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.
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Surface density of states in superconductors with inhomogeneous pairing constant
31 January in 11:30 at scientific council
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 infinitederivative inflection point of the DOS curve at $E=\Delta_0$ with squareroot 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 at scientific council
Igor Lukyanchuk
Formation of unusual textures of polarization is imminent for nanoscale 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 energeticallyunfavorable depolarization charge. The endurance of ferroelectric formations with respect to highenergy 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 nearsurface layer and diminish the depolarization energy. However their existence have long been considered as barely possible until the direct theoretical predictions [13] and experimental evidences [46] in thin oxidebased 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 fieldinduced averaged polarization. This phenomenon is currently considered as the platform for realization of the dissipationfree high performance nanocircuits [8]. Moreover, in subTHz region the resonance plasmonic effect can be induced by oscillating domain walls [9] and can be suitable for design of the ultrasmall lowenergy THz chips.
Multivortex [10] and skyrmion [11] states can be formed inside ferroelectric cylindrical nanodots 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 multidomain and topological excitations in FE nanodots as a platform for ITsecured 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. FernandezPena, 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 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 solidonsolid) models, which are twodimensional 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 at scientific council
Bogatyrev A.B. (INM RAS)
Many model physical and engineering problems admit closed form solutions in terms of functiontheoretic 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.
