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Accessing topological superconductivity via a combined STM and renormalization group analysis
(2015)
The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.
Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z\(_3\) states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
Background
In Europe, men have lower rates of attempted suicide compared to women and at the same time a higher rate of completed suicides, indicating major gender differences in lethality of suicidal behaviour. The aim of this study was to analyse the extent to which these gender differences in lethality can be explained by factors such as choice of more lethal methods or lethality differences within the same suicide method or age. In addition, we explored gender differences in the intentionality of suicide attempts.
Methods and Findings
Methods. Design: Epidemiological study using a combination of self-report and official data. Setting: Mental health care services in four European countries: Germany, Hungary, Ireland, and Portugal. Data basis: Completed suicides derived from official statistics for each country (767 acts, 74.4% male) and assessed suicide attempts excluding habitual intentional self-harm (8,175 acts, 43.2% male).
Main Outcome Measures and Data Analysis. We collected data on suicidal acts in eight regions of four European countries participating in the EU-funded "OSPI-Europe"-project (www.ospi-europe.com). We calculated method-specific lethality using the number of completed suicides per method * 100 /(number of completed suicides per method + number of attempted suicides per method). We tested gender differences in the distribution of suicidal acts for significance by using the \(\chi\)\(^{2}\)-test for two-by-two tables. We assessed the effect sizes with phi coefficients (φ). We identified predictors of lethality with a binary logistic regression analysis. Poisson regression analysis examined the contribution of choice of methods and method-specific lethality to gender differences in the lethality of suicidal acts.
Findings Main Results
Suicidal acts (fatal and non-fatal) were 3.4 times more lethal in men than in women (lethality 13.91% (regarding 4106 suicidal acts) versus 4.05% (regarding 4836 suicidal acts)), the difference being significant for the methods hanging, jumping, moving objects, sharp objects and poisoning by substances other than drugs. Median age at time of suicidal behaviour (35-44 years) did not differ between males and females. The overall gender difference in lethality of suicidal behaviour was explained by males choosing more lethal suicide methods (odds ratio (OR) = 2.03; 95% CI = 1.65 to 2.50; p < 0.000001) and additionally, but to a lesser degree, by a higher lethality of suicidal acts for males even within the same method (OR = 1.64; 95% CI = 1.32 to 2.02; p = 0.000005). Results of a regression analysis revealed neither age nor country differences were significant predictors for gender differences in the lethality of suicidal acts. The proportion of serious suicide attempts among all non-fatal suicidal acts with known intentionality (NFSAi) was significantly higher in men (57.1%; 1,207 of 2,115 NFSAi) than in women (48.6%; 1,508 of 3,100 NFSAi) (\(\chi\)\(^{2}\) = 35.74; p < 0.000001).
Main limitations of the study
Due to restrictive data security regulations to ensure anonymity in Ireland, specific ages could not be provided because of the relatively low absolute numbers of suicide in the Irish intervention and control region. Therefore, analyses of the interaction between gender and age could only be conducted for three of the four countries. Attempted suicides were assessed for patients presenting to emergency departments or treated in hospitals. An unknown rate of attempted suicides remained undetected. This may have caused an overestimation of the lethality of certain methods. Moreover, the detection of attempted suicides and the registration of completed suicides might have differed across the four countries. Some suicides might be hidden and misclassified as undetermined deaths.
Conclusions
Men more often used highly lethal methods in suicidal behaviour, but there was also a higher method-specific lethality which together explained the large gender differences in the lethality of suicidal acts. Gender differences in the lethality of suicidal acts were fairly consistent across all four European countries examined. Males and females did not differ in age at time of suicidal behaviour. Suicide attempts by males were rated as being more serious independent of the method used, with the exceptions of attempted hanging, suggesting gender differences in intentionality associated with suicidal behaviour. These findings contribute to understanding of the spectrum of reasons for gender differences in the lethality of suicidal behaviour and should inform the development of gender specific strategies for suicide prevention.