High Chern number quantum anomalous Hall phases in graphene ribbons with Haldane orbital coupling

We investigate possible phase transitions among the different quantum anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of the exchange field. The effective tight-binding Hamiltonian for graphene is made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as well as the Haldane orbital term. We find that the variation of the exchange field results in bulk gap-closing phenomena and phase transitions occur in the graphene system. If the Haldane orbital coupling is absent, the phase transition between the chiral (anti-chiral) edge state $\nu=+2$ ($\nu=-2$) and the pseudo-quantum spin Hall state ($\nu=0$) takes place. Surprisingly, when the Haldane orbital coupling is taken into account, an intermediate QSH phase with two additional edge modes appears in between phases $\nu=+2$ and $\nu=-2$. This intermediate phase is therefore either the hyper-chiral edge state of high Chern number $\nu=+4$ or anti-hyper-chiral edge state of $\nu=-4$ when the direction of exchange field is reversed. We present the band structures, edge state wave functions and current distributions of the different QAH phases in the system. We also report the critical exchange field values for the QAH phase transitions.Comment: 4 figure

A modified T. Chan’s preconditioner for Toeplitz systems

AbstractWe present a modified T. Chan’s preconditioner for solving Toeplitz linear systems by the preconditioned conjugate gradient (PCG) method in this paper. Especially, we give some results when the matrices are Hermitian positive definite Toeplitz matrices. The operation and convergence of the PCG method are discussed. Numerical examples presented illustrate the effectiveness of the preconditioner obtained

Some remarks on compositeness of Tcc+T^+_{cc}

Recently LHCb experimental group find an exotic state $T^+_{cc}$ from the process $p\bar{p} \to D^0D^0\pi^+ + X$. A key question is if it is just a molecule or may have confined tetraquark ingredient. To investigate this, different methods are taken, including two channel ($D^{*+}D^0$ and $D^{*0}D^+$) K-matrix unitarization and single channel Flatt\'e-like parametrization method analysed by pole counting rule and spectral density function sum rule. It demonstrates that $T^+_{cc}$ is a molecular state, though the possibility that there may exist elementary ingredient can not be excluded, by rough analysis on its production rate

Clinical effect of high-flow revascularization in microsurgery combined with endoscopic endonasal surgery for skull base tumors with intracranial and extracranial involvement

BackgroundThe objective of the study is to investigate the surgical methods and clinical effects of high-flow revascularization in microsurgery combined with endoscopic endonasal surgery for skull base tumors with intracranial and extracranial involvement.MethodsThe relationships between skull base tumors and internal carotid artery (ICA), tumor location and size, and the extent of tumor invasion were assessed. Preoperative CT perfusion (CTP), magnetic resonance (MR) perfusion-weighted imaging (PWI) (MR-PWI), and digital subtraction angiography (DSA) were performed to evaluate collateral circulation and brain tissue perfusion. Then craniotomy through the fronto-orbitozygomatic approach was performed, based on which four cases received extended middle skull base approach+Dolenc approach + Fukushima bypass type I, and six cases received extended middle skull base approach+Fukushima bypass type III. After surgery, DSA, CT angiogram (CTA), and CTP/PWI were performed to evaluate the patency of the reconstructed vessels and cerebral perfusion, and contrast-enhanced MRI to evaluate the degree of tumor resection. All patients were followed up for 6–12 months.ResultsAmong the 10 cases investigated, gross total resection was achieved in 8 cases, subtotal resection in 1 case, and partial resection in 1 case, as confirmed by CT and enhanced MRI. The patency of revascularization vessels was observed using fluorescein angiography during the operation in all patients and via DSA and CTA postoperatively in nine patients. One patient underwent ventilator-assisted ventilation because of respiratory failure and failed to undergo DSA and CTA. Regarding postoperative complications, one patient developed watershed cerebral infarction on the operated side but no sequelae after drug treatment, three patients developed facial numbness, which improved after 3 months, and two patients experienced worsened diplopia. After 6 to 12 months of follow-up on the nine evaluable patients, the Glasgow Outcome Scale (GOS) was 4–5 after surgery. In addition, 6-month follow-up results showed that one patient with clival chondrosarcoma developed recurrence on contrast-enhanced MRI, while no relapse was observed in the other patients.ConclusionFor skull base tumors with intracranial and extracranial invasion and involving the ICA, revascularization might improve the total resection rate and reduce the recurrence rate and risk of intraoperative bleeding and postoperative ischemia

{μ2-6,6′-Dimeth­oxy-2,2′-[butane-1,4-diylbis(nitrilo­methyl­idyne)]diphenolato}trinitratocopper(II)neodymium(III)

In the title complex, [CuNd(C20H22N2O4)(NO3)3], the CuII ion is coordinated in a distorted square-planar environment by two O atoms and two N atoms of a tetra­dentate Schiff base ligand. The NdIII ion is ten-coordinated by three bis-chelating nitrate groups and four O atoms of the Schiff base ligand. The atoms of one of the nitrato ligands are disordered over two sets of sites, with refined occupancies of 0.567 (13) and 0.433 (17)

Factorization and Unitarity in Superstring Theory

The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes involved and determined their overall coefficients in a consistent way.Comment: LaTex file, 19 pages, 4 figures; v2, minor corrections and figures corrected; v3, minor corrections with the English, to be published in JHE