Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene

Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy Landau level of a Dirac hamiltonian is not lifted by gauge field disorder, for example due to ripples, whereas other Landau levels become broadened by the inhomogenous effective magnetic field. That also the bilayer hamiltonian supports such protected bulk zero-modes was proved formally by Katsnelson and Prokhorova to hold on a compact manifold by using the Atiyah-Singer index theorem. Here we complement and generalize this result in a pedestrian way by pointing out that the simple argument by Aharonov and Casher for degenerate zero-modes of a Dirac hamiltonian in the infinite plane extends naturally to the multilayer case. The degeneracy remains, though at nonzero energy, also in the presence of a gap. These threshold modes make the spectrum asymmetric. The rest of the spectrum, however, remains symmetric even in arbitrary gauge fields, a fact related to supersymmetry. Possible benefits of this connection are discussed.Comment: 6 pages, 2 figures. The second version states now also in words that the conjugation symmetry that in the massive case gets replaced by supersymmetry is the chiral symmetry. Changes in figure

CD62L (L-selectin) shedding for assessment of perioperative immune sensitivity in patients undergoing cardiac surgery with cardiopulmonary bypass

OBJECTIVE: To investigate the suitability of blood granulocyte and monocyte sensitivity, as measured by the quantity of different agonists required to induce CD62L shedding, for assessment of perioperative immune changes in patients undergoing cardiac surgery with cardiopulmonary bypass. METHODS: Patients scheduled for aortocoronary bypass grafting or for valve surgery were included in this prospective observational study. Blood samples were drawn before anesthesia induction, directly after surgery and 48 hours after anesthesia induction. We determined the concentration of two different inflammatory stimuli--lipoteichoic acid (LTA) and tumor necrosis factor alpha (TNF)--required to induce shedding of 50% of surface CD62L from blood granulocytes and monocytes. In parallel monocyte surface human leukocyte antigen (HLA)-DR, and plasma interleukin (IL)-8, soluble (s)CD62L, soluble (s)Toll-like receptor (TLR)-2 and ADAM17 quantification were used to illustrate perioperative immunomodulation. RESULTS: 25 patients were enrolled. Blood granulocytes and monocytes showed decreased sensitivity to the TLR 2/6 agonist Staphylococcus aureus LTA immediately after surgery (p = 0.001 and p = 0.004 respectively). In contrast, granulocytes (p = 0.01), but not monocytes (p = 0.057) displayed a decreased postoperative sensitivity to TNF. We confirmed the presence of a systemic inflammatory response and a decreased immune sensitivity in the post-surgical period by measuring significant increases in the perioperative plasma concentration of IL-8 (p </= 0.001) and sTLR (p = 0.004), and decreases in monocyte HLA-DR (p<0.001), plasma sCD62L (p </= 0.001). In contrast, ADAM17 plasma levels did not show significant differences over the observation period (p = 0.401). CONCLUSIONS: Monitoring granulocyte and monocyte sensitivity using the "CD62L shedding assay" in the perioperative period in cardiac surgical patients treated with the use of cardiopulmonary bypass reveals common changes in sensitivity to TLR2/6 ligands and to TNF stimulus. Further long-term follow-up studies will address the predictive value of these observations for clinical purposes