In 1976 Jackiw and Rebbi found 1/2 of a fermion number by using Dirac equation. Schrieffer, in several proposals made an effort to suggest that there is a fractional charge. The calculations of Peierls distortion, Berry’s phase and classical action were presented to accomodate the fractional charge in non-relativistic theory. Laughlin used the antisymmetry to define the charge density per unit ...

The spectrum of a segment of InAs nanowire, confined between two superconducting leads, was measured as function of gate voltage and superconducting phase difference using a third normal-metal tunnel probe. Subgap resonances for odd electron occupancy-interpreted as bound states involving a confined electron and a quasiparticle from the superconducting leads, reminiscent of Yu-Shiba-Rusinov sta...

We use electron tunneling to measure electronic energy levels in individual nm-scale Al particles. For sufficiently large particles (*5 nm in radius), the eigenstate energies reveal the existence of a superconducting excitation gap V which is driven continuously to zero by an applied magnetic field. The presence of V increases the voltage threshold for tunneling in a particle with an even numbe...

Dissociation of diatomic molecules with odd number of electrons always causes the unpaired electron to localize on one of the two resulting atomic fragments. In the simplest diatomic molecule H2+ dissociation yields a hydrogen atom and a proton with the sole electron ending up on one of the two nuclei. That is equivalent to breaking of a chemical bond-the most fundamental chemical process. Here...

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many–particle configuration space. Electron-magnetic field and electron-electron interactions under FQHE conditions are treated as functional connections over the torus, the torus being the underlying two-dimensional manifold. Relations to the (2+1)–dimens...

We revisit the constraints imposed by electric dipole moments (EDMs) of nucleons and heavy atoms on new CP -violating sources within supersymmetric theories. We point out that certain two-loop renormalization group corrections induce significant mixing between the basis-invariant CP -odd phases. In the framework of the constrained minimal supersymmetric standard model (CMSSM), the CP -odd invar...