Transport properties of a two-dimensional electron liquid at high magnetic field

The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors $\nu<1$ -- without reference to the quantum Hall effect. Based on this model, we develop a formalism to calculate the Landauer-B\"uttiker conductances in generic experimental set-ups including multiple leads and voltage probes. In the absence of tunneling between the edges the "ideal" Hall conductances ($G_{ij}= \frac{e^2 \nu}{h}$ if lead $j$ is immediately upstream of lead $i$, and $G_{ij}=0$ otherwise) are recovered. Tunneling of quasiparticles of fractional charge $e^*$ between different edges is then included as an additional term in the Hamiltonian. In the limit of weak tunneling we obtain explicit expressions for the corrections to the ideal conductances. As an illustration of the formalism we compute the current- and temperature-dependent resistance $R_{xx}(I,T)$ of a quantum point contact localized at the center of a gate-induced constriction in a quantum Hall bar. The exponent $\alpha$ in the low-current relation $R_{xx}(I,0) \sim I^{\alpha -2}$ shows a nontrivial dependence on the strength of the inter-edge interaction, and its value changes as $e^*V_H$, where $V_H = \frac{h I}{\nu e^2}$ is the Hall voltage, falls below a characteristic crossover energy $\frac{\hbar c}{d}$, where $c$ is the edge wave velocity and $d$ is the length of the constriction. The consequences of this crossover are discussed vis-a-vis recent experiments in the weak tunneling regime.Comment: 20 pages, 8 figures, Revtex4, adjourned with referee's comments, added references and typos correcte

Non- V -representability of currents in time-dependent many-particle systems

URL:http://link.aps.org/doi/10.1103/PhysRevB.71.245103 DOI:10.1103/PhysRevB.71.245103We argue that an arbitrarily chosen time-dependent current density is generically non-V-representable in a many-particle system; i.e., it cannot be obtained by applying only a time-dependent scalar potential to the system. Furthermore, we show by a concrete example that even a current that is V-representable in an interacting many-particle system may (and in general will) turn out to be non-V-representable when the interaction between the particles is turned off.The authors acknowledge support from NSF Grant No. DMR-0313681