# 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.

You can subscribe and receive announcements about ITP seminars. If you have any questions, please contact the scientific secretary Sergey Krashakov.

## Physics at the Edge of a QHE setting

25 October, tomorrow in 11:30

Yuval Gefen (Weizmann Institute of Science, Israel)

The structure of the edge of a QHE edge is constrained, but not dictated, by the topology of the bulk. Particularly interesting is the class of hole-conjugate fractional QH states. For such states the edge hosts counter-propagating modes that are responsible for quantized electrical and thermal conductance. In the coherent quantum limit renormalized edge modes emerge, which may involve neutral modes with non-trivial exchange statistics. I will discuss the behavior of topology-influenced transport coefficient both in the coherent and the fully equilibrated regimes, topological classification of non-equilibrium shot noise, and the relation to recent experiments.

## Zeroes of S-matrix entries and random 'anti-lasing'

25 October, tomorrow in 15:00

Yan V. Fyodorov (Dept. of Mathematics, King’s College London)

Motivated by recent experimental interest in 'random anti-lasing' (e.g. K. Pichler et al. Nature 567, 351 (2019)) I consider manifestations of zeroes of scattering matrices in wave-chaotic cavities.
In particular, I will introduce the notion of Reflection Time Difference playing the same role for the S-matrix zeroes as the Wigner time delay plays for the S-matrix poles, and a possibility of its experimental measurement.
I will then discuss how statistics of complex zeroes of scattering matrix entries can be described in the framework of RMT-based model of resonance scattering.

Presentation will be based on papers arXiv:1908.06920 and J. Phys. A 50, 30LT01 (2017).

Presentation will be based on papers arXiv:1908.06920 and J. Phys. A 50, 30LT01 (2017).

## Column coherent vortices in a rapidly rotating turbulent fluid: a minimal theory

1 November in 11:30

S.S. Vergeles, L.L. Ogorodnikov, I.V. Kolokolov

We investigate analytically, what is a mechanism surviving a column coherent vortex is statistically steady state in rapidly rotating turbulent three-dimensional incompressible fluid. The Rossby number is assumed to be small both for small-scale eddies and the large-scale coherent vortex, which axis is directed along the rotation axis. The small-scale eddies are assumed to be excited by a random force with homogeneous statistics in time and space. The fast dynamics of the eddies is dynamics of inertia waves. Within rapid distortion theory approach, we track how the inertia waves are affected by local shear flow produced by the differential rotation in the vortex before they die out due to viscosity. We show that the shear flow influence leads to the power of the excitation force is transferred via the small eddies to the vortex, where it is dissipated due to viscosity. We establish equation determining the radial mean velocity profile in the vortex and find the profile itself.

## Zeeman spin-orbit coupling and magnetic quantum oscillations in antiferromagnetic conductors

8 November in 11:30

P.D. Grigoriev, R. Ramazashvili, M. V. Kartsovnik

Using the symmetry arguments we show that in many metals with antiferromagnetic ordering the effective g-factor of charge carries, measured from magnetic quantum oscillations, is exactly zero. The experimental study of this effect is performed in several compounds and compared with the proposed theory. We find that the Néel state of the layered organic conductor κ-(BETS)

_{2}FeBr_{4}shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to the paramagnetic state of the same material. This is evidence of spin degeneracy of Landau levels -- a direct manifestation of the generic Zeeman spin-orbit coupling, predicted for antiferromagnetic conductors. Likewise, we find no spin modulation in the angle dependence of the slow Shubnikov-de Haas oscillations in the optimally electron-doped cuprate Nd_{2−x}Ce_{x}CuO_{4}. This points to the presence of Néel order in this superconductor even at optimal doping.## Competition of band anticrossing and charge-density wave

8 November in 11:30 (short)

P.D. Grigoriev, P.A. Vorobyev, A.A. Sinchenko

We calculate the electron susceptibility of rare-earth tritelluride compounds RTe

[1] P.A. Vorobyev, P.D. Grigoriev, K.K. Kesharpu and V.V. Khovaylo, Materials 12, 2264 (2019).

[2] P.D. Grigoriev, A.A. Sinchenko, P.A. Vorobyev, A. Hadj-Azzem, P. Lejay, A. Bosak, P. Monceau, Phys. Rev. B 100, 081109(R) (2019).

_{3}as a function of temperature, wave vector, and electron-dispersion parameters. Comparison of the results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to make predictions about the evolution of electron-dispersion parameters with the variation of the atomic number of rare-earth elements (R). Our measurements of the Hall coefficient in RTe_{3}compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We propose that this effect may result from the interplay between two instabilities: band crossing of the Te p_{x}and p_{y}orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in the Hall effect measurements.[1] P.A. Vorobyev, P.D. Grigoriev, K.K. Kesharpu and V.V. Khovaylo, Materials 12, 2264 (2019).

[2] P.D. Grigoriev, A.A. Sinchenko, P.A. Vorobyev, A. Hadj-Azzem, P. Lejay, A. Bosak, P. Monceau, Phys. Rev. B 100, 081109(R) (2019).

## Landau theory for smectic-A–hexatic-B coexistence in smectic films

6 December in 11:30

E. S. Pikina, E. I. Kats, V. V. Lebedev

We explain theoretical peculiarities of the smectic-A–hexatic-B equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy et al., Phys. Rev. E 98, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase
transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness L

_{c}, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.## Effect of small dissipation on the NLS anomalous waves recurrence.

13 December in 11:30

P.G. Grinevich, P.M. Santini

We provide analytic formulas decribing the effect of small loss/gain on the recurrence of anomalous waves in the focusing Nonlinear Schrodinger equation. We show that very small loss or gain essentially affects the statistics and the character of the recurrence. In particular, our formulas explains the results of numerical simulations from the paper by
O. Kimmoun, H.C. Hsu, H. Branger, M.S. Li, Y.Y. Chen, C. Kharif, M. Onorato, E.J.R. Kelleher, B. Kibler, N. Akhmediev, A. Chabchoub (2016).

## KP-2 solutions in the form of soliton sequences.

13 December in 11:30 (short)

P.G. Grinevich, S. Abenda

Some photos of the ocean surface demonstrate waves looking like lattices formed by solitons. They can be modelled by finite-gap Kadomtsev-Petviashvili 2 solutions corresponding to almost dgenerate spectral curves. We show how to construct such solutions in the first non-trivial case corresponding to GR(4,2).