Symmetry dictated universal helicity redistribution of Dirac fermions in transport

Helicity is a fundamental property of Dirac fermions. Yet, how it changes in transport processes remains largely mysterious. We uncover, theoretically, the rule of spinor state transformation and consequently universal helicity redistribution in two cases of transport through potentials of electrostatic and mass types, respectively. The former is dictated by Lorentz boost and its complex counterpart in Klein tunneling regime. The latter is governed by an abstract rotation group we identified, which reduces to SO(2) when acting on the plane of effective mass and momentum. This endows an extra structure foliating the Hilbert space of Dirac spinors, establishes miraculously a unified yet latent connection between helicity, Klein tunneling, and Lorentz boost. Our results thus deepen the understanding of relativistic quantum transport, and may open a new window for exotic helicity-based physics and applications in mesoscopic systems.Comment: 6 pages, 4 figure

Dimension Increase via Hierarchical Hydrogen Bonding from Simple Pincer-like Mononuclear complexes

A tetradentate symmetric ligand bearing both coordination and hydrogen bonding sites, N1,N3-bis(1-(1H-benzimidazol-2-yl)-ethylidene)propane-1,3-diamine (H2bbepd) was utilized to synthesize a series of transition metal complexes, namely [Co(H2bbepd)(H2O)2]·2ClO4 (1), [Cu(H2bbepd)(OTs-)]·OTs- (2),[Cu(bbepd)(CH3OH)] (3), [Cd(H2bbepd)(NO3)2]·CH3OH (4), [Cd(H2bbepd)(CH3OH)Cl]·Cl (5), and [Cd(bbepd)(CH3OH)2] (6). These complexes show similar discrete pincer-like coordination units, possessing different arrangements of hydrogen bonding donor and acceptor sites. With or without the aid of uncoordinated anions and solvent molecules, such mononuclear units have been effectively involved in the construction of hierarchical hydrogen bonding assemblies (successively via level I and level II), leading to discrete binuclear ring (complex 2), one-dimensional chain or ribbon (complexes 3, 4 and 6) and two-dimensional layer (complexes 1 and 5) aggregates