3D Topological Semimetal Phases of Strained α\alpha-Sn on Insulating Substrate

$\alpha$-Sn is an elemental topological material, whose topological phases can be tuned by strain and magnetic field. Such tunability offers a substantial potential for topological electronics. However, InSb substrates, commonly used to stabilize $\alpha$-Sn allotrope, suffer from parallel conduction, restricting transport investigations and potential applications. Here, the successful MBE growth of high-quality $\alpha$-Sn layers on insulating, hybrid CdTe/GaAs(001) substrates, with bulk electron mobility approaching 20000 cm$^2$V$^{-1}$s$^{-1}$ is reported. The electronic properties of the samples are systematically investigated by independent complementary techniques, enabling thorough characterization of the 3D Dirac (DSM) and Weyl (WSM) semimetal phases induced by the strains and magnetic field, respectively. Magneto-optical experiments, corroborated with band structure modeling, provide an exhaustive description of the bulk states in the DSM phase. The modeled electronic structure is directly observed in angle-resolved photoemission spectroscopy, which reveals linearly dispersing bands near the Fermi level. The first detailed study of negative longitudinal magnetoresistance relates this effect to the chiral anomaly and, consequently, to the presence of WSM. Observation of the $\pi$ Berry phase in Shubnikov-de Haas oscillations agrees with the topologically non-trivial nature of the investigated samples. Our findings establish $\alpha$-Sn as an attractive topological material for exploring relativistic physics and future applications.Comment: Main text: 35 pages, 7 figures; Supplementary Materials: 22 pages, 12 figure

Edge coloring of graphs of signed class 1 and 2

Recently, Behr introduced a notion of the chromatic index of signed graphs and proved that for every signed graph $(G$, $\sigma)$ it holds that $$\Delta(G)\leq\chi'(G\text{, }\sigma)\leq\Delta(G)+1\text{,}$$ where $\Delta(G)$ is the maximum degree of $G$ and $\chi'$ denotes its chromatic index. In general, the chromatic index of $(G$, $\sigma)$ depends on both the underlying graph $G$ and the signature $\sigma$. In the paper we study graphs $G$ for which $\chi'(G$, $\sigma)$ does not depend on $\sigma$. To this aim we introduce two new classes of graphs, namely $1^\pm$ and $2^\pm$, such that graph $G$ is of class $1^\pm$ (respectively, $2^\pm$) if and only if $\chi'(G$, $\sigma)=\Delta(G)$ (respectively, $\chi'(G$, $\sigma)=\Delta(G)+1$) for all possible signatures $\sigma$. We prove that all wheels, necklaces, complete bipartite graphs $K_{r,t}$ with $r\neq t$ and almost all cacti graphs are of class $1^\pm$. Moreover, we give sufficient and necessary conditions for a graph to be of class $2^\pm$, i.e. we show that these graphs must have odd maximum degree and give examples of such graphs with arbitrary odd maximum degree bigger that $1$

Infinite chromatic games

In the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic one, are related: our new parameter is an upper bound for the game chromatic number

The Effect of Season of the Year on the Frequency and Degree of Damage during Commercial Thinning in Black Alder Stands in Poland

The aim of this study was to investigate the effect of season of the year on the frequency and degree of damage to residual trees caused during winter and summer timber harvesting operations in young alder stands. Analyses were conducted in pure black alder (Alnus glutinosa Gaertn.) stands aged 38 and 40 years, located in north-eastern Poland. Chainsaw logging was performed in the cut-to-length (CTL) system, while timber was extracted using an agricultural tractor with a trailer with manual timber loading and unloading. Damage caused in the stand as a result of early thinning operations was evaluated in terms of: (1) damage location, (2) wound size, (3) wound depth, and (4) the distance of the damaged tree from the skid trail. Timber harvesting caused damage in 8.3% of trees remaining in the stand. Both the total number of damaged trees (p = 0.001) and the number of trees damaged during felling (p = 0.01) and extraction of timber (p < 0.001) were greater in summer than in winter. Irrespective of the season, two-thirds of all cases of damage were caused during timber extraction, with 67.7% of damage recorded on trunks or root collars and 32.3% on roots. Irrespective of the season and the technological operation, slightly over 50% of cases of damage were small wounds of max. 10 cm2. The proportions of medium-sized wounds (11–100 cm2) and large wounds (over 100 cm2) were comparable. The majority of damaged trees (85.1%) were found in the vicinity (<1 m) of the skid trails. The frequency of tree damage near the skid trail was twice as large in summer as in winter (p < 0.001)

Przerzuty wyściółczaka anaplastycznego do skóry wymagające przeszczepu wolnego płata skórnego

Ependymomas are glial central nervous system tumors that derive from the ependymal lining of the ventricular system or central canal of the spinal cord. They may occur anywhere along the neuraxis, but most commonly in the posterior fossa in the floor of the fourth ventricle and in the location of the conus medullaris, cauda equina and filum terminale. According to the World Health Organization (WHO) classification ependymomas are divided into four groups on the basis of their histologic appearance: myxopapillary ependymoma; subependymoma (WHO grade I); ependymoma with cellular, papillary, clear cell and tanycytic variants (WHO grade II); anaplastic ependymoma (WHO grade III). Anaplastic ependymomas are characterized by increased cellularity, cytological atypia, mitotic figures, vascular proliferation and areas of necrosis. Ependymomas, including the anaplastic type, have the potential to spread via the cerebrospinal fluid pathways; nevertheless intraspinal dissemination or metastasis of fourth ventricle tumor is a rare condition. The incidence is higher with higher WHO grade. Intracranial and spinal ependymomas frequently relapse at the primary site in case of incomplete surgical removal. For this reason, gross total resection followed by craniospinal radiation therapy is the treatment of choice. The extremely rare presence of metastases outside the central nervous system and even primary extraneural ependymomas were reported in the literature. Herein, we describe an unusual case of extraneural metastases of supratentorial anaplastic ependymoma with its treatment history.Wyściółczaki są guzami pochodzenia glejowego wywodzącymi się z linii komórek wyściółki układu komorowego lub kanału centralnego rdzenia kręgowego. Mogą zajmować każdą lokalizację wzdłuż osi nerwowej, ale najczęściej występują w tylnej jamie, w obrębie dna czwartej komory, w stożku rdzenia, ogonie końskim i nici końcowej. Zgodnie z klasyfikacją Światowej Organizacji Zdrowia (WHO) w zależności od typu histologicznego wyróżnia się 4 postaci wyściółczaka: wyściółczaka śluzowobrodawkowatego; podwyściółczaka (stopień I według WHO); wyściółczaki o wariantach komórkowym, brodawkowatym, jasnokomórkowym i tanacytarnym (stopień II według WHO); wyściółczaka anaplastycznego (stopień III według WHO). Wyściółczak anaplastyczny charakteryzuje się podwyższoną komórkowatością, atypią komórkową, figurami podziału mitotycznego, proliferacją naczyniową i obszarami martwicy. Wyściółczaki, w tym anaplastyczny, mają zdolność do szerzenia się drogą płynu mózgowo- -rdzeniowego. Pomimo tego rozsiew śródrdzeniowy i przerzuty do czwartej komory występują rzadko. Im wyższy jest stopień w klasyfikacji WHO, tym większe ryzyko przerzutu. Wyściółczaki rdzenia i mózgu często dają wznowę w miejscu ich pierwotnego występowania, jeśli nie zostaną usunięte całkowicie. Z tego powodu radykalne leczenie operacyjne oraz następująca po nim radioterapia czaszki i rdzenia jest metodą leczenia z wyboru. W literaturze podaje się nieliczne przypadki przerzutów wyściółczaka poza ośrodkowy układ nerwowy oraz wyściółczaka o pierwotnej lokalizacji poza układ nerwowy. Poniżej przedstawiono przypadek i historię leczenia rzadko spotykanego przerzutu nadnamiotowego wyściółczaka anaplastycznego poza układ nerwowy

Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb1-x Snx Se

Funding Information: The International Center for Interfacing Magnetism and Superconductivity with Topological Matter MagTop is supported by the Foundation for Polish Science through the IRA Programme co-financed by EU within SG OP (Grant No. MAB/2017/1). We acknowledge the Helmholtz-Zentrum Berlin for provision of synchrotron radiation beamtime at UE112 PGM-2a- of BESSY II under the EU CALIPSO Grant No. 312284. W.B. also acknowledges support by Narodowe Centrum Nauki (NCN, National Science Centre, Poland) Project No. 2019/34/E/ST3/00404. G.S. also acknowledges support by Austrian Science Fund, Projects No. P30960-N27 and No. I 4493-N. Publisher Copyright: © 2021 American Physical Society.Many conductors, including recently studied Dirac materials, show saturation of coherence length on decreasing temperature. This surprising phenomenon is assigned to external noise, residual magnetic impurities, or two-level systems specific to noncrystalline solids. Here, by considering the SnTe-class of compounds as an example, we show theoretically that breaking of mirror symmetry deteriorates Berry's phase quantization, leading to additional dephasing in weak-antilocalization magnetoresistance (WAL-MR). Our experimental studies of WAL-MR corroborate these theoretical expectations in (111) Pb1-xSnxSe thin film with Sn contents x corresponding to both topological crystalline insulator and topologically trivial phases. In particular, we find the shortening of the phase coherence length in samples with intentionally broken mirror symmetry. Our results indicate that the classification of quantum transport phenomena into universality classes should encompass, in addition to time-reversal and spin-rotation invariances, spatial symmetries in specific systems.Peer reviewe