel correlated ground state if and only if the bands are flat enough, i.e. the transition is impossible in the case of conventional parabolic bands. Although this state is not superconducting in the usual sense and does not exhibit a gap in its excitation spectrum, it is nevertheless immune to elastic scattering caused by any kind of disorder, and is therefore expected to exhibit high electric conductivity at low temperature, mimicking the behavior of a real superconductor. Having in mind the recent experimental realizations of flat-band electronic systems in twisted multilayers, we foresee an exciting opportunity for observing a new class of highly conductive materials., Comment: 12 pages strongly revised

Excitonic insulators conduct neither electrons nor holes but bound electron-hole pairs, excitons. Unfortunately, it is not possible to inject and detect the electron and hole currents independently within a single semiconducting layer. However, interlayer excitonic insulators provide a spatial separation of electrons and holes enabling exciton current measurements. The problem is that the spatial separation weakens electron-hole pairing and may lead to interlayer exciton disassociation. Here we develop an explicitly solvable model to determine an interlayer separation that is strong enough to prevent electron and hole hopping across the layers but still allows for electron-hole pairing sufficient for transition into an interlayer excitonic insulator state. An ideal junction to realize such a state would comprise a pair of identical narrow-gap two-dimensional semiconductors separated by a wide-gap dielectric layer with low dielectric permittivity. The present study quantifies parameters of such a junction by taking into account interlayer coherence effects., Comment: 7 pages, 4 figures

A water monolayer squeezed between two solid planes experiences strong out-of-plane confinement effects while expanding freely within the plane. As a consequence, the transport of such two-dimensional water combines hydrodynamic and nanofluidic features, intimately linked with each other. In this paper, we propose and explicitly solve a non-linear hydrodynamic equation describing two-dimensional water flow with viscosity parameters deduced from molecular dynamic simulations. We demonstrate that the very ability of two-dimensional water to flow in short channels is governed by the second (dilatational) viscosity coefficient, leading to flow compression and velocity saturation in the high-pressure limit. The viscosity parameter values depend strongly on whether graphene or hexoganal boron nitride layers are used to confine 2D water that offers an interesting opportunity to obtain various nanofluids out of the same water molecules just by using alternate materials to fabricate the 2D channels., Comment: 10+ pages, 6 figures. The supplementary information and multimedia files are available via doi link to the Springer Nature publisher

2D water, confined by atomically flat layered materials, may transit into various crystalline phases even at room temperature. However, to gain full control over the crystalline state, we should not only confine water in the out of plane direction but also restrict its in plane motion, forming 2D water clusters or ribbons. One way to do this is by using an electric field, in particular the intrinsic electric field of an adjacent polar material. We have found that the crystalline phases of 2D water clusters placed between two hexagonal boron nitride hBN nanoribbons are crucially determined by the nanoribbons edges, the resulting polarity of the nanoribbons, and their interlayer distance. We make use of density functional theory with further assistance of molecular dynamics simulations to establish the comprehensive phase diagrams demonstrating transitions between liquid and solid phases and between the states of different crystalline orders. We also show that the crystalline orders are maintained when water flows between hBN channels under external pressure. Our results open a promising pathway towards the control of water structure and its flow by the use of the microscopic electric field of polar materials.

Being used in optoelectronic devices as ultra-thin conductor-insulator junctions, detailed investigations are needed about how exactly h-BN and graphene hybridize. Here, we present a comprehensive ab initio study of hot carrier dynamics governed by electron-phonon scattering at the h-BN/graphene interface, using graphite (bulk), monolayer and bilayer graphene as benchmark materials. In contrast to monolayer graphene, all multilayer structures possess low-energy optical phonon modes that facilitate carrier thermalization. We find that the h-BN/graphene interface represents an exception with comparatively weak coupling between low-energy optical phonons and electrons. As a consequence, the thermalization bottleneck effect, known from graphene, survives hybridization with h-BN but is substantially reduced in all other bilayer and multilayer cases considered. In addition, we show that the quantum confinement in bilayer graphene does not have a significant influence on the thermalization time compared to graphite and that bilayer graphene can hence serve as a minimal model for the bulk counterpart., Comment: 6 figures, journal article

Two-dimensional (2D) materials can roll up, forming stable scrolls under suitable conditions. However, the great diversity of materials and fabrication techniques has resulted in a huge parameter space significantly complicating the theoretical description of scrolls. In this Letter, we describe a universal binding energy of scrolls determined solely by their material parameters, the bending stiffness, and the Hamaker coefficient. Aiming to predict the stability of functionalized scrolls in water solutions, we consider the electrostatic double-layer repulsion force that may overcome the binding energy and flatten the scrolls. Our predictions are represented as comprehensive maps indicating the stable and unstable regions of a rolled-up conformation state in the space of material and external parameters. While focusing mostly on functionalized graphene in this work, our approach is applicable to the whole range of 2D materials able to form scrolls., Comment: The main text is as published in PRL with the supplemental material added

Research on 2D materials has been one of the fastest-growing fields in condensed matter physics and materials science in the past 10 years. The low dimensionality and strong correlations of 2D systems give rise to electronic and structural properties, in the form of collective excitations, that do not have counterparts in ordinary 3D materials used in modern technology. These 2D materials present extraordinary opportunities for new technologies, such as in flexible electronics. In this Review, we focus on plasmons, excitons, phonons and magnons in 2D materials. We discuss the theoretical formalism of these collective excitations and elucidate how they differ from their 3D counterparts.

In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a Z-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that can not be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing graded-wild automorphisms.

Gallium oxide with a corundum structure ({\alpha}-Ga2O3) has recently attracted great attention in view of electronic and photonic applications due to its unique properties including a wide band gap exceeding that of the most stable beta phase (\b{eta}-Ga2O3). However, the lower thermal stability of the {\alpha}-phase at ambient conditions in comparison with the \b{eta}-phase requires careful investigation of its resistance to other external influences such as ion irradiation, ion doping, etc. In this work, the structural changes under the action of Al+ ion irradiation have been investigated for a polymorphic gallium oxide layers grown by hydride vapor phase epitaxy on c-plane sapphire and consisting predominantly of {\alpha}-phase with inclusions of {\alpha}(\k{appa})-phase. It is established by the X-ray diffraction technique that inclusions of {\alpha}(\k{appa})-phase in the irradiated layer undergo the expansion along the normal to the substrate surface, while there is no a noticeable deformation for the {\alpha}-phase. This speaks in favor of the different radiation tolerance of various Ga2O3 polymorphs, especially the higher radiation tolerance of the {\alpha}-phase. This fact should be taken into account when utilizing ion implantation to modify gallium oxide properties in terms of development of efficient doping strategies.

Deterioration of the operation parameters of Al/SiO2/p-type Si surface barrier detector upon irradiation with alpha-particles at room temperature was investigated. As a result of 40-days irradiation with a total fluence of 8*10^9 {\alpha}-particles, an increase of {\alpha}-peak FWHM from 70 keV to 100 keV was observed and explained by increase of the detector reverse current due to formation of a high concentration of near mid-gap defect levels. Performed CV measurements revealed the appearance of at least 6*10^12 cm-3 radiation-induced acceptors at the depths where according to the TRIM simulations the highest concentration of vacancy-interstitial pairs was created by the incoming {\alpha}-particles. The studies carried out by current-DLTS technique allowed to associate the observed increase of the acceptor concentration with the near mid-gap acceptor level at EV+0.56 eV. This level can be apparently associated with V2O defects recognized previously to be responsible for the space charge sign inversion in the irradiated n-type Si detectors., Comment: 8 pages, 4 figures

Membranes are ubiquitous in nature with primary functions that include adaptive filtering and selective transport of chemical and molecular species. Being critical to cellular functions, they are also fundamental in many areas of science and technology. Of particular importance are the adaptive and programmable membranes that can change their permeability or selectivity depending on the environment. Here, we explore implementation of such biological functions in artificial membranes and demonstrate two dimensional self assembled heterostructures of graphene oxide and polyamine macromolecules, forming a network of ionic channels that exhibit regulated permeability of water and monovalent ions. This permeability can be tuned by a change of pH or the presence of certain ions. Unlike traditional membranes, the regulation mechanism reported here relies on specific interactions between the membranes internal components and ions. This allows fabrication of membranes with programmable, predetermined permeability and selectivity, governed by the choice of components, their conformation and their charging state., Comment: Nat. Nanotechnol. (2020)

By a commutative action on a smooth quadric $Q_n$ in $P^{n+1}$ we mean an effective action of a commutative connected algebraic group on $Q_n$ with an open orbit. We show that for $n \geq 3$ all commutative actions on $Q_n$ are additive actions described by Sharoiko in 2009. So there is a unique commutative action on $Q_n$ up to equivalence. For $n = 2$ there are three commutative actions on $Q_2$ up to equivalence, for $n = 1$ there are two commutative actions on $Q_1$ up to equivalence.

The precision measurement of the $\beta-$spectrum shape for $^{210}$Bi (historically RaE) have been performed with a spectrometer based on semiconductor Si(Li) detector. This first forbidden non-unique transition has the transition form-factor strongly deviated from unity and knowledge of its spectrum would play an important role in low-background physics in presence of $^{210}$Pb background. The measured transition form-factor could be approximated as $S(W) = 1 + (-0.4363 \pm 0.0037) W + (0.0523 \pm 0.0010) W^2$, that is in good agreement with previous studies and has significantly increased parameter precision., Comment: 8 pages, 6 figures

Strong many-body interactions in two-dimensional (2D) semiconductors give rise to efficient exciton-exciton annihilation (EEA). This process is expected to result in the generation of unbound high energy carriers. Here, we report an unconventional photoresponse of van der Waals heterostructure devices resulting from efficient EEA. Our heterostructures, which consist of monolayer transition metal dichalcogenide (TMD), hexagonal boron nitride (hBN), and few-layer graphene, exhibit photocurrent when photoexcited carriers possess sufficient energy to overcome the high energy barrier of hBN. Interestingly, we find that the device exhibits moderate photocurrent quantum efficiency even when the semiconducting TMD layer is excited at its ground exciton resonance despite the high exciton binding energy and large transport barrier. Using ab initio calculations, we show that EEA yields highly energetic electrons and holes with unevenly distributed energies depending on the scattering condition. Our findings highlight the dominant role of EEA in determining the photoresponse of 2D semiconductor optoelectronic devices., Comment: 6 pages, 3 figures, two-column style

A search for resonant absorption of solar axions by $^{169}$Tm nuclei was carried out. A newly developed approach involving low-background cryogenic bolometer based on Tm$_3$Al$_5$O$_{12}$ crystal was used that allowed for significant improvement of sensitivity in comparison with previous $^{169}$Tm based experiments. The measurements performed with $8.18$ g crystal during $6.6$ days exposure yielded the following limits on axion couplings: $|g_{A\gamma} (g_{AN}^0 + g_{AN}^3) \leq 1.44 \times 10^{-14}$ GeV$^{-1}$ and $|g_{Ae} (g_{AN}^0 + g_{AN}^3) \leq 2.81 \times 10^{-16}$., Comment: 7 pages, 5 figures

Van der Waals semiconductor heterostructures could be a platform to harness hot photoexcited carriers in the next generation of optoelectronic and photovoltaic devices. The internal quantum efficiency of hot-carrier devices is determined by the relation between photocarrier extraction and thermalization rates. Using \textit{ab-initio} methods we show that the photocarrier thermalization time in single-layer transition metal dichalcogenides strongly depends on the peculiarities of the phonon spectrum and the electronic spin-orbit coupling. In detail, the lifted spin degeneracy in the valence band suppresses the hole scattering on acoustic phonons, slowing down the thermalization of holes by one order of magnitude as compared to electrons. Moreover, the hole thermalization time behaves differently in MoS$_2$ and WSe$_2$ because spin-orbit interactions differ in these seemingly similar materials. We predict that the internal quantum efficiency of a tunneling van der Waals semiconductor heterostructure depends qualitatively on whether MoS$_2$ or WSe$_2$ is used.

Electrons commonly couple through Fr\"ohlich interactions with longitudinal optical phonons to form polarons. However, trions possess a finite angular momentum and should therefore couple instead to rotational optical phonons. This creates a polaronic trion whose binding energy is determined by the crystallographic orientation of the lattice. Here, we demonstrate theoretically within the Fr\"ohlich approach and experimentally by photoluminescence emission that the bare trion binding energy (20 meV) is significantly enhanced by the phonons at the interface between the two-dimensional semiconductor MoS$_2$ and the bulk transition metal oxide SrTiO$_3$. The low-temperature {binding energy} changes from 60 meV in [001]-oriented substrates to 90 meV for [111] orientation, as a result of the counter-intuitive interplay between the rotational axis of the MoS$_2$ trion and that of the SrTiO$_3$ phonon mode., Comment: 5+ pages (4 figures) + Suppl. Materials (7 figures), to appear in Phys. Rev. Lett. (August 2020)

While cadmium telluride (CdTe) thin films are being used in solar cell prototyping for decades, the recent advent of two-dimensional (2D) materials challenges the fundamental limit for thickness of conventional CdTe layers. Here, we report our theoretical predictions on photocarrier dynamics in an ultimately thin (about 1 nm) CdTe slab. It corresponds to a layer that is just a single unit cell thick, when the bulk parent crystal in the zinc blende phase is cleaved along the [110] facet. Using an \textit{ab-initio} method based on density functional theory (DFT) and the Boltzmann equation in the relaxation time approximation (RTA), we determine the thermalization time for charge carriers excited to a certain energy for instance through laser irradiation. Our calculations include contributions arising from all phonon branches in the first Brillouin zone (BZ), thus capturing all relevant inter- and intraband carrier transitions due to electron-phonon scattering. We find that the photocarrier thermalization time is strongly reduced, by one order of magnitude for holes and by three orders of magnitude for electrons, once the CdTe crystal is thinned down from the bulk to a monolayer. Most surprisingly, the electron thermalization time becomes independent of the electron excess energy up to about 0.5~eV, when counted from the conduction band minimum (CBM). We relate this peculiar behavior to the degenerate and nearly parabolic lowest conduction band that yields a constant density of states (DOS) in the 2D limit. Our findings may be useful for designing novel CdTe-based optoelectronic devices, which employ nonequilibrium photoexcited carriers to improve the performance.

A purely electronic mechanism is proposed for the unconventional superconductivity recently observed in twisted bilayer graphene (tBG) close to the magic angle. Using the Migdal-Eliashberg framework on a one parameter effective lattice model for tBG we show that a superconducting state can be achieved by means of collective electronic modes in tBG. We posit robust features of the theory, including an asymmetrical superconducting dome and the magnitude of the critical temperature that are in agreement with experiments., Comment: 5 pages, 3 figures