K. A. Chao

A theory of ferromagnetism in the Hubbard model with infinite Coulomb interaction

On the basis of a regular perturbation theory in the form of diagrammatic technique with X-operators, a ferromagnetic state in the Hubbard model with infinite on-site Coulomb interaction U is studied for a wide range of electron concentration n. Treating the kinetic energy of electrons as perturbation, we get the exact graphic representations for three Green’s functions and for electrons with spin ↑ and ↓ (spontaneous magnetic moment is in ↑ direction) and for spin waves. All of them are expressed through the unique system of four-point and three-point vertex parts for effective electron-magnon and electron-electron interactions. These vertex parts are calculated in two approximations: a low-density approximation for n≪1 or nh=1–n≫1, and the generalized random-phase approximation (GRPA), which was suggested earlier by us for the description of paramagnetic phase in this model. An important result in both cases is the understanding of essential difference of electron states with spin ↑ and ↓. The state for ↑ has coherent character in all region of electron concentration (n>nc) where a ferromagnetic state exists, while the state for spin ↓ has mixed characters including both coherent and incoherent contribution. For the saturated ferromagnetism (n>ns) when nh≪1, is an entirely incoherent (nonquasiparticle) state. Appearance of incoherent state is probably a general property of strongly correlated systems distinguishing its behavior from the Fermi liquid. We show also that the Hubbard-I approximation has no region of applicability for the electron with spin ↓ in a ferromagnet and we found a new factor describing the correlation-narrowing of ↓ spin electron band. Green’s function calculated in two different limits n≪1 and nh≪1, are jointed together to allow us to calculate ns which lies in the intermediate concentration regime. For simple cubic lattice we found ns=0.87. In the limit nh≪1 our results reduce to the earlier known ones, including Nagaoka’s result for the spin wave energy. We point out the way to construct a rigorous theory for ferromagnetic state in the intermediate range of electron concentration. In the conclusion several important problems are discussed in connection to the continuation of the present work.

Resonant tunneling: from model Hamiltonian to modern electronic devices

The single-electron theory of resonant-tunneling through a double-barrier structure with perfect interfaces has been reviewed, and the future direction of theoretical development including the electron-electron interaction and rough interfaces is outlined. The theoretical understanding of this system reveals its potential application to quantum electronic devices.

Raman scattering from a circular quantum dot

Electronic Raman scattering from a doped circular quantum dot is studied within the random phase approximation. The Raman spectrum of the spin density fluctuation channel consists of only sharp peaks due to single-particle excitations. However, for the charge density fluctuation channel, the broadened plasmon peak in a small quantum dot may overlap with the sharp single-particle peaks, resulting in fine structures in the Raman spectrum.

Optimization of charge sensitivity of a single electron tunneling transistor with a superconducting grain

Assuming the absence of 1/f noise, we have calculated the charge sensitivity (CS) of a capacitive‐coupled double‐junction single electron tunneling transistor (SETT) with a superconducting grain, operating at low temperature and low bias voltage such that the tunneling current is dominated by the Andreev process. In this case the effect of co‐tunneling is suppressed without using the complicated fabrication method. We have used a realistic sample to demonstrate the procedure of optimizing the CS of a SETT with respect to relevant physical parameters and structure parameters. With the presently available fabrication technology, our theoretical analysis can serve as a guide for increasing the CS of a SETT beyond 10−6 e/√Hz.