Relation between flux formation and pairing in doped antiferromagnets

We demonstrate that patterns formed by the current-current correlation function are landmarks which indicate that spin bipolarons form in doped antiferromagnets. Holes which constitute a spin bipolaron reside at opposite ends of a line (string) formed by the defects in the antiferromagnetic spin background. The string is relatively highly mobile, because the motion of a hole at its end does not raise extensively the number of defects, provided that the hole at the other end of the line follows along the same track. Appropriate coherent combinations of string states realize some irreducible representations of the point group C_4v. Creep of strings favors d- and p-wave states. Some more subtle processes decide the symmetry of pairing. The pattern of the current correlation function, that defines the structure of flux, emerges from motion of holes at string ends and coherence factors with which string states appear in the wave function of the bound state. Condensation of bipolarons and phase coherence between them puts to infinity the correlation length of the current correlation function and establishes the flux in the system.Comment: 5 pages, 6 figure

Kondo effect in systems with dynamical symmetries

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets $|S_{i}M_{i}>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_{i}}$ are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators ${\bf R}_{n}$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $\ne 0$. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin ${\bf s}$ with the operators of the dot then contains new exchange terms, $J_{n} {\bf s} \cdot {\bf R}_{n}$ beside the ubiquitous ones $J_{i} {\bf s}\cdot {\bf S}_{i}$. The operators ${\bf S}_{i}$ and ${\bf R}_{n}$ generate a dynamical group (usually SO(n)). Remarkably, the value of $n$ can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators ${\bf R}_{n}$ and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in triple quantum dot with four electrons.Comment: 24 two-column page