Electronic Raman scattering in Tl2Ba2CuO6+x: symmetry of the order parameter, oxygen doping effects, and normal state scattering

Single crystals of the optimally doped, moderately and strongly overdoped high temperature superconductor Tl2Ba2CuO6+x (Tl-2201) with Tc=80, 56 and 30K, respectively, have been investigated by polarized Raman scattering. By taking the peak position of the B_1g component of electronic Raman scattering as 2Delta_0 we found that the reduced gap value (2Delta_0/k_BT_c) strongly decreases with increasing doping. The behavior of the low frequency scattering for the B_1g and B_2g scattering components is similar for optimally doped and overdoped crystals and can be described by a w^3 - and w -law, respectively, which is consistent with a d-wave symmetry of the order parameter. In contrast to the optimally doped Tl-2201 in both, moderately and strongly overdoped Tl-2201, the relative (compared to the B_1g) intensity of the A_1g scattering component is suppressed. We suggest that the van Hove singularity is responsible for the observed changes of Raman intensity and reduced gap value with doping. Electronic Raman scattering in the normal state is discussed in the context of the scattering from impurities and compared to the existing infrared data. The scattering rate evaluated from the Raman measurements is smaller for the overdoped samples, compared to the moderately overdoped samples.Comment: 7 pages, 7 figure

Реализация алгоритмов подсчета точек в якобианах гиперэллиптических кривых рода 2, основанных на парадоксе дней рождения

Представлена эффективная программная реализация алгоритма Годри — Шоста и его модификации Гэлбрайта — Рупрая для подсчёта точек в якобианах гипе-рэллиптических кривых. Эти алгоритмы представляют собой версии алгоритма Мацуо — Чао — Цуджия с малым использованием памяти и реализуют стратегию Гельфонда — Шенкса больших и малых шагов. Выводится оптимальный размер памяти, позволяющий минимизировать время работы указанных алгоритмов и получить на практике ожидаемое время их работы, близкое к теоретическим оценкам 2;45pN и 2;38pN для алгоритмов Годри — Шоста и Гэлбрайта — Рупрая соответственно. Здесь N — размер двумерной области поиска, равный порядку якобиана кривой, уменьшенному в m раз с помощью других методов. Предлагаемая реализация алгоритмов имеет многопоточный режим работы. Представлена статистическая зависимость времени работы от размера входных данных. Данная реализация алгоритма Гэлбрайта — Рупрая для размерности 2 является первой опубликованной многопоточной реализацией этого алгоритма с открытым исходным кодом

A flexible polymer chain in a critical solvent: Coil or globule?

We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute polymer solution is expressed as a function of the radius of gyration of the polymer and the average solvent number density within the gyration volume at the level of the mean-field approximation. Varying the strength of attraction between polymer and solvent we show that two qualitatively different regimes occur at the liquid-gas critical point. In case of weak polymer-solvent interactions the polymer chain is in a globular state. On the contrary, in case of strong polymer-solvent interactions the polymer chain attains an expanded conformation. We discuss the influence of the critical solvent density fluctuations on the polymer conformation. The reported effect could be used to excert control on the polymer conformation by changing the thermodynamic state of the solvent. It could also be helpful to estimate the solvent density within the gyration volume of the polymer for drug delivery and molecular imprinting applications

On the Ado Theorem for finite Lie conformal algebras with Levi decomposition

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.Comment: 11 page

Multivalued current-phase relationship in a.c. Josephson effect for a three-dimensional Weyl semimetal WTe2_2

We experimentally study electron transport between two superconducting indium leads, coupled to a single WTe$_2$ crystal, which is a three-dimensional Weyl semimetal. We demonstrate Josephson current in long 5~$\mu$m In-WTe$_2$-In junctions, as confirmed by the observation of integer (1,2,3) and fractional (1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of fractional a.c. Josephson effect indicates multivalued character of the current-phase relationship, which we connect with Weyl topological surface states contribution to Josephson current. In contrast to topological insulators and Dirac semimetals, we do not observe $4\pi$ periodicity in a.c. Josephson effect for WTe$_2$ at different frequencies and power, which might reflect chiral character of the Fermi arc surface states in Weyl semimetal.Comment: the text is seriously corrected. arXiv admin note: text overlap with arXiv:1801.0955