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

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

Bound state properties of four-body muonic quasi-atoms

Total energies and various bound state properties are determined for the ground states in all six four-body muonic $a^{+} b^{+} \mu^{-} e^{-}$ quasi-atoms. These quasi-atoms contain two nuclei of the hydrogen isotopes $p^{+}, d^{+}, t^{+}$, one negatively charged muon $\mu^{-}$ and one electron $e^{-}$. In general, each of the four-body muonic $a^{+} b^{+} \mu^{-} e^{-}$ quasi-atoms, where $(a, b) = (p, d, t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus $a^{+} b^{+} \mu^{-}$ which has a finite number of bound states. Furthermore, all properties of such quasi-nuclei $a^{+} b^{+} \mu^{-}$ are determined from highly accurate computations performed for the three-body muonic ions $a^{+} b^{+} \mu^{-}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound state spectra of such quasi-atoms are similar to the spectrum of the regular hydrogen atoms, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogen-like systems, including the lowest-order relativistic and QED corrections

Multiple magnon modes in the Co3_3Sn2_2S2_2 Weyl semimetal candidate

We experimentally investigate electron transport in kagome-lattice ferromagnet Co$_3$Sn$_2$S$_2$, which is regarded as a time-reversal symmetry broken Weyl semimetal candidate. We demonstrate $dV/dI(I)$ curves with pronounced asymmetric $dV/dI$ spikes, similar to those attributed to current-induced spin-wave excitations in ferromagnetic multilayers. In contrast to multilayers, we observe several $dV/dI$ spikes' sequences at low, $\approx$10$^4$ A/cm$^2$, current densities for a thick single-crystal Co$_3$Sn$_2$S$_2$ flake in the regime of fully spin-polarized bulk. The spikes at low current densities can be attributed to novel magnon branches in magnetic Weyl semimetals, which are predicted due to the coupling between two magnetic moments mediated by Weyl fermions. Presence of spin-transfer effects at low current densities in Co$_3$Sn$_2$S$_2$ makes the material attractive for applications in spintronics.Comment: final versio