# Seminars

Regular seminars are held on Thursdays in the Kapitza Institute in Moscow and on Fridays at the scientific council of the Landau Institute in Chernogolovka.

Departments of the institute hold their own seminars; the topic are determined by the scientific orientation of the related department.

Seminars information is also sent via e-mail. If you want to receive seminar announcements, please subscribe.

## Unrestricted electron bunching at the helical edge

28 February, the day after tomorrow in 11:30 at scientific council

I.S. Burmistrov

A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>½$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=½$ the Fano factor is bounded between 1 and 2, generalizing earlier studies. Based on paper P.D. Kurilovich, V.D. Kurilovich, I.S. Burmistrov, Y. Gefen, M. Goldstein "Unrestricted electron bunching at the helical edge", Phys. Rev. Lett. 123, 056803 (2019).

## Lattice models, deformed Virasoro algebra and reduction equation

28 February, the day after tomorrow in 11:30 at scientific council (short)

M.Lashkevich, Y.Pugai, J.Shiraishi, Y.Tutiya

The deformed Virasoro algebra is closely related to the so called RSOS (restricted solid-on-solid) models, which are two-dimensional exactly solvable lattice models of statistical mechanics. An important role in studying these models belongs to form factor, i.e. matrix elements in the quantum space of the transfer matrix with respect to eigenvectors of the transfer matrix. These form factors are explicitly expressed in terms of traces of vertex operators over representations of the deformed Virasoro algebra. It was observed some time ago that some excitations in the quantum space of RSOS models coincide. Nevertheless, the explicit expressions for the corresponding matrix elements differ, and their coincidence can only be established by numerical evaluation or expansions in small parameters. We found a homotopy operator that relates representatives of coincident excitations in the free field representation of the deformed Virasoro algebra. Thus, we showed that the corresponding traces over representation of the deformed Virasoro algebra coincide, whence the identities between form factors follow.

## Spin-torque resonance due to diffusive dynamics at a surface of a topological insulator

6 March in 11:30 at scientific council

Pavel Ostrovsky

We investigate spin-orbit torques on magnetization in an insulating ferromagnetic layer that is brought into close proximity to a topological insulator (TI). In addition to the well-known fieldlike spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i.e., for a spatially homogeneous electric field or current), but it may, nevertheless, have a strong impact on spin-torque resonance at finite frequency provided the external field is neither parallel nor perpendicular to the TI surface. The required electric-field configuration can be created by a grated top gate.

## Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO

6 March in 11:30 at scientific council (short)

Pavel Ostrovsky

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a well-known double degeneracy of the electronic bands (Kramers degeneracy). When the degeneracy is lifted, spin textures can be directly observed in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is very difficult to observe directly. Here, we use quantum interference measurements combined with first-principle band structure calculations to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type 3D Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL signal at low doping is fitted using a single interference channel, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement, giving rise to robust WAL. Our work sheds light on the subtle role of spin and pseudospin, when both could contribute to the same quantum effect.

## O vliyanii konechnosti shaga pri sluchainom bluzhdanii na ploskosti na tochnost’ otsenki veroyatnosti pervogo peresecheniya

13 March in 11:30 at scientific council (short)

L.N. Shchur

Поставлен вопрос о влиянии конечности шага на оценку вероятности пересечения окружности при случайном блуждании на плоскости. Численно выявлена зависимость точности оценки от величины шага. Предложен аналитический вид зависимости. Предложен эффективный алгоритм изменения величины шага.
[1] Olga Klimenkova, Anton Menshutin, Lev N. Shchur, "Influence of the random walk finite step on the first-passage probability", Physics and beyond (CSP2017), 9-12 Oct., 2017, Moscow
[2] Olga Klimenkova, Anton Yu. Menshutin, Lev N. Shchur, "Variable-step-length algorithms for a random walk: hitting probability and computation performance", Computer Phys. Commun., 241, 28-32 (2019)

## Localized conical edge modes and laser emission in photonic liquid crystals

13 March in 11:30 at scientific council (short)

V.A. Belyakov

Most studies of the localized edge (EM) and defect (DM) modes in cholesteric liquid crystals (CLC) are related to the localized modes in a collinear geometry, i.e. for the case of light propagation along the spiral axis. Much less attention was paid to the localized modes in CLC for a non-collinear geometry. It is due to the fact that all photonic effects in CLC are most pronounced just for the collinear geometry and also partially due to the fact that a simple exact analytic solution of the Maxwell equations is known for the collinear geometry, whereas for a non-collinear geometry there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. It is why in papers related to the localized modes in CLC for a non-collinear geometry and observing phenomena similar to the case of a collinear geometry their interpretation is not so clear. Problems related to the localized modes for a non-collinear geometry are studied here in the two wave dynamic diffraction theory approximation. The dispersion equation for non-collinear localized edge modes (called conical modes (CEM)) is found and analytically solved for the case of thick layers and for this case found the lasing threshold and the conditions of the anomalously strong absorption effect. Shown that qualitatively CEMs are very similar to the EMs, however differing by their polarization properties (the CEM eigen polarizations are elliptical one depending on the degree of CEM deviation from the collinear geometry in contrast to the circular eigen polarizations in the EM case). What is concerned of the CEM quantitative values of the parameters they are “worth” than for the corresponding ones for EM. The CEM lasing threshold is higher than the one for EM and etc. Performed theoretical studies of possible conversion of EMs into CEMs showed that it can be due to the EM reflection at dielectric boundaries at the conditions of a high pumping wave focusing. Known experimental results on the CEM are discussed and optimal conditions for CEM observations are formulated.
1. V.A. Belyakov, S.V. Semenov, Localized conical edge modes of higher orders in photonic liquid crystals, Crystals, 9(10), 542 (2019);
2. V.A. Belyakov, Localized Conical Edge Modes in Optics of Spiral Media (First Diffraction Order), Crystals, 9(12), 674 (2019).

## Zeros of Riemann’s Zeta Functions in the Line z=1/2+it0

19 June in 11:30 at scientific council

Yu.N. Ovchinnikov

Investigation of Josephson effect, current flow in narrow superconducting stripes, dynamical states in superconductors lead to the necessity to deal with an important phenomenon: phase slip events. The study of the distribution of zeros for Riemann's Zeta function also requires an analisis of the same phenomenon.
It was found that, in addition to trivial zeros in points ($z = -2N, N = 1, 2, ...$, natural numbers), the Riemann’s zeta function $\zeta(z)$ has zeros only on the line {$z = 1/2 + i t_0$, $t_0$ is real}. All zeros are numerated, and for each number, N, the positions of the non-overlap intervals with one zero inside are found. The simple equation for the determination of centers of intervals is obtained. The analytical function $\eta(z)$), leading to the possibility fix the zeros of the zeta function $\zeta(z)$, was estimated. To perform the analysis, the well-known phenomenon, phase-slip events, is used. This phenomenon is the key ingredient for the investigation of dynamical processes in solid-state physics, for example, if we are trying to solve the TDGLE (time-dependent Ginzburg-Landau equation).
J. Supercond. Novel Magn., 32(11), 3363-3368 (2019)