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Thermoelectric effects in $p-n$ junctions are widely used for energy generation with thermal gradients, creation of compact Peltier refrigerators and, most recently, for sensitive detection of infrared and terahertz radiation. It is conventionally assumed that electrons and holes creating thermoelectric current are in equilibrium and share the common quasi-Fermi level. We show that lack of interband equilibrium results in an anomalous sign and magnitude of thermoelectric voltage developed across the $p-n$ junction. The anomalies appear provided the diffusion length of minority carriers exceeds the size of hot spot at the junction. Normal magnitude of thermoelectric voltage is partly restored if interband tunneling at the junction is allowed. The predicted effects can be relevant to the cryogenically cooled photodetectors based on bilayer graphene and mercury cadmium telluride quantum wells., Comment: 5 pages, 3 figures

By developing the mean-field theory valid for large $N$, we investigate the problem of two light fermions interacting via a zero-range potential with $N$ heavy fermions in two dimensions. We obtain numerical evidence that this system is never fully bound. It always splits into droplets containing a single light atom. This is in contrast to the one-dimensional case where any number of heavy and light fermions can be bound together., Comment: 11 pages, 1 figure

The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density $n$, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of $n$, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables., Comment: 36 pages, Proceedings of the International School of Physics "Enrico Fermi", Course 211 - Quantum Mixtures with Ultra-cold Atoms, July 2022

The Coulomb drag is a many-body effect observed in proximized low-dimensional systems. It appears as emergence of voltage in one of them upon passage of bias current in another. The magnitude of drag voltage can be strongly affected by exchange of plasmonic excitations between the layers; however, the reverse effect of Coulomb drag on properties of plasmons has not been studied. Here, we study the plasmon spectra and damping in parallel two-dimensional systems in the presence of Coulomb drag. We find that Coulomb drag leads to selective damping of one of the two fundamental plasma modes of a coupled bilayer. For identical electron doping of both layers, the drag suppresses the acoustic plasma mode; while for symmetric electron-hole doping of the coupled pair, the drag suppresses the optical plasma mode. The selective damping can be observed both for propagating modes in extended bilayers and for localized plasmons in bilayers confined by source and drain contacts. The discussed effect may provide access to the strength of Coulomb interaction in 2d electron systems from various optical and microwave scattering experiments.

We investigate the ground state properties of $N$ bosons with attractive zero-range interactions characterized by the scattering length $a>0$ and confined to the surface of a sphere of radius $R$. We present the analytic solution of the problem for $N=2$, mean-field analysis for $N\rightarrow \infty$, and exact diffusion Monte-Carlo results for intermediate $N$. For finite $N$, we observe a smooth crossover from the uniform state in the limit $a/R\gg 1$ (weak attraction) to a localized state at small $a/R$ (strong attraction). With increasing $N$ this crossover narrows down to a discontinuous transition from the uniform state to a soliton of size $\sim R/\sqrt{N}$. The two states are separated by an energy barrier, tunneling under which is exponentially suppressed at large $N$. The system behavior is marked by a peculiar competition between space-curvature effects and beyond-mean-field terms, both breaking the scaling invariance of a two-dimensional mean-field theory., Comment: 10 pages, 3 figures

We study binding of $N$ identical heavy fermions by a light atom in two dimensions assuming zero-range attractive heavy-light interactions. By using the mean-field theory valid for large $N$ we show that the $N+1$ cluster is bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being scale invariant in two dimensions, predicts only the shapes of the clusters leaving their sizes and energies undefined. By taking into account beyond-mean-field effects we find closed-form expressions for these quantities. We also discuss differences between the Thomas-Fermi and Hartree-Fock approaches for treating the heavy fermions., Comment: 11 pages, 3 figures

Microwave absorption spectra of a single square of two-dimensional electrons (2DES) have been investigated using an optical detection technique. Fundamental dipole and harmonic quadrupole plasmon modes have been identified and compared to those in the disk geometry. In the square-shaped 2DES, a strong interaction is discovered between the neighboring plasmon modes, whereas no such hybridization is observed in the disk-shaped geometry. We establish a rigid theoretical platform to analytically describe the magneto-optical response of confined two-dimensional systems. The developed theory provides a proper description of the obtained experimental results.

For sufficiently large mass ratios the attractive exchange force caused by a single light atom interacting with a few heavy identical fermions can overcome their Fermi degeneracy pressure and bind them into an $N+1$ cluster. Here, by using a mean-field approach valid for large $N$, we find that $N+1$ clusters can attract each other and form a self-bound charge density wave, the properties of which we fully characterize. Our work shows that there are no fundamental obstacles for having self-bound states in fermionic mixtures with zero-range interactions., Comment: 11 pages, 4 figures

We consider the problem of $N$ identical fermions interacting via a zero-range attractive potential with a lighter atom in one dimension. Using the few-body approach based on the Skorniakov and Ter-Martirosian equation, we determine the energies and the critical mass ratios for the emergence of the tetramer, pentamer, and hexamer. For large $N$, we solve the problem analytically by using the mean-field theory based on the Thomas-Fermi approximation. The system becomes bound when the heavy-to-light mass ratio exceeds a critical value which grows as $N^3$ at large $N$. We also employ a more sophisticated Hartree-Fock approach, which turns out to be equivalent to the Thomas-Fermi approximation for determining the energies, but provides a better description of the microscopic structure of the clusters., Comment: 6 pages, 2 figures

The atomic structure of well-ordered single steps on the Si(111)-\sqrt{3}\times\sqrt{3}-Sn surface and the dynamics of Sn adatoms in the vicinity of these steps was studied. The work was performed using low-temperature scanning tunneling microscopy (STM) and ab initio calculations based on the density-functional theory. The STM tip was used to record the tunneling current versus time on top of oscillating adatoms, keeping the feedback loop turned off. The dynamics of adatoms, detected as the telegraph noise present in the tunneling current, was registered near the steps at 80 K. The atomic structure model of the single steps consisting of Sn atomic chains along the steps was developed. This structure leads to the formation of potential double wells near the steps acting as traps for Sn atoms and explains the fluctuating current recorded in these areas., Comment: 9 pages, 8 figures

The Yakutsk Extensive Air Shower Array has been continuously operating for more than 50 years (since 1970) and up until recently it has been one of world's largest ground-based instruments aimed at studying the properties of cosmic rays in the ultra-high energy domain. In this report we discuss results recently obtained at the array - on cosmic rays energy spectrum, mass composition and directional anisotropy - and how they fit into the world data. Special attention is paid to the measurements of muonic component of extensive air showers. Theoretical results of particle acceleration at shocks are also briefly reviewed. Future scientific and engineering plans on the array modernization are discussed., Comment: 24 pages, 7 figures. Accepted for publication in Physics of Atomic Nuclei. For color figures see ISCRA-2021 contribution: https://indico.nevod.mephi.ru/event/6/contributions/161/

Sound propagation in the ocean is considered. We demonstrate a novel algorithm for full wavefield reconstruction using pointwise measurements by means of a vertical array. The algorithm is based on the so-called discrete variable representation and can be implemented both for tonal and pulse signals. It is shown that the algorithm is robust against array distortions and ambient noise of moderate amplitude. Efficiency of reconstruction is verified by means of numerical simulation with a model of a shallow-sea waveguide. It is found that the effect of bottom sound attenuation enables accurate reconstruction with arrays having relatively low density of hydrophones., Comment: 20 pages, 10 figures

The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent cubic pyramids and invariant bipentatopes. The theoretical properties of the refinement strategy are rigorously analyzed and evaluated. In addition, a new class of fully symmetric quadrature rules with positive weights are generated for the cubic pyramid. These rules are capable of exactly integrating polynomials with degrees up to 12. Their effectiveness is successfully demonstrated on polynomial and transcendental functions. Broadly speaking, the refinement strategy and quadrature rules in this paper open new avenues for four-dimensional hybrid meshing, and space-time finite element methods., Comment: 30 pages, 15 figures

We develop the perturbation theory for bosons interacting via a two-body potential $V$ of vanishing mean value. We find that the leading nonpairwise contribution to the energy emerges in the third order in $V$ and represents an effective three-body interaction, the sign of which in most cases (although not in general) is anticorrelated with the sign of the long-range tail of $V$. Explicit results are obtained for a few particular two-body interaction potentials and we perform a detailed perturbative analysis of tilted dipoles in quasi-low-dimensional geometries., Comment: 11 pages, 1 figure

Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect which occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments., Comment: 2 figures; 9 pages

Detectors of high-frequency radiation based on high-electron-mobility transistors benefit from low noise, room-temperature operation, and the possibility to perform radiation spectroscopy using gate-tunable plasmon resonance. Despite successful proof-of-concept demonstrations, the responsivity of transistor-based detectors of THz radiation, at present, remains fairly poor. To resolve this problem, we propose a class of devices supporting singular plasmon modes, i.e. modes with strong electric fields near keen electrodes. A large plasmon-enhanced electric field results in amplified non-linearities, and thus efficient ac-to-dc conversion. We analyze sub-terahertz detectors based on a two-dimensional electron system (2DES) in the Corbino geometry as a prototypical and exactly solvable model and show that the responsivity scales as $1/r_0^{2}$ with the radius of the inner contact $r_0$. This enables responsivities exceeding 10 kV/W at sub-THz frequencies for nanometer-scale contacts readily accessible by modern nanofabrication techniques., Comment: 6 paged, 5 figures

We theoretically demonstrate that dc electron flow across the junction of two-dimensional electron systems leads to excitation of edge magnetoplasmons. The threshold current for such plasmon excitation does not depend on contact effects and approaches zero for ballistic electron systems, which makes a strong distinction from the well-known Dyakonov-Shur and Cerenkov-type instabilities. We estimate the competing plasmon energy gain from dc current and loss due to electron scattering. We show that plasmon self excitation is feasible in GaAs-based heterostructures at $T\lesssim 200$ K and magnetic fields $B \lesssim 10$ T., Comment: 6 pages, 3 figures

We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE., Comment: 5 pages, 1 figure

We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion., Comment: 3 figures

We calculate the effective three-body force for bosons interacting with each other by a two-body potential tuned to a narrow zero crossing in any dimension. We use the standard two-channel model parametrized by the background atom-atom interaction strength, the amplitude of the open-channel to closed-channel coupling, and the atom-dimer interaction strength. The three-body force originates from the atom-dimer interaction, but it can be dramatically enhanced for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This effect can be used to stabilize quasi-two-dimensional dipolar atoms and molecules., Comment: published version

Perturbation theory is an indispensable tool in quantum mechanics and electrodynamics that handles weak effects on particle motion or fields. However, its extension to plasmons involving complex motion of {\it both} particles and fields remained challenging. We show that this challenge can be mastered if electron motion obeys the laws of hydrodynamics, as recently confirmed in experiments with ultra-clean heterostructures. We present a unified approach to evaluate corrections to plasmon spectra induced by carrier drift, magnetic field, Berry curvature, scattering, and viscosity. As a first application, we study the stability of direct current in confined two-dimensional electron systems against self-excitation of plasmons. We show that arbitrarily weak current in the absence of dissipation is unstable provided the structure lacks mirror symmetry. As a second application, we indicate that in extended periodic systems -- plasmonic crystals -- carrier drift induces anomalous Doppler shift, which can be both below and higher than its value in uniform systems. Finally, we exactly evaluate the effect of Berry curvature on spectra of edge plasmons and demonstrate the non-reciprocity induced by anomalous velocity.