Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator

The discovery that spin-orbit coupling can generate a new state of matter in the form of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While QSH states from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if the state instead results from interaction-generated symmetry breaking. In particular, topological defects of the corresponding order parameter provide a route to exotic quantum phase transitions. Here, we introduce a model in which the condensation of skyrmion defects in an interaction-generated QSH insulator produces a superconducting (SC) phase. Because vortex excitations of the latter carry a spin-$1/2$ degree of freedom numbers, the SC order may be understood as emerging from a gapless spin liquid normal state. The QSH-SC transition is an example of a deconfined quantum critical point (DQCP), for which we provide an improved model with only a single length scale that is accessible to large-scale quantum Monte Carlo simulations.Comment: 14 pages, 11 figures, 3 table

New Application of Weierstrass Function Methods to Two Types of Boussninesq Equations

Abstract:For the two generalized forms of the well-known Boussinesq equation, we apply the theory of Weierstrass function method that has been applied by Kuru and so on. We get some traveling wave solutions that never seen before. The method is direct and concise, and free of the tedious calculation. The traveling wave solutions are expressed by the hyperbolic functions and confirmed to be solitary wave solutions

Exact Solutions of the Generalized Benjamin-Bona-Mahony Equation

We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbitrary-order nonlinearity

Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition

Thermodynamic and dynamical properties of a model of Dirac fermions with a deconfined quantum critical point (DQCP) separating an interaction-generated quantum spin-Hall insulator from an s-wave superconductor [Nature Comm.~{\bf 10}, 2658 (2019)] are studied by quantum Monte Carlo simulations. Inside the deconfined quantum critical region bound by the single-particle gap, spinons and spinless charge-2e skyrmions emerge. Since the model conserves total spin and charge, and has a single length scale, these excitations lead to a characteristic linear temperature dependence of the uniform spin and charge susceptibilities. At the DQCP, the order parameter dynamic structure factors show remarkable similarities that support emergent Lorentz symmetry. Above a critical temperature, superconductivity is destroyed by the proliferation of spin-1/2 vortices.Comment: 8 pages and 8 figure

Effective model for superconductivity in magic-angle graphene

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moir\'e valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge $2e$ and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1) $\times \mathbb{Z}_2$. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation.Comment: 6 pages, 5 figures, supplemental materia

Smaller Genetic Risk in Catabolic Process Explains Lower Energy Expenditure, More Athletic Capability and Higher Prevalence of Obesity in Africans

Lower energy expenditure (EE) for physical activity was observed in Africans than in Europeans, which might contribute to the higher prevalence of obesity and more athletic capability in Africans. But it is still unclear why EE is lower among African populations. In this study we tried to explore the genetic mechanism underlying lower EE in Africans. We screened 231 common variants with possibly harmful impact on 182 genes in the catabolic process. The genetic risk, including the total number of mutations and the sum of harmful probabilities, was calculated and analyzed for the screened variants at a population level. Results of the genetic risk among human groups showed that most Africans (3 out of 4 groups) had a significantly smaller genetic risk in the catabolic process than Europeans and Asians, which might result in higher efficiency of generating energy among Africans. In sport competitions, athletes need massive amounts of energy expenditure in a short period of time, so higher efficiency of energy generation might help make African-descendent athletes more powerful. On the other hand, higher efficiency of generating energy might also result in consuming smaller volumes of body mass. As a result, Africans might be more vulnerable to obesity compared to the other races when under the same or similar conditions. Therefore, the smaller genetic risk in the catabolic process might be at the core of understanding lower EE, more athletic capability and higher prevalence of obesity in Africans

Bandwidth controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor

The quantum spin Hall state can be understood in terms of spontaneous O(3) symmetry breaking. Topological skyrmion configurations of the O(3) order parameter vector carry a charge 2e, and as shown previously, when they condense, a superconducting state is generated. We show that this topological route to superconductivity survives easy-plane anisotropy. Upon reducing the O(3) symmetry to O(2)$\times$ Z$_2$, skyrmions give way to merons that carry a unit charge. On the basis of large-scale auxiliary field quantum Monte Carlo simulations, we show that at the particle-hole symmetric point, we can trigger a continuous and direct transition between the quantum spin Hall state and s-wave superconductor by condensing pairs of merons. This statement is valid in both strong and weak anisotropy limits. Our results can be interpreted in terms of an easy-plane deconfined quantum critical point. However, in contrast to the previous studies in quantum spin models, our realization of this quantum critical point conserves $U(1)$ charge, such that skyrmions are conserved

Application of statins in management of glioma: Recent advances

Gliomas are common primary intra-cerebral tumors in adults, and seriously threaten the health and life of affected patients, especially highly-malignant gliomas, such as glioblastoma multiforme. The clinical prognosis of glioma patients is poor, even for those who have received comprehensive treatment including surgery and concurrent chemo- and/or radio-therapy. As a structural analog of β-hydroxy-β- methylglutaryl coenzyme A (HMG CoA) reductase, statins are a restrictive enzyme in the metabolism of cholesterol. Recent laboratory studies and clinical trials have demonstrated that statins can exert antitumor effect, improve clinical prognosis and significantly prolong the survival time of glioma patients. This article is aimed to highlight the mechanisms of the anti-glioma effect of statins and review recent advances in the management of the disease.Keywords: Glioma, Glioblastoma multiforme, Intra-cerebral tumors, Statins, Prognosis, Survival time, β-Hydroxy-β-methylglutaryl coenzyme A (HMG CoA) reductas