Institution - L.D. Landau Institute for Theoretical Physics (RAS)
Recently, there has been increasing interest in studying the behavior of many-particle systems in nonequilibrium states. The development of experimental platforms simulating such systems (for example, ultracold atoms and exciton-polariton systems) entails the need to construct an appropriate theory. In this paper, we consider a two-band dissipative fermionic system proposed in [1]. It is a two-dimensional fermionic gas with a quadratic spectrum corresponding to a topological insulator and subject to dissipation in the framework of the Gorini-Kosakovski-Sudarshan-Lindblad (GKSL) equation. The introduced Lindblad operators preserve the number of particles and are aimed at transferring the population from the upper zone of the Hamiltonian spectrum to the lower one. The dissipation is conceived in such a way as to stabilize the ground state of the Hamiltonian, the dark state, corresponding to the complete filling of the lower zone due to the depletion of the upper one. In the paper [2], which has not yet been published, it is shown that in the model under study there is an interval of spatial and temporal scales with diffusive dynamics of quasiparticles. We emphasize that diffusion arises due to operators of \"quantum jumps\" in the absence of any disorder. The aim of our work is a more complete description of the diffusive regime. Using the approach of the Keldysh functional integral for the GKSL equation [3], we obtained an expression for the diffuson describing the dynamics of quasiparticles near the bottom of the upper band. The derived diffusion coefficient is inversely proportional to the dissipation force and coincides with the result of [2]. The self-energy of diffusons was also calculated, which is related to the diagrams beyond the ladder approximation. The work is supported by the RSF project 22-22-00641. References [1] F. Tonielli, J. C. Budich, A. Altland, S. Diehl, Phys. Rev. Lett. 124, 240404 (2020). [2] P. A. Nosov, D. S. Shapiro, M. Goldstein, I. S. Burmistrov, arXiv:2301.05258 (2023). [3] L. M. Sieberer, M. Buchhold, S. Diehl, Rep. Prog. Phys. 79, 096001 (2016).
Institution - Princeton University
We consider quantum field theory with selfinteractions in various patches of Minkowski and de Sitter space-times. Namely, in Minkowski space-time we consider separately right (left) Rindler wedge, past wedge and future wedge. In de Sitter space-time we consider expanding Poincare patch, static patch, contracting Poincare patch and global de Sitter itself. In all cases we restrict our considerations to the isometry invariant states leading to maximally analytic propagators. We prove that loop corrections in right (left) Rindler wedge, in the past wedge (of Minkowski space-time), in the static patch and in the expanding Poincare patch (of de Sitter space-time) respect the corresponding isometries of the corresponding symmetric space-times. All these facts are related to the causality and analyticity properties of the propagators for the states that we consider. At the same time in the future wedge, in the contracting Poincare patch and in global de Sitter space-time infrared effects violate the isometries. Besides, we discuss IR divergences in the contracting Poincare patch and resum them for quadratic interactions.
Institution - Landau Institute for Theoretical Physics
Minimal Liouville gravity is a toy model of two-dimensional quantum gravity, formulated using conformal field theory. Studying the correlation functions of a particular class of operators (\"tachyons\") in this model would allow to establish connection with other approaches, such as matrix models; however, \"first-principle\" calculation of such correlators is a difficult task. We will review some new results in this direction, such as the recently developed method to calculate analytically one-point correlators in torus topology and understanding the properties of these correlators in semiclassical limit via geometry of moduli spaces. The presentation is based on arXiv/2203.06629, arxiv/2210.14568 and some work in progress. This work was supported by the Russian Science Foundation grant (project no. 23-12-00333).
Institution - Ioffe Institute, 194021 St. Petersburg
We consider superlattice formed by tunnel-connected periodically placed identical holes in a 2D topological insulator. We study tunneling transport through helical edges of these holes and demonstrate that band structure of such helical crystal can be controlled by both gate electrodes and external magnetic field. For zero magnetic field and for fields corresponding to half-integer magnetic fluxes (in units of the flux quantum) through the holes, there are Weyl points in the spectrum whose positions as well as velocities in the corresponding Dirac cones can be tuned by gates. When magnetic field deviates from these special values, there appear gaps in the Dirac cones, which depend on magnetic field. For some values of parameters, double Weyl points appear. We investigate the effect of interaction, which leads to strong renormalization of the effective tunneling coupling and angle controlling tunnel spin flip processes. We plot renormalization flow in the plane and find that interaction leads to multicritical behavior of the crystal – there is a multicritical fully unstable fixed point separating three different phases: independent rings, independent shoulders, and perfect spin-flip channels. We also find that defects in the crystal lead to formation of topologically protected qubits which are not destroyed by temperature and can be also manipulated both by gates and by magnetic field. The possibility of purely electrical high-temperature control of the qubits opens a wide avenue for application in the area of quantum computing. The work was supported by the Russian Science Foundation (Grant No. 20-12- 00147).
Institution - Higher School of Economics (Moscow)
The use of edge modes for quantum computing is one of the prospective realizations of topological quantum computations. The ability of chiral edge states to move along the boundary without any manipulations from outside makes it possible to simplify quantum operations. We have shown the possibility of performing quantum computations using edge states in the honeycomb Kitaev model [1, 2]. Edge states were described for different types of sample boundaries of the Kitaev model and possible ways of performing quantum operations using these edge states were proposed. We demonstrated various methods of interaction between the edge of a sample and an external qubit, which provide an ability to \\'record\\' the state of the qubit as a superposition of edge modes. We have shown how this connection may be used to exchange quantum states of two external qubits interacting with the edge of the Kitaev model sample. We also numerically and analytically investigated the fidelity of this quantum operation for various types of noise - static δ-correlated disorder, δ-correlated 1/f noise, and spatially homogeneous noise. [1] I. L. Timoshuk, Y. G. Makhlin, arXiv:2302.10101 (2023). [2] I. L. Timoshuk, K. S. Tikhonov, Y. G. Makhlin, arXiv:2302.10123 (2023).
Institution - Landau Institute for Theoretical Physics of RAS
We study thermocapillary instability within small oblate droplet in a presence of the vertical heat flow. This formulation differs from that of the classical problem for a thin layer in two free surfaces and a finite lateral size (or a smooth variation of the layer height). Within the framework of the adiabatic approximation with respect to the small curvature of the drop surface and using the neutral stability curves for infinite plane layer, we obtained: • correction to the critical temperature gradient (δMac ∼ H/R); • localization size of the critical perturbation ∼ √ HR, which being parametrically smaller than the drop size, nevertheless contains many critical vortices. Using the analytical complete basis for the solutions of Stokes equation in spheroidal coordinates, a numerical solution of a generalized eigenvalue problem was obtained.
Institution - AIX-MARSEILLE UNIVERSITY
Liouville field theory was introduced by Polyakov in the eighties in the context of string theory. Liouville theory appeared there under the form of a 2D Feynman path integral, describing fluctuating metrics over Riemann surfaces. Since then, this theory has been extensively studied in physics and this interest has more recently spread among the maths community. I will review recent works with G. Baverez, C. Guillarmou, A. Kupiainen and V. Vargas about a probabilistic construction of the path integral describing this theory. Then I will explain how it led to a rigorous formulation of the conformal bootstrap for the Liouville model.
Institution - L. D. Landau Institute for Theoretical Physics, Semenova 1-a, 142432 Chernogolovka, Russia; Moscow Institute for Physics and Technology, 141700 Moscow, Russia
In this study, we explore the complex interactions between superconductivity and magnetism in superconductor-ferromagnet heterostructures in the form of an interplay between Néel-type skyrmions and Pearl vortices in thin heterostructures. Our analysis of stray fields reveals how the presence of a vortex-antivortex pair influences the skyrmion radius and highlights the potential for the spontaneous generation of these pairs under certain conditions when a Néel-type skyrmion is present [1]. Furthermore, we investigate the repulsion between Néel-type skyrmions and Pearl vortices in chiral ferromagnetic films [2], finding that the repulsion is suppressed when the dimensionless strength of the vortex magnetic field increases. This results in intricate changes in the free energy and equilibrium distance between the skyrmion and vortex. Finally, we develop a theory for the coaxial configuration of Néel-type skyrmions and Pearl vortices in thin superconductor-chiral ferromagnetic heterostructures [3]. By employing exact numerical solutions of the Euler-Lagrange equation and micromagnetic simulations, we show the significant impact of the Pearl vortex\\'s inhomogeneous magnetic field on the skyrmion profile, including a dramatic increase in skyrmion radius and the inversion of its chirality. We introduce a novel twoparameter ansatz to represent the magnetization profile of the skyrmion in the presence of the vortex, demonstrating that both the material parameters of the heterostructure and the thickness of the superconductor control chirality inversion and radius expansion. Our findings offer valuable insights into Majorana modes localized at skyrmion-vortex pairs and carry implications for future research in superconductivity and magnetism. [1] E.S. Andriyakhina, I.S. Burmistrov, \"Interaction of a Neel-type skyrmion with a superconducting vortex\", Phys. Rev. B 103, 174519 (2021) arxiv:2102.05434 [2] E.S. Andriyakhina, S. Apostoloff, I.S. Burmistrov, \"Repulsion of a Néel-type skyrmion from a Pearl vortex in thin ferromagnet-superconductor heterostructures\", Pis\\'ma v ZhETF, 116, 801 (2022) arxiv:2210.08790 [3] S.S. Apostoloff, E.S. Andriyakhina, P.A. Vorobyev, O.A. Tretiakov, I.S. Burmistrov, \"Chirality inversion and radius blow-up of a Néel-type skyrmion by a Pearl vortex\", arxiv:2212.08351
Institution - L. D. Landau Institute for Theoretical Physics, Semenova 1-a, 142432, Chernogolovka, Russia
Recently, studing of criticality in quantum systems has attracted a great interest. There are some theoretical evidences of SQHE in two dimensional superconducting system with dx2 -y2+id xy pairing [1]. In this study we develop the theory of the spin quantum Hall transition, using the generalization of Pruisken replica NLσM with θ-term [2] on superconducting class C [3,4]. Using NLσM action, we show presence of the non-trivial topological configurations of Q-matrix field, called instantons. To find the analytical form of such configurations with topological charge equals to one, we construct solutions of self-duality (anti-self-duality) equations, using the symmetries of target coset space G/K = Sp(2N )/U(N ). In Gaussian approximation we find action for small fluctuactions around the instanton. We find whole instanton manifold and identify eight instanton eigenparameters as zero modes of kinetic operators for fluctuations. Our aim is to compute instanton contribution to the partition function, density of states, longitudinal and transverse spin conductivities. Bibliography [1] Senthil, T., and M. P. A. Fisher, Phys. Rev. B 60 (1999) [2] A. M. M. Pruisken, Nucl. Phys. B 285, 719 (1987). [3] Ferdinand Evers and Alexander D. Mirlin \\\"Anderson transitions\\\". Rev. Mod. Phys. 80 (2008) [4] Babkin, S. S., and I. S. Burmistrov, Physical Review B 106.12 (2022). This work was supported by the Russian Science Foundation (Grant No. 22-42-04416)
Institution - L. D. Landau Institute for Theoretical Physics, Semenova 1-a, 142432, Chernogolovka, Russia
In recent years, transport properties of superconductive junctions have been an important topic. One of the proximity effects, detected in such structures, is Andreev reflections (AR)[2], which were studied. In this work, we consider long diffusive superconductor-normal metal-superconductor junctions with low transparency interfaces at sufficiently low temperatures, ETh ≪ T ≪Δ. In our computation, we take into account proximity effects alongside with inelastic scattering processes in a normal region, which leads to thermalization in the weak link. Our calculations reveal, that current-voltage characteristic of such a junction has peculiarities on specific values of voltage bias, corresponding to AR. Furthermore, we find that weak exchange field in normal region produces linear splitting of these peculiarities. We assume, that such splitting is a direct consequence of thermalization in normal region, therefore we propose a modification of Blonder-Tinkham-Klapwijk [1] semiconductor scheme of calculating voltages, corresponding to AR. References [1] M. Octavio, M. Tinkham, G. E. Blonder, and T. M. Klapwijk. Subharmonic energy-gap structure in superconducting constrictions. Phys. Rev. B, 27:6739–6746, Jun 1983. [2] Rafael Taboryski, Jonatan Kutchinsky, Jorn Bindslev Hansen, Morten Wildt, Claus B. Sorensen, and Poul Erik Lindelof. Multiple andreev reflections in diffusive sns structures. Superlattices and Microstructures, 25(5):829–837, 1999.
Institution - Moscow Institute of Physics and Technology
In this Letter we consider the out-of-equilibrium phenomena in the complex Sachdev-Ye-Kitaev (SYK) model supplemented with the attractive Hubbard interaction (SYK+U). This model provides the clear-cut transition from non-Fermi liquid phase in pure SYK to the superconducting phase through the pseudogap phase with non-synchronized Cooper pairs. We investigate the quench of the phase soft mode in this model and the relaxation to the equilibrium state. Using the relation with Hamiltonian mean field (HMF) model we show that the SYK+U model enjoys the several interesting phenomena, like violent relaxation, quasi-stationary long living states, out-of-equilibrium finite time phase transitions, non-extensivity and tower of condensates. We comment on the holographic dual gravity counterparts of these phenomena.
Institution - L.D. Landau Institute For Theoretical Physics
We calculate the quasiparticle density of states (DoS) inside the vortex core in a granular superconductor[1], generalizing the classical solution applicable for dirty superconductors [2]. A discrete version of the Usadel equation for a vortex is derived and solved numerically for a broad range of parameters. Electron DoS is found to be gapful when the vortex size ξ becomes comparable to the distance between neighboring grains l. Minigap magnitude Eg grows from zero at ξ≈1.4l to third of superconducting gap ∆0 at ξ ≈ 0.5l. The absence of low-energy excitations explains strong suppression of microwave dissipation in a mixed state of granular Al observed recentelly [3]. [1] D. E. Kiselov, M. A. Skvortsov and M. V. Feigel’man, arXiv:2212.01862v1 (2022) [2] R. J. Watts-Tobin and G. M. Waterworth, Z. Physik 261, 249 (1973). [3] B. L. T. Plourde, invited talk at the International Workshop “Localization, Interactions and Superconductivity”, Chernogolovka, Russia, June 30 – July 4, 2018.
Institution - Moscow Institute of Physics and Technology
Using the random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity inside a wave-chaotic cavity fed with incoming waves via a finite number of open channels, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that in the absence of internal losses the probability density for the single-point intensity decays as a powerlaw for large intensities. This behaviour is in marked difference with the Rayleigh law(exponential decay) which turns out to be valid only in the limit of infinite channels. We also find the joint probability density of intensities in L>1 observation points, and then extract the corresponding statistics for the minimal and maximal intensity in the observation pattern. For $L\\to \\infty$ the resulting limiting extreme value statistics (EVS) turns out to be very different from the classical EVS distributions.
Institution - Moscow Institute of Physics and Technology
This work is devoted to study of integrable structures in superconformal field theory and more general coset CFT’s related to the affine Yangian Y(gl(2)). We derive the relation between the RLL and current realizations and prove Bethe anzatz equations for the spectrum of Integrals of Motion
Institution - Moscow Institute of Physics and Technology
We consider Heisenberg spin chain with next nearest neighbour interaction. In work [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)] it was conjectured that this model is quasi-integrable. We examine this conjecture using Adiabatic Gauge Potential and construct the infinite set of quasi-conserved quantities explicitly.
Institution - Kirensky Institute of Physics
We studied the formation of a special type of magnetic skyrmions – in which the azimuthal angle of magnetization (vorticity) φ = n φ, where φ is the angle of polar coordinate system in the plane of the film and |n| > 1. Such structures are called higher- order magnetic skyrmions (HOMS) [1]. They are much less studied compared to the ordinary skyrmions because the Dzyaloshinskii–Moriya interaction does not stabilize such structures. The several models have been proposed in which HOMS arose due to frustrated exchange interaction [2, 3, 4]. However, such a mechanism requires a very fine selection of magnetic materials and lacks flexibility to change HOMS characteristics suitable for practical applications. In the work [5], we propose a new mechanism for the formation of HOMS, based on the orbital effects of the inhomogeneous magnetic field. Due to wide experimental possibilities for the creation of various magnetic field profiles, it is clear that the proposed mechanism may be more promising when creating HOMS, compared with the mechanisms described above. From the magnetic point of view, the orbital effects of the magnetic field are responsible for emergence of the so-called scalar chiral interaction, which in the case of homogeneous field is proportional to the density of the topological charge of magnetic structure, and in the inhomogeneous fields can lead to new structures. At the same time, we noticed that in strongly correlated electron systems, the contribution from the scalar chiral interaction to the HOMS energy can be comparable to that of the Dzyaloshinsky- Moriya interaction for ordinary skyrmions. Taking into account the hierarchy of effective spin interactions, an analytical theory on the optimal sizes of HOMS is developed for axially symmetric magnetic fields of the form h(r) ∼ r β . The HOMS themselves could act as promising carriers of Majorana modes in superconductor / ferromagnet hybrids [6]. The work was supported by the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools, Grant No. MK-4687.2022.1.2.
Institution - MIPT, LPI RAS
Out-of-time order correlation functions are widely used as a measure of quantum chaos and quantum butterfly effect, but give false-positive quantum Lyapunov exponents in integrable systems with unstable fixed points. I suggest an alternative measure of quantum chaos, which does not have this problem. To illustrate this approach, I numerically calculate ``true\\'\\' quantum Lyapunov exponents in the Lipkin-Meshkov-Glick and Feingold-Peres models, and analytically estimate the exponents in the large-N vector mechanics, SYK model, and JT gravity.
Institution - L. D. Landau Institute for Theoretical Physics
This work is devoted to the development of the problem of statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case when the external force is white noise, the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval was found in our recent work [1] using transfer matrix analysis of supersymmetric field theory. We generalize our approach to the case of finite time intervals and various initial and final conditions. Multipoint correlation functions are calculated, as well as the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory. [2] [1] N.A. Stepanov, M.A. Skvortsov, Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry, SciPost Phys. 13(2), 021 (2022). [2] Н.А. Степанов, М.А. Скворцов, Ляпуновская экспонента в задаче Уитни со случайной накачкой, Письма в ЖЭТФ, 112 (6), 394-400 (2020) [N.A. Stepanov, M.A. Skvortsov, Lyapunov exponent for Whitney’s problem with random drive, JETP Letters, 112(6), 376-382 (2020)]. [1] N.A. Stepanov, M.A. Skvortsov, Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry, SciPost Phys. 13(2), 021 (2022). [2] Н.А. Степанов, М.А. Скворцов, Ляпуновская экспонента в задаче Уитни со случайной накачкой, Письма в ЖЭТФ, 112 (6), 394-400 (2020) [N.A. Stepanov, M.A. Skvortsov, Lyapunov exponent for Whitney’s problem with random drive, JETP Letters, 112(6), 376-382 (2020)]. [1] N.A. Stepanov, M.A. Skvortsov, Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry, SciPost Phys. 13(2), 021 (2022). [2] Н.А. Степанов, М.А. Скворцов, Ляпуновская экспонента в задаче Уитни со случайной накачкой, Письма в ЖЭТФ, 112 (6), 394-400 (2020) [N.A. Stepanov, M.A. Skvortsov, Lyapunov exponent for Whitney’s problem with random drive, JETP Letters, 112(6), 376-382 (2020)]. [1] N.A. Stepanov, M.A. Skvortsov, Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry, SciPost Phys. 13(2), 021 (2022). [2] Н.А. Степанов, М.А. Скворцов, Ляпуновская экспонента в задаче Уитни со случайной накачкой, Письма в ЖЭТФ, 112 (6), 394-400 (2020) [N.A. Stepanov, M.A. Skvortsov, Lyapunov exponent for Whitney’s problem with random drive, JETP Letters, 112(6), 376-382 (2020)]. [1] N.A. Stepanov, M.A. Skvortsov, Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry, SciPost Phys. 13(2), 021 (2022). [2] Н.А. Степанов, М.А. Скворцов, Ляпуновская экспонента в задаче Уитни со случайной накачкой, Письма в ЖЭТФ, 112 (6), 394-400 (2020) [N.A. Stepanov, M.A. Skvortsov, Lyapunov exponent for Whitney’s problem with random drive, JETP Letters, 112(6), 376-382 (2020)].
Institution - L. D. Landau Institute for Theoretical Physics
We propose and study a theoretical model of insulators which show de Haas-van Alphen oscillations as well as periodic dependence of the magnetization on inverse temperature. The insulating behavior is due to the Coulomb interaction driven hybridization of fermions at the crossing point of their energy bands. We show that the leading contribution to the oscillations at small magnetic fields is due to the oscillatory dependence of the hybridization gap on the magnetic field. In order to see this the hybridization is derived from a self-consistent non-linear equation. We show that the amplitude of the de Haas-van Alphen is periodic in inverse temperature with a period defined by a combination of the hybridization gap and magnetic field. Based on these findings, we present arguments that a modification of our model to the heavy fermion system may explain the giant temperature peak experimentally observed in SmB$_6$.
Institution - MIPT, MI RAS
One of the most interesting directions in the study of integrable systems is the search for possible dualities between integrable models. Two well-known examples of such dualities are the spectral duality and the Ruijsenaars (or PQ-) duality. Spectral duality describes the duality between two spin systems that have a Lax representation that depends on the spectral parameter z. The spectral curves for such dual systems coincide; in particular, the trigonometric Gaudin model and the Heisenberg chain turn out to be spectral dual. The Ruijsenaars duality for N-particle systems builds a correspondence between the coordinate variables of one system and the action variables of another. Such a duality is known, for example, between the trigonometric Calogero model and the rational Ruijsenaars-Schneider model. We have shown that PQ-duality for these models can be described in terms of spectral duality. In particular, one can make a gauge transformation that adds dependence on the spectral parameter to the Lax matrix of the trigonometric Calogero system without changing the Lax equation. Having done such a transformation, we have shown that the resulting Lax matrix can be described as a degenerate Gaudin type Lax matrix. The spectrally dual system after the inverse gauge transformation of the Lax matrix turns into the Lax matrix of the PQ-dual rational Ruijsenaars-Schneider model. Hense we can consider PQ-duality as a special case of spectral duality.
Institution - MIPT, LPI RAS
We extend the powerful property of Yangian invariance to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. We formulate Yangian symmetry in terms of a chain of Lax operators acting on the fixed coordinates around the graph, and we also extend this construction to the case of infinite-dimensional auxiliary space. Yangian invariance leads to new differential and integral equations for individual, highly nontrivial, Feynman graphs, and we present them explicitly for several examples. The graphs we consider determine correlators in the recently proposed loom fishnet CFTs. We also describe a generalization to the case with interaction vertices inside open faces of the diagram. Our construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs.
Institution - YerPhI
We systematically construct two-dimensional $Z_3$ symmetry-protected topological (SPT) three-state Potts paramagnets with gapless edge modes on a triangular lattice. First, we study microscopic lattice models for the gapless edge and, using the density-matrix renormalization group (DMRG) approach, investigate the finite size scaling of the low-lying excitation spectrum and the entanglement entropy. Based on the obtained results, we identify the universality class of the critical edge, namely the corresponding conformal field theory and the central charge. Finally, we discuss the inherent symmetries of the edge models and the emergent winding symmetry distinguishing between two SPT phases. As a result, the two topologically nontrivial and the trivial phases define a general one-dimensional chain supporting a tricriticality, which we argue supports a gapless SPT order in one dimension.
Institution - Kirensky Institute of Physics
In this report, we will present the results of an analytical and numerical study of the Coulomb interaction problem in one of the standard models of a higher-order topological superconductor, which describes a 2D topological insulator on a square lattice with s±- superconducting pairing. In particular, attention is paid to both limiting cases: weak and strong charge correlations [1,2]. In the first situation, it is shown that the boundaries of the topologically nontrivial phase are extended due to the many-body interaction. For a system with open boundary conditions, a crossover of the ground state was found with increasing repulsion intensity. Before the crossover, the charge density distribution has C4 symmetry and does not depend on spin, and the energy of the Majorana corner state is determined by the overlap of the wave functions localized in different corners. After the crossover, the concentration correlator depends on the spin projection and has a spontaneously broken symmetry. In turn, the energy of the corner state ceases to depend on the size of the system. The dependence of this crossover on the shape of the boundary of the 2D system is discussed. The possibility to realize the Majorana corner states in the limit of the infinitely strong repulsion is demonstrated based on the analysis of the Dirac mass of edge states of Hubbard fermions induced by the superconducting pairing. It is shown that the boundaries of the topologically nontrivial phase become strongly renormalized due to the Hubbard corrections. In the regime of strong but finite Coulomb repulsion, the effective Hamiltonian of the higher-order topological superconductor is obtained. The study was supported by Russian Science Foundation Project No. 22-22-20076, and Krasnoyarsk Regional Fund of Science. [1] S. V. Aksenov, A. D. Fedoseev, M. S. Shustin, and A. O. Zlotnikov, Phys. Rev. B 107, 125401 (2023). [2] S. V. Aksenov, A. D. Fedoseev, M. S. Shustin, and A. O. Zlotnikov, Phys. Sol. St., in press (2023).x
Institution - Higher School of Economics (Moscow)
We investigate the coexistence of localized and delocalized states in the Anderson impurity model with a power-law hopping amplitude J ∝ r^{-β} with D < β < 3D/2, proposed by K.S. Tikhonov, A.S. Ioselevich, M. V. Feigel’man (2021). We demonstrate that, strictly speaking, the genuine localized states do not occur at E>0, but, instead of them, quasilocalized ones arise in the vicinity of optimal fluctuations. We provide a derivation of the explicit form for the quasilocalized wave function in the presence of the optimal fluctuation potential, determine the behavior of the Inverse Participation Ratio as a function of the energy and system size, and consider the effects of scattering at typical weak potential fluctuations.
Institution - L. D. Landau Institute for Theoretical Physics
We investigate the current-phase relation in a planar diffuse tunnelling SIS\\'IS-junction in which the S\\'-layer contains in addition a strong spin-orbit interaction and a Zeeman term. The possibility of calculating the current-phase relation depending on the phase jump of the order parameter at each boundary by perturbation theory methods allows us to find the current dependence on the applied magnetic field. Since taking into account the spin-orbit and Zeeman terms leads effectively to the appearance of an additional contribution to the vector potential, each harmonic of the current-phase relation is shifted, which as a consequence leads to the anomalous Josephson effect in this system.
Institution - Institute of Physics, Yerevan State University
The vacuum expectation values (VEVs) of the field squared and energy-momentum tensor for a massive scalar field with general curvature coupling parameter are investigated inside and outside a spherical shell in background of de Sitter (dS) spacetime. It is assumed that the field, obeying Robin boundary condition on the sphere, is prepared in the hyperbolic vacuum state. The latter differs from the maximally symmetric Bunch-Davies vacuum state and is realized by the mode functions corresponding to the foliation of dS spacetime by spatial sections having a constant negative curvature. In the flat spacetime limit the hyperbolic vacuum is reduced to the conformal vacuum in the Milne universe. The sphere-induced contributions in the VEVs are extracted explicitly and their behavior in various asymptotic regions of the parameters are investigated. An interesting sphere-induced effect is the appearance of the energy flux along the radial direction, which corresponds to the nonzero off-diagonal component of the vacuum energy-momentum tensor. The latter is a purely boundary-induced effect and is absent in the boundary-free geometry. Depending on the value of the coefficient entering in the boundary condition on the sphere, the energy flux can be directed either from the sphere or towards the sphere. Detailed asymptotic and numerical analysis are presented for the vacuum characteristics in both exterior and interior regions of the sphere. At early stages of the cosmological expansion the effects of the spacetime curvature on the sphere-induced VEVs are weak and the leading terms in the corresponding expansions coincide with those for a sphere in the Milne universe. The influence of the gravitational field is essential at late stages of the expansion. Depending on the field mass and the curvature coupling parameter, the decay of the sphere-induced VEVs, as functions of the time coordinate, is either monotonic or damping oscillatory. At large distances from the sphere, the fall-off of the sphere-induced VEVs, as functions of the geodesic distance, is exponential for both massless and massive fields.
Institution - Max Planck Institute for Solid State Research, Germany
We study localization phenomena in an SNS junction with a disordered metallic wire of length $L$ as its normal part. Standard description of the Josephson effect in such systems is based on the Usadel equation. Depending on the ratio between $L$ and superconducting coherence length $\\\\\\\\xi$, two limiting cases of short and long junctions are distinguished. For short junctions $L \\\\\\\\ll \\\\\\\\xi$, Josephson current is proportional to the superconducting gap and to the normal conductance of the junction and hence obeys the Ambegaokar-Baratoff relation. For a long junction $L \\\\\\\\gg \\\\\\\\xi$, the current is given by a similar relation but with the superconducting gap replaced by the Thouless energy of the wire. However, these classical results remain valid only while the junction is shorter than the localization length $\\\\\\\\xi_\\\\\\\\text{loc}$. In the opposite limit, localization effects become important and the quasiclassical Usadel equation is no longer valid. We develop a general theory of the Josephson effect taking into account all localization contributions. Our theory is based on the nonlinear sigma model and covers the limit of long junctions $L \\\\\\\\gg \\\\\\\\xi_\\\\\\\\text{loc}$ when a fully quantum description is required. We identify three qualitatively different regimes in this limit. One regime is an extension of the classical short wire limit. We show that critical current still obeys the Ambegaokar-Baratoff relation up to the length of the order of $\\\\\\\\xi_\\\\\\\\text{loc} \\\\\\\\ln^2(\\\\\\\\xi/\\\\\\\\xi_\\\\\\\\text{loc})$. Once this length is exceeded, an additional exponential factor suppresses the Josephson current. Finally, the third regime sets in when $L$ exceeds $\\\\\\\\xi_\\\\\\\\text{loc} \\\\\\\\ln^3(\\\\\\\\xi/\\\\\\\\xi_\\\\\\\\text{loc})$. In this limit suppressing factor grows much slower, as an exponent of $(L/\\\\\\\\xi_\\\\\\\\text{loc})^{1/3}$. If the length of a classically long Josephson junction exceeds $\\\\\\\\xi_\\\\\\\\text{loc}$, it immediately falls into the third regime. In all three cases, we have also found the current-phase relations.
Institution - Moscow Institute of Physics and Technology
A system consisting of a Rydberg atom and ultracold molecules is considered. Recently, it has been actively investigated in connection with possible applications in quantum computing. We have considered the dynamics of the system when one or more molecules are inside the Rydberg. A molecular blockade was obtained by analogy with the Rydberg blockade. Due to energy shifts and the existence of \"dark\" and \"light\" states, we can control optical excitations by using molecules. Moreover, a possible contraction in the effects of Rydberg blockade and molecular blockade has been shown. This may make it possible to selectively add 2-photon excitation for a pair of Rydberg atoms that completely banned in the Rydberg blockade.
Institution - Massachusetts Institute of Technology
We propose and study theoretically a new mechanism of electron-impurity scattering in doped semiconductors with large dielectric constant. It is based upon the idea of vector character of deformations caused in the crystalline lattice by any point defects siting asymmetrically in the unit cell. In result, local lattice compression due to the elastic deformations decay with the square of the distance from impurity. Electron scattering (due to standard deformation potential) on such defects leads to low-temperature mobility which follows a power-law scaling with the electron concentration with an exponent of -2/3. This result is close to experimental observations on a number of relevant materials.