# Seminars at the Landau Institute scientific council

Seminars are held on Fridays in the conference hall of Landau Institute for Theoretical Physics in Chernogolovka, beginning at 11:30.

## Mesoscopic supercurrent fluctuations in diffusive magnetic Josephson junctions

23 November in 11:30

P. A. Ioselevich, P. M. Ostrovsky, Ya. V. Fominov

We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than the magnetic pair-breaking length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase relation (CPR) along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by magnetism in the link. We find that all harmonics are present in the CPR. Each harmonic has its own sample-dependent amplitude and phase shift with no correlation between different harmonics. Depending on the type of magnetic weak link, the system can realize a \varphi_0 or \varphi junction in the fluctuational regime. Full supercurrent statistics is obtained at arbitrary relation between temperature, superconducting gap, and the Thouless energy of the weak link.

## Statistics of eigenstates near the localization transition on random regular graphs

23 November in 11:30

Konstantin Tikhonov

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes below the correlation volume and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast diffusion which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate limit of the Anderson model in spatial dimensions.

## Two-sphere partition functions and Kahler potentials on CY moduli spaces

14 December in 11:30 (short)

A. Belavin, K. Aleshkin, A. Litvinov

We study the relation between exact partition functions of gauged $N=(2,2)$ linear sigma-models on $S^{2}$ and K\"ahler potentials of CY manifolds proposed by Jockers et all. We suggest to use a mirror version of this relation. For a class of manifolds given by a Fermat hypersurfaces in weighted projective space we check the relation by explicit calculation.
Aleshkin K., Belavin A., Litvinov A., “Two-sphere partition functions and Kähler potentials on CY moduli spaces”, Письма в ЖЭТФ, 108(10), 725 (2018)

## Probing spin susceptibility of a correlated two-dimensional electron system by transport and magnetization measurements

14 December in 11:30 (short)

I.S. Burmistrov

I report theoretical support of the data on measuring the spin susceptibility at different temperatures and electron concentrations in a two-dimensional electron system based on a silicon field-effect transistor in the group of V.M. Pudalov (Lebedev Institute).
The short talk is based on the work of V. M. Pudalov, A. Yu. Kuntsevich, M.E. Gershenson, I.S. Burmistrov, and M. Reznikov, Phys. Rev. B 98, 155109 (2018).

## A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current

14 December in 11:30

I.S. Burmistrov

We consider a small itinerant ferromagnet exposed to an external magnetic field and strongly driven by a thermally induced spin current. For this model, we derive the quasi-classical equations of motion for the magnetization where the effects of a dynamical non-equilibrium distribution function are taken into account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation supplemented by a spin-transfer torque term of Slonczewski form. We identify a regime of persistent precessions in which we find an enhancement of the thermoelectric current by the pumping current.
The talk is based on T. Ludwig, I.S. Burmistrov, Y. Gefen, A. Shnirman, "A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current", arxiv:1808.01192

## TBA

21 December in 11:30 (short)

B.G. Zakharov

## Quantum corrections to conductivity of disordered electrons due to inelastic scattering off magnetic impurities

21 December in 11:30

I.S. Burmistrov

We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type.
The talk is based on I. S. Burmistrov and E. V. Repin, Phys. Rev. B 98, 045414 (2018)

## Magnetism of Bi2Se3 thin films with Eu-rich flat inclusions

21 December in 11:30 (short)

I.S. Burmistrov

I report about theoretical support of experimental data on the measurement of the magnetic properties of thin films of bismuth selenide doped with europium atoms, which form flat inclusions. The magnitudes of the various mechanisms of magnetic ordering are theoretically estimated. The estimates obtained are in satisfactory agreement with the experimental data.
Report is based on the paper: L.N. Oveshnikov, Ya.I. Rodionov, K.I. Kugel, I.A. Karateev, A.L. Vasiliev, Yu.G. Selivanov, E.G. Chizhevskii, I.S. Burmistrov and B.A. Aronzon, "Magnetism of Bi2Se3 Thin Films with Eu-rich flat inclusions", J. Phys .: Condens. Matter 30, 445801 (2018)

## Volterra chain and Catalan numbers

21 December in 11:30 (short)

The model problem on the decay of a step for the Volterra chain is formulated as a Cauchy problem with initial condition equal to 0 in one node and 1 in the others. We show that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for Catalan numbers. Asymptotic formulas for the solution are obtained.

28 December in 11:30

Pavel Ostrovskii

Doklad po predstavlyaemoi k zashchite doktorskoi dissertatsii.

## Dual description of integrable sigma-models

11 January 2019 in 11:30

Litvinov Alexey

In my talk I will discuss an example of the weak / strong coupling duality, i.e. equivalence seemingly distinct quantum field theories, so that the strong coupling regime of one theory describes the weak coupling regime of the other, and vice versa. In my example, these are two-dimensional sigma models and boson field theories with exponential interaction. Both theories are integrable. To explain the duality, I will construct a W-algebra commuting with a set of screening operators on one side and solve the Ricci flow equation with given ultraviolet asymptotic boundary conditions.
The report is based joint work with Fateev and Spodyneiko.

## On complex angular diagrams of magnetic conductivity in strong magnetic fields

11 January 2019 in 11:30

A.Ya. Maltsev

We consider angular conductivity diagrams for normal (single-crystal) metals with complex Fermi surfaces in the presence of strong magnetic fields. The behavior of conductivity in this case strongly depends on the direction of the magnetic field and the stable nontrivial regimes of this behavior correspond to special zones of stability on the angular diagram corresponding to certain (topological) properties of the conductivity tensor. As we show, in the general case such diagrams can be divided into two general types, simple (type A) and complex (type B). We will be interested in the diagrams of the second type, which have a number of specific features (an infinite number of stability zones, the presence of chaotic regimes, etc.), which we will consider in more detail.