External voltage sources and Tunneling in quantum wires

We (re) consider in this paper the problem of tunneling through an impurity in a quantum wire with arbitrary Luttinger interaction parameter. By combining the integrable approach developed in the case of Quantum Hall edge states with the introduction of radiative boundary conditions to describe the adiabatic coupling to reservoirs, we are able to obtain the exact equilibrium and non equilibrium current. One of the most striking features observed is the appearance of negative differential conductances out of equilibrium in the strongly interacting regime g <=.2. In spite of the various charging effects, a remarkable form of duality is still observed. New results on the computation of transport properties in integrable impurity problems are gathered in appendices. In particular, we prove that the TBA results satisfy a remarkable relation, originally derived using the Keldysh formalism, between the order T^2 correction to the current out of equilibrium and the second derivative of this current at T=0 with respect to the voltage.Comment: 16 pages, 7 figure

Transport theory of carbon nanotube Y junctions

We describe a generalization of Landauer-B\"uttiker theory for networks of interacting metallic carbon nanotubes. We start with symmetric starlike junctions and then extend our approach to asymmetric systems. While the symmetric case is solved in closed form, the asymmetric situation is treated by a mix of perturbative and non-perturbative methods. For N>2 repulsively interacting nanotubes, the only stable fixed point of the symmetric system corresponds to an isolated node. Detailed results for both symmetric and asymmetric systems are shown for N=3, corresponding to carbon nanotube Y junctions.Comment: submitted to New Journal of Physics, Focus Issue on Carbon Nanotubes, 15 pages, 3 figure

Current bistability and hysteresis in strongly correlated quantum wires

Nonequilibrium transport properties are determined exactly for an adiabatically connected single channel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter $g$, for very strong interactions g\lapx 0.2, and sufficiently low temperatures, we find an S-shaped current-voltage relation. The unstable branch with negative differential conductance gives rise to current oscillations and hysteretic effects. These non perturbative and non linear features appear only out of equilibrium.Comment: 4 pages, 1 figur

Inter edge Tunneling in Quantum Hall Line Junctions

We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors $\nu\sim1$ the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter $K$, leading to the appearance of a zero-bias differential conductance peak of magnitude $G_t=Ke^2/h$ at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value $\nu^* \gtrsim 1$, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage $V$, the crossover scale $T_K$, and the temperature $T$. The low height of the zero bias peak $\sim 0.1e^2/h$ observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for $\nu \gtrsim 2$ can be explained as an effect caused by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a small polarization near $\nu\sim2$. We also predict that as the temperature is lowered $\nu^*$ should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for $\nu \gtrsim 2$.Comment: 17 pages, 8 figure