Pavel Vagner

Electron–impurity scattering in free-standing quantum wires: Effect of dielectric confinement

We calculate the impurity-scattering limited mobility of the one-dimensional electron gas in a rectangular GaAs quantum wire confined in the vertical (growth) direction by n-modulation doped AlGaAs layers and free-standing along the transverse direction. The Fourier-transformed scattering potential of the ionized impurity is obtained analytically by solving the Poisson equation with z-dependent electrostatic permittivity. An abrupt permittivity change at the GaAs(AlGaAs)/air interfaces gives rise to the image charge effect which strongly modifies the unperturbed scattering potential. We show that the “image impurity” scattering tends to drastically reduce the electron mobility for sufficiently small (∼10 nm) transverse wire widths.

Persistent current of correlated electrons in mesoscopic ring with impurity

The persistent current of correlated electrons in a continuous one-dimensional ring with a single scatterer is calculated by solving the many-body Schrodinger equation for several tens of electrons interacting via the electron-electron (e-e) interaction of finite range. The problem is solved by the configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. The CI and DMC results are in good agreement. In both cases, the persistent current I as a function of the ring length L exhibits the asymptotic dependence I α L -1-α typical of the Luttinger liquid, where the power a depends only on the e-e interaction. The numerical values of a agree with the known formula of the renormalization-group theory.

Tunneling of interacting one-dimensional electrons through a single scatterer: Luttinger liquid behavior in the Hartree–Fock model

We study tunneling of weakly interacting spinless electrons at zero temperature through a single δ barrier in one-dimensional wires and rings of finite lengths. Our numerical calculations are based on the self-consistent Hartree-Fock approximation, nevertheless, our results exhibit features known from correlated many-body models. In particular, the transmission in a wire of length L at the Fermi level is proportional to L -2α with the universal power α (depending on the electron-electron interaction only, not on the strength of the δ barrier). Similarly, the persistent current in a ring of the circumference L obeys the rule I ∝ L -1-α known from the Luttinger liquid and Hubbard models. We show that the transmission at the Fermi level in the wire is related to the persistent current in the ring at the magnetic flux h/4e.

Coherent transport of interacting electrons through a single scatterer

Using the self-consistent Hartree-Fock method, we calculate the persistent current of weakly interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We find that the persistent current decays with the system length (L) asymptotically like I∝ α L -1-α , where α>0 is the power depending only on the electron-electron interaction. We also simulate tunneling of the weakly interacting one-dimensional electron gas through a single δ barrier in a finite wire biased by contacts. We find that the Landauer conductance decays with the system length asymptotically like L -2α . The power laws L -1-α and L -2α have so far been observed only in correlated models. Their existence in the Hartree-Fock model is thus surprising.