Dirac points with giant spin-orbit splitting in the electronic structure of two-dimensional transition-metal carbides

Two-dimensional (2D) materials, especially their most prominent member, graphene, have greatly influenced many scientific areas. Moreover, they have become a base for investigating the relativistic properties of condensed matter within the emerging field of Dirac physics. This has ignited an intense search for new materials where charge carriers behave as massless or massive Dirac fermions. Here, we theoretically show the existence of Dirac electrons in a series of 2D transition-metal carbides, known as MXenes. They possess twelve conical crossings in the 1st Brillouin zone with giant spin-orbit splitting. Our findings indicate that the 2D band structure of MXenes is protected against external perturbations and preserved even in multilayer phases. These results, together with the broad possibilities to engineer the properties of these materials phases, make Dirac MXenes a potential candidate for studying and developing novel Dirac-physics-based technologies.Comment: 4 figures and supplementar

Electrically driven optical interferometry with spins in silicon carbide

Interfacing solid-state defect electron spins to other quantum systems is an ongoing challenge. The ground-state spin's weak coupling to its environment bestows excellent coherence properties, but also limits desired drive fields. The excited-state orbitals of these electrons, however, can exhibit stronger coupling to phononic and electric fields. Here, we demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently drive the divacancy's excited-state orbitals and induce Landau-Zener-Stuckelberg interference fringes in the resonant optical absorption spectrum. Additionally, we find remarkably coherent optical and spin subsystems enabled by the basal divacancy's symmetry. These properties establish divacancies as strong candidates for quantum communication and hybrid system applications, where simultaneous control over optical and spin degrees of freedom is paramount.Comment: 17 pages, 4 figure

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Male breast cancer in BRCA1 and BRCA2 mutation carriers: Pathology data from the Consortium of Investigators of Modifiers of BRCA1/2

Background: BRCA1 and, more commonly, BRCA2 mutations are associated with increased risk of male breast cancer (MBC). However, only a paucity of data exists on the pathology of breast cancers (BCs) in men with BRCA1/2 mutations. Using the largest available dataset, we determined whether MBCs arising in BRCA1/2 mutation carriers display specific pathologic features and whether these features differ from those of BRCA1/2 female BCs (FBCs). Methods: We characterised the pathologic features of 419 BRCA1/2 MBCs and, using logistic regression analysis, contrasted those with data from 9675 BRCA1/2 FBCs and with population-based data from 6351 MBCs in the Surveillance, Epidemiology, and End Results (SEER) database. Results: Among BRCA2 MBCs, grade significantly decreased with increasing age at diagnosis (P = 0.005). Compared with BRCA2 FBCs, BRCA2 MBCs were of significantly higher stage (P for trend = 2 × 10-5) and higher grade (P for trend = 0.005) and were more likely to be oestrogen receptor-positive [odds ratio (OR) 10.59; 95 % confidence interval (CI) 5.15-21.80] and progesterone receptor-positive (OR 5.04; 95 % CI 3.17-8.04). With the exception of grade, similar patterns of associations emerged when we compared BRCA1 MBCs and FBCs. BRCA2 MBCs also presented with higher grade than MBCs from the SEER database (P for trend = 4 × 10-12). Conclusions: On the basis of the largest series analysed to date, our results show that BRCA1/2 MBCs display distinct pathologic characteristics compared with BRCA1/2 FBCs, and we identified a specific BRCA2-associated MBC phenotype characterised by a variable suggesting greater biological aggressiveness (i.e., high histologic grade). These findings could lead to the development of gender-specific risk prediction models and guide clinical strategies appropriate for MBC management

Male breast cancer in BRCA1 and BRCA2 mutation carriers: pathology data from the Consortium of Investigators of Modifiers of BRCA1/2.

Background BRCA1 and, more commonly, BRCA2 mutations are associated with increased risk of male breast cancer (MBC). However, only a paucity of data exists on the pathology of breast cancers (BCs) in men with BRCA1/2 mutations. Using the largest available dataset, we determined whether MBCs arising in BRCA1/2 mutation carriers display specific pathologic features and whether these features differ from those of BRCA1/2 female BCs (FBCs).Methods We characterised the pathologic features of 419 BRCA1/2 MBCs and, using logistic regression analysis, contrasted those with data from 9675 BRCA1/2 FBCs and with population-based data from 6351 MBCs in the Surveillance, Epidemiology, and End Results (SEER) database.Results Among BRCA2 MBCs, grade significantly decreased with increasing age at diagnosis (P = 0.005). Compared with BRCA2 FBCs, BRCA2 MBCs were of significantly higher stage (P for trend = 2 × 10(-5)) and higher grade (P for trend = 0.005) and were more likely to be oestrogen receptor-positive [odds ratio (OR) 10.59; 95 % confidence interval (CI) 5.15-21.80] and progesterone receptor-positive (OR 5.04; 95 % CI 3.17-8.04). With the exception of grade, similar patterns of associations emerged when we compared BRCA1 MBCs and FBCs. BRCA2 MBCs also presented with higher grade than MBCs from the SEER database (P for trend = 4 × 10(-12)).Conclusions On the basis of the largest series analysed to date, our results show that BRCA1/2 MBCs display distinct pathologic characteristics compared with BRCA1/2 FBCs, and we identified a specific BRCA2-associated MBC phenotype characterised by a variable suggesting greater biological aggressiveness (i.e., high histologic grade). These findings could lead to the development of gender-specific risk prediction models and guide clinical strategies appropriate for MBC management

Electrically driven optical interferometry with spins in silicon carbide

We demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently drive the divacancy’s excited-state orbitals and induce Landau-Zener-Stückelberg interference fringes in the resonant optical absorption spectrum. In addition, we find remarkably coherent optical and spin subsystems enabled by the basal divacancy’s symmetry. These properties establish divacancies as strong candidates for quantum communication and hybrid system applications, where simultaneous control over optical and spin degrees of freedom is paramount