# Browsing by Subject "Luttinger liquid"

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Item Open Access Electron Transport through Carbon Nanotube Quantum Dots in A Dissipative Environment(2012) Mebrahtu, Henok TesfamariamThe role of the surroundings, or environment , is essential in understanding funda- mental quantum-mechanical concepts, such as quantum measurement and quantum entanglement. It is thought that a dissipative environment may be responsible for certain types of quantum (i.e. zero-temperature) phase transitions. We observe such a quantum phase transition in a very basic system: a resonant level coupled to a dissipative environment. Specifically, the resonant level is formed by a quantized state in a carbon nanotube, and the dissipative environment is realized in resistive leads; and we study the shape of the resonant peak by measuring the nanotube electronic conductance.

In sequential tunneling regime, we find the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weakly than the conventional T-1. Moreover, the observed scaling signals a close connec- tion between fluctuations that influence tunneling phenomenon and macroscopic models of the electromagnetic environment.

In the resonant tunneling regime (temperature smaller than the intrinsic level width), we characterize the resonant conductance peak, with the expectation that the width and height of the resonant peak, both dependent on the tunneling rate, will be suppressed. The observed behavior crucially depends on the ratio of the coupling between the resonant level and the two contacts. In asymmetric barriers the peak width approaches saturation, while the peak height starts to decrease.

Overall, the peak height shows a non-monotonic temperature dependence. In sym- metric barriers case, the peak width shrinks and we find a regime where the unitary conductance limit is reached in the incoherent resonant tunneling. We interpret this behavior as a manifestation of a quantum phase transition.

Finally, our setup emulates tunneling in a Luttinger liquid (LL), an interacting one-dimensional electron system, that is distinct from the conventional Fermi liquids formed by electrons in two and three dimensions. Some of the most spectacular properties of LL are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Our setup allows us to address many prediction of resonant tunneling in a LL, which have not been experimentally tested yet.

Item Open Access Zigzag Phase Transition in Quantum Wires and Localization in the Inhomogeneous One-Dimensional Electron Gas(2013) Mehta, Abhijit CIn this work, we study two important themes in the physics of the interacting one-dimensional (1D) electron gas: the transition from one-dimensional to higher dimensional behavior, and the role of inhomogeneity. The interplay between interactions, reduced dimensionality, and inhomogeneity drives a rich variety of phenomena in mesoscopic physics. In 1D, interactions fundamentally alter the nature of the electron gas, and the homogeneous 1D electron gas is described by Luttinger Liquid theory. We use Quantum Monte Carlo methods to study two situations that are beyond Luttinger Liquid theory --- the quantum phase transition from a linear 1D electron system to a quasi-1D zigzag arrangement, and electron localization in quantum point contacts.

Since the interacting electron gas has fundamentally different behavior in one dimension than in higher dimensions, the transition from 1D to higher dimensional behavior is of both practical and theoretical interest. We study the first stage in such a transition; the quantum phase transition from a 1D linear arrangement of electrons in a quantum wire to a quasi-1D zigzag configuration, and then to a liquid-like phase at higher densities. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition occurs even in narrow wires with strong quantum fluctuations, and that it has characteristics which are qualitatively different from the classical transition.

Experiments in quantum point contacts (QPC's) show an unexplained feature in the conductance known as the ``0.7 Effect''. The presence of the 0.7 effect is an indication of the rich physics present in inhomogeneous systems, and we study electron localization in quantum point contacts to evaluate several different proposed mechanisms for the 0.7 effect. We show that electrons form a Wigner crystal in a 1D constriction; for sharp constriction potentials the localized electrons are separated from the leads by a gap in the density, while for smoother potentials, the Wigner crystal is smoothly connected to the leads. Isolated bound states can also form in smooth constrictions if they are sufficiently long. We thus show that localization can occur in QPC's for a variety of potential shapes and at a variety of electron densities. These results are consistent with the idea that the 0.7 effect and bound states observed in quantum point contacts are two distinct phenomena.