The unusual tunneling effects of massless chiral fermions (mCF) and massive chiral fermions (MCF) in a single layer graphene and bilayer graphene represent some of the most bizarre quantum transport phenomena in condensed matter system. Here we show that in a two-dimensional semiconductor with Rashba spin-orbit coupling (R2DEG), the real-spin chiral-like tunneling of electrons at normal inciden...

Chiral pyrrolidines and pyrrolizidines with spirooxindole ring systems are the central skeletons for numerous alkaloids and pharmacologically important compounds. Gelesmine, pseudotabersonine, formosanine, isoformosanine, morroniside and mitraphylline are some of the alkaloids containing spirooxindole ring systems. Derivatives of spirooxindole find very wide biological applications as anti micr...

This paper is a continuation of our previous work [18]. We obtain two more functional relations for the eigenvalues of the transfer matrices for the sl(3) chiral Potts model at q2 = −1. This model, up to a modification of boundary conditions, is equivalent to the threelayer three-dimensional Zamolodchikov model. From these relations we derive the Bethe ansatz equations. On leave of absence from...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model for roots of unity and the superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations, by which w...

We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N × N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the non-compact manifold Gl(n, C)/U(1)× ... × U(1) (matrix Macdonald function). The correlation function is shown to be al...

We report on progress towards an attempt to understand the representations of infinite dimensional groups that arise from quantum field theories on Riemann surfaces. We consider some examples that arise from the correspondence between chiral Potts integrable models and monopoles established by Atiyah and Murray and explore the Fermi-Bose correspondence on a general Riemann surface. Mathematics ...

We discuss some algebraic setting of chiral SU (N) K models in terms of the satistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral SU (N) K models are calculated from their braid matrices. Furthermore, at level K = 2, we present the characteristic polynomials of their fusion matrices in a factored form.

We establish the Bethe equation of the τ -model in the N -state chiral Potts model (including the degenerate selfdual cases) with alternating vertical rapidities. The eigenvalues of a finite-size transfer matrix of the chiral Potts model are computed by use of functional relations. The significance of the ”alternating superintegrable” case of the chiral Potts model is discussed, and the degener...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...

Recent advances in graphene-nanoribbon-based research have demonstrated the controlled synthesis of chiral graphene nanoribbons (chGNRs) with atomic precision using strategies of on-surface chemistry. However, their electronic characterization, including typical figures of merit like band gap or frontier band's effective mass, has not yet been reported. We provide a detailed characterization of...