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

## Quantum phase slips in inhomogeneous Josephson junction chains

24 January in 11:30

A. Svetogorov, D. M. Basko

We study coherent quantum phase-slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase
oscillations in the ring (Mooij-Schön modes). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total QPS amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.

## Electric dipole moment searches using storage rings

24 January in 11:30

Frank Rathmann (Institut f. Kernphysik, Forschungszentrum Juelich, Germany)

The Standard Model (SM) of Particle Physics is not capable to account for the apparent matter-antimatter asymmetry of our Universe. Physics beyond the SM is required and is either probed by employing highest energies (e.g., at LHC), or by striving for ultimate precision and sensitivity (e.g., in the search for electric dipole moments). Permanent electric dipole moments (EDMs) of particles violate both time reversal (T) and parity (P) invariance, and are via the CPT-theorem also CP-violating. Finding an EDM would be a strong indication for physics beyond the SM, and pushing upper limits further provides crucial tests for any corresponding theoretical model, e.g., SUSY.
Up to now, EDM searches focused on neutral systems (neutrons, atoms, and molecules). Storage rings, however, offer the possibility to measure EDMs of charged particles by observing the influence of the EDM on the spin motion in the ring. Direct searches of proton and deuteron EDMs, however, bear the potential to reach sensitivities beyond 10−29 e⋅cm. Since the Cooler Synchrotron COSY at the Forschungszentrum Jülich provides polarized protons and deuterons up to momenta of 3.7 GeV/c, it constitutes an ideal testing ground and starting point for such an experimental program. Besides the discussion of the achievements of the JEDI collaboration, and the description of an effort to perform a first direct deuteron EDM measurement at COSY, the talk will highlight in addition future technical developments that will pave the way toward EDM searches in dedicated rings. A recent advancement that grew out of the successful work performed by JEDI is the formation of the CPEDM Collaboration, which aims at the design of an EDM prototype ring that could be hosted either at CERN or at COSY, will be discussed as well.

## Surface density of states in superconductors with inhomogeneous pairing constant

31 January in 11:30

Ya.V. Fominov, A.A. Mazanik, M.V. Razumovskiy

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a ``vertical'' peculiarity of the DOS around an energy equal to the bulk order parameter $\Delta_0$, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E < \Delta_0$ and $E > \Delta_0$, so the peculiarity is asymmetric.
The talk is based on the paper [Ya.V. Fominov, A.A. Mazanik, M.V. Razumovskiy, Phys. Rev. B 100, 224513 (2019)].

## Ferroelectric as topological material: Hopf fibrations, multilevel logic, negative capacitance and THz vibrations

31 January in 11:30

Igor Lukyanchuk

Formation of unusual textures of polarization is imminent for nano-scale ferroelectric
samples, films, rods, and granules, where the depolarization surface effects play the crucial role. The topologically protected stability of such textures and security of information storage is coming from polarization vorticity, provided by condition of absence of the energetically-unfavorable depolarization charge. The endurance of ferroelectric formations with respect to high-energy irradiation makes them ideal for the aerospace industry, and the periodic domain walls structures can be used as a platform for terahertz radiation generators and detection devices.
Polarization domains that alternate the surface charge distribution can be formed in ferroelectric thin films as an effective mechanism to confine the depolarization field to the near-surface layer and diminish the depolarization energy. However their existence have long been considered as barely possible until the direct theoretical predictions [1-3] and experimental evidences [4-6] in thin oxide-based superlattices. Very recently we have demonstrated that the effective capacitance of ferroelectric layers with domains is negative [7]. This effect is explained by the opposite orientation of the depolarizing field with respect to the field-induced averaged polarization. This phenomenon is currently considered as the platform for realization of the dissipation-free high performance nano-circuits [8]. Moreover, in sub-THz region the resonance plasmonic effect can be induced by oscillating domain walls [9] and can be suitable for design of the ultra-small low-energy THz chips.
Multi-vortex [10] and skyrmion [11] states can be formed inside ferroelectric cylindrical nano-dots and nanorods to reduce the depolarization energy. We study the stability of such states and demonstrate that the topological class of the most stable topological excitations can be driven by the geometrical and electrical parameters of the system, external field and temperature. We target the multi-domain and topological excitations in FE nanodots as a platform for IT-secured multivalued logic units, breaking ground for neuromorphic computing [12,13].

[1] A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. 84, 3177 (2000).

[2] V. A. Stephanovich, I. A. Luk'yanchuk, and M. G. Karkut, Phys. Rev. Lett., 94, 047601 (2005)

[3] I. Luk'yanchuk, L. Lahoche, and A. Sene, Phys. Rev. Lett., 102, 147601 (2009)

[4] S. K. Streiffer, J. A. Eastman, D. D. Fong et al., Phys. Rev. Lett. 89, 067601 (2002);

[5] S. O. Hruszkewycz, M. J. Highland, et al., Phys. Rev. Lett.110, 177601 (2013).

[6] Yadav, A. K., Nelson,et al.. Nature, 530 (7589), 198. (2016)

[7] P. Zubko, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk’yanchuk, J.-M. Triscone
& J. Íñiguez, Nature, 534, 524 (2016)

[8] Khan, A. I., Chatterjee, K., Wang B. et al. Nature Materials 14, 182–186 (2015).

[9] I. Luk'yanchuk, A.Pakhomov, A.Sené, A. Sidorkin, V. Vinokur, arXiv:1410.3124

[10] G. Pascoli L. Lahoche, I. Luk'yanchuk, Integrated Ferroelectrics, 99, 60 (2008)

[11] L Baudry, A Sené, IA Luk'yanchuk, L Lahoche, and JF Scott, Phys. Rev. B 90, 024102 (2014)

[12] P.-W. Martelli, S. M. Mefire, I. Luk'yanchuk, Europhys. Lett. 111, 50001 (2015)

[13] Baudry, L., Lukyanchuk, I. & Vinokur, V. M. Sci. Rep. 7: 42196 (2017)

## Lattice models, deformed Virasoro algebra and reduction equation

14 February in 11:30 (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.

## Effective function theory on Riemann surfaces and applications.

21 February in 11:30

Bogatyrev A.B. (INM RAS)

Many model physical and engineering problems admit closed form solutions in terms of function-theoretic objects on Riemann surfaces or spaces of their moduli. We consider issues of effective and robust calculation of such objects (Abelian integrals,
their periods, linear and quadratic differentials, meromorphic functions ...) for surfaces of a high genus (greater than one).
Examples of solving several problems will be given.