Electron transport in interacting hybrid mesoscopic systems

A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific circumstances. In such a formulation, the requirement of gauge invariance for the current is satisfied automatically. Moreover, one can judge unambiguously what quantities can be measured in the transport experiment

The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy

The CDW Hartree-Fock state at half filling and half electron per unit cell is examined. Firstly, an exact solution in terms of Bloch-like states is presented. Using this solution we discuss the dynamics near half filling and show the mass to diverge logarithmically as this filling is approached. We also show how a uniform density state may be constructed from a linear combination of two degenerate solutions. Finally we show the second order correction to the energy to be an order of magnitude larger than that for competing CDW solutions with one electron per unit cell.Comment: 14 pages, no figures, extended acknowledgements, two new references include

Pair formation in two electron correlated chains

We study two correlated electrons in a nearest neighbour tight- binding chain, with both on site and nearest neighbour interaction. Both the cases of parallel and antiparallel spins are considered. In addition to the free electron band for two electrons, there are correlated bands with positive or negative energy, depending on wheather the interaction parameters are repulsive or attractive. Electrons form bound states, with amplitudes that decay exponentially with separation. Conditions for such states to be filled at low temperatures are discussed.Comment: To appear in J. Phys: Condens. Matter 15 (2003

Azbel-Hofstadter model on triangular lattice revisited

In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be related to the logarithm of the partition function of the two dimensional Ising model and has a connection to the asymptotic bandwidth. We find that the correspondence of this quantity to the logarithm of the partition function of the two dimensional Ising model is not complete for the triangular lattice. Moreover, the detailed connection between this quantity and the asymptotic bandwidth is not valid. Thus the conclusions for the mean of Lyapunov exponents suggested previously depend on the lattice geometry.Comment: RevTeX, 4 page, no figur

Fano resonances and Aharonov-Bohm effects in transport through a square quantum dot molecule

We study the Aharonov-Bohm effect in a coupled 2$\times$2 quantum dot array with two-terminals. A striking conductance dip arising from the Fano interference is found as the energy levels of the intermediate dots are mismatched, which is lifted in the presence of a magnetic flux. A novel five peak structure is observed in the conductance for large mismatch. The Aharonov-Bohm evolution of the linear conductance strongly depends on the configuration of dot levels and interdot and dot-lead coupling strengths. In addition, the magnetic flux and asymmetry between dot-lead couplings can induce the splitting and combination of the conductance peak(s).Comment: 15 pages, 7 figures, Revtex, to be published in Phys. Rev.

Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations

Two-dimensional Bloch electrons in a uniform magnetic field exhibit complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these new symmetries. We have also found an electric-modulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.Comment: 8 pages, 6 figures (reduced in sizes), submitted to Phys. Rev.

Absorption and wavepackets in optically excited semiconductor superlattices driven by dc-ac fields

Within the one-dimensional tight-binding minibands and on-site Coloumbic interaction approximation, the absorption spectrum and coherent wavepacket time evolution in an optically excited semiconductor superlattice driven by dc-ac electric fields are investigated using the semiconductor Bloch equations. The dominating roles of the ratios of dc-Stark to external ac frequency, as well as ac-Stark to external ac frequency, is emphasized. If the former is an integer ${\cal N}$, then also ${\cal N}$ harmonics are present within one Stark frequency, while the fractional case leads to the formation of excitonic fractional ladders. The later ratio determines the size and profile of the wavepacket. In the absence of excitonic interaction it controls the maximum size wavepackets reach within one cycle, while the interaction produces a strong anisotropy and tends to palliate the dynamic wavepacket localization.Comment: 14 pages, 7 postscript figure