We study a system of one-dimensional electrons in the regime of strong repulsive interactions, where the spin exchange coupling J is small compared with the Fermi energy, and the conventional Tomonaga-Luttinger theory does not apply. We show that the tunneling density of states has a form of an asymmetric peak centered near the Fermi level. In the spin-incoherent regime, where the temperature is large compared to J, the density of states falls off as a power law of energy epsilon measured from the Fermi level, with the prefactor at positive energies being twice as large as that at the negative ones. In contrast, at temperatures below J the density of states forms a split peak with most of the weight shifted to negative epsilon.
We present data from Mo/a-Si/Mo tunnel junctions together with calculations that show that hopping transport via localized states in amorphous silicon is highly correlated. Localized states whose single-particle energies lie well below the Fermi level participate in transport due to the large on-site Coulomb interaction U. The results also imply that the density of these states is roughly constant over a wide energy range of order U.Electron-electron interactions are believed to play an important role in transport through disordered insulators with a high density of localized states. Efros and Shklovskii predicted that the Coulomb interactions between electrons on different sites in a system exhibiting Mott variable range hopping (VRH) should lead to a gap in the density of states at sufficiently low temperature and to a crossover from the Mott T ' law to a T ' 2 law. 'The experimental evidence from many different systems strongly indicates the presence of this crossover. Little attention has been paid, however, to the role of the on-site Coulomb interaction in hopping transport. Glazman and Matveev predicted that in a tunnel junction with a thin disordered insulating barrier, the on-site Coulomb interaction would lead to correlated resonant tunneling via localized states, which would reveal itself in the magnetic-field dependence of the conductance. Two of us (D.E. and M.R.B) have recently demonstrated this effect experimentally using deposited amorphous silicon (a-Si) tunnel barriers, but were led to postulate correlations in the hopping transport channels incorporating two localized states in order to account fully for the data.In this paper, we confirm the correlated nature of both the resonant and the multisite hopping channels and present theoretical calculations in quantitative agreement with the data. In addition, our results demonstrate that because of the correlated nature of the transport, localized states far below the Fermi energy can participate in transport in disordered insulators, in contrast to the usual single-particle picture. Finally, we note the implications of these results for the magnetoresistance in the variable-range-hopping regime.To understand the physics of these correlations, consider resonant tunneling through a single site near the Fermi level and situated in the center of the barrier for simplicity. In the absence of any Coulomb interactions, the two spin-degenerate localized states associated with the single site support two independent resonant conduction channels. If U is much greater than both e V and kT, however, then these two channels become highly correlated. %'hile an electron is tunneling through one of the I U mmw4Lm w~e eaaMmal l (b) + (c) , 2' FIG. 1. Schematic representation of correlated resonant tunneling via localized states. A large on-site Coulomb energy U allows only one electron to tunnel through a given site at a time (a), but also enables electrons to tunnel through sites found roughly U below the Fermi level {b); the number of e8'ective channels is between...
Electron tunneling in transverse magnetic fields is studied with regard to multiple-subbarrier scattering by phonons. It is shown that the electron-phonon interaction facilitates tunneling considerably because of the shift of the magnetic-oscillator center upon scattering. This involves, in particular, a strong temperature dependence of the tunnel-junction conductance in magnetic fields parallel to the dielectric-interlayer plane. These eA'ects may show up in the hopping conductivity in a magnetic field.Electron tunneling is known to be strongly suppressed by a transverse magnetic field. In particular, in the presence of a field H directed along the z axis the asymptotic behavior exp( r/a)of the wave function of the ground state of an impurity-bound electron is substituted by
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