Hall conductivity as bulk signature of topological transitions in superconductors

Topological superconductors may undergo transitions between phases with different topological numbers which, like the case of topological insulators, are related to the presence of gapless (Majorana) edge states. In $\mathbb{Z}$ topological insulators the charge Hall conductivity is quantized, being proportional to the number of gapless states running at the edge. In a superconductor, however, charge is not conserved and, therefore, $\sigma_{xy}$ is not quantized, even in the case of a $\mathbb{Z}$ topological superconductor. Here it is shown that while the $\sigma_{xy}$ evolves continuously between different topological phases of a $\mathbb{Z}$ topological superconductor, its derivatives display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO) coupling and externally applied Zeeman spin splitting. Generalization to the cases where the pairing vector is not aligned with that of the SO coupling is given. We generalize also to the cases where the normal system is already topologically non-trivial.Comment: 10 pages, 10 figure

Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain

Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S (k,ω) and S (k,ω)=S (k,ω). The contribution of Bethe strings to S (k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S (k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S (k,ω), S (k,ω)=S (k,ω), and S (k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities. +− xx yy zz −+ +− xx yy zzJ. M. P. C. would like to thank the Boston University's Condensed Matter Theory Visitors Program for support and Boston University for hospitality during the initial period of this research. He acknowledges the support from FCT through the Grants PTDC/FIS-MAC/29291/2017, SFRH/BSAB/142925/2018, and POCI-01-0145-FEDER-028887. J. M. P. C. and T. Č. acknowledge the support from FCT through the Grant UID/FIS/04650/2013. T. Č. gratefully acknowledges the support by the Institute for Basic Science in Korea (IBS-R024-D1). P. D. S. acknowledges the support from FCT through the Grants UID/CTM/04540/2013 and UID/CTM/04540/2019

Change of an insulator's topological properties by a Hubbard interaction

We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A topologically non-trivial insulator is then realized if there is one fermion per site. When interactions in the framework of the Hubbard model are introduced, the effective hopping parameters are renormalized and the system's topological number can change at a certain interaction strength, $U=\bar U$, smaller than that for the Mott transition. Two different situations may then occur: either the anomalous Hall conductivity $\sigma_{xy}$ changes abruptly at $\bar U$, as the system undergoes a transition from one topologically non-trivial insulator to another, or the transition is through an anomalous Hall metal, and $\sigma_{xy}$ changes smoothly between two different quantized values as $U$ grows. Restoring time-reversal symmetry by adding spin to spinless models, the half-filled system becomes a $\mathbb{Z}_2$ topological insulator. The topological number $\nu$ then changes at a critical coupling $\bar U$ and the quantized spin Hall response changes abruptly.Comment: 5 pages, 3 figure

Vorticity and magnetic shielding in a type-II superconductor

We study in detail, solving the Bogoliubov-de Gennes equations, the magnetic field, supercurrent and order parameter profiles originated by a solenoid or magnetic whisker inserted in a type-II superconductor. We consider solutions of different vorticities, n, in the various cases. The results confirm the connection between the vorticity, the internal currents and the boundstates in a self-consistent way. The number of boundstates is given by the vorticity of the phase of the gap function as in the case with no external solenoid. In the limiting case of an infinitely thin solenoid, like a Dirac string, the solution is qualitatively different. The quasiparticle spectrum and wave functions are a function of n-n_ext, where n_ext is the vorticity of the solenoid. The flux is in all cases determined by the vorticity of the gap function.Comment: revised version, 25 pages, LaTex, 10 figure

Type 2 diabetes progression differently affects endothelial function and vascular contractility in the aorta and the pulmonary artery

© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Type 2 diabetes (T2D) is associated with cardiovascular and pulmonary disease. How T2D affects pulmonary endothelial function is not well characterized. We investigated the effects of T2D progression on contractility machinery and endothelial function in the pulmonary and systemic circulation and the mechanisms promoting the dysfunction, using pulmonary artery (PA) and aorta. A high-fat (HF, 3 weeks 60% lipid-rich diet) and a high-fat/high-sucrose (HFHSu, combined 60% lipid-rich diet and 35% sucrose during 25 weeks) groups were used as prediabetes and T2D rat models. We found that T2D progression differently affects endothelial function and vascular contractility in the aorta and PA, with the contractile machinery being altered in the PA and aorta in prediabetes and T2D animals; and endothelial function being affected in both models in the aorta but only affected in the PA of T2D animals, meaning that PA is more resistant than aorta to endothelial dysfunction. Additionally, PA and systemic endothelial dysfunction in diabetic rats were associated with alterations in the nitrergic system and inflammatory pathways. PA dysfunction in T2D involves endothelial wall mineralization. The understanding of the mechanisms behind PA dysfunction in T2D can lead to significant advances in both preventative and therapeutic treatments of pulmonary disease-associated diabetes.B.F.M. is supported by PhD Grant from Portuguese Foundation for Science and Technology Reference PD/BD/128336/2017. FOM and JFS are supported by Portuguese Foundation for Science and Technology contracts CEECIND/04266/2017 and CEECIND/02428/2018.info:eu-repo/semantics/publishedVersio