In this letter we describe the preparation of large-area, two-dimensional metallic structures using shadow nanosphere lithography. By varying the position of the substrate with respect to the evaporation source during the sample preparation, we make morphologies such as cups, rods, and wires, that are not accessible by the standard nanosphere lithography. This technique also allows for an encapsulation of the metallic structures, to prevent them from oxidation. Morphologies predicted by our computer simulations have been subsequently confirmed experimentally.
arXiv:1205.0239v1 [cond-mat.str-el] 1 May 2012Luttinger liquid theory of purple bronze Li 0.9 Mo 6 O 17 in the charge regime.P. Chudzinski, T. Jarlborg, and T. Giamarchi DPMC, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland (Dated: March 4, 2018 Molybdenum purple bronze Li0.9Mo6O17 is an exceptional material known to exhibit one dimensional (1D) properties for energies down to a few meV. This fact seems to be well established both in experiments and in band structure theory. We use the unusual, very 1-dimensional band dispersion obtained in ab-initio DFT-LMTO band calculations as our starting point to study the physics emerging below 300meV. A dispersion perpendicular to the main dispersive direction is obtained and investigated in detail. Based on this, we derive an effective low energy theory within the Tomonaga Luttinger liquid (TLL) framework. We estimate the strength of the possible interactions and from this deduce the values of the TLL parameters for charge modes. Finally we investigate possible instabilities of TLL by deriving renormalization group (RG) equations which allow us to predict the size of potential gaps in the spectrum. While 2kF instabilities strongly suppress each other, the 4kF instabilities cooperate, which paves the way for a possible CDW at the lowest energies. The aim of this work is to understand the experimental findings, in particular the ones which are certainly lying within the 1D regime. We discuss the validity of our 1D approach and further perspectives for the lower energy phases. [12]. Although the main effort of those investigations was focused on the nature of a mysterious phase transition at around 25K, interesting knowledge about higher energy phase was also gathered. Certain properties of the one dimensional (1D) metal, the Luttinger liquid (TLL), have been invoked to explain the measured data [2,3,13,14] and nowadays the presence of the 1D physics is well established experimentally [15,16], at least in some energy range.On the theoretical side, band structure calculations have shown a quasi-1D character of molybdenum purple bronze. A remarkably simple band structure emerges from rather complex crystal structure. At the Fermi surface there are only two bands, lying very close to each other, in the form of flat sheets dispersing well only along the b-axis. This gives a hope that purple bronze can indeed be a rare realization of the 1D physics.The key problem is that several possible mechanisms has been invoked to explain the observed properties, which made the subject quite unclear and controversial. In our opinion the reason for this situation is that each of previous attempts was focused only on one out of many peculiar properties of Li 0.9 M o 6 O 17 and most of them searched for an explanation in the low energy regime (below 5meV ), where indeed the properties of Li 0.9 M o 6 O 17 are the most spectacular. By now, not enough attention has been paid even to the parameters of the 1D state. It is only agreed that it emerges at energies as hi...
In the weak-coupling limit, we investigate two-leg ladders with a unit cell containing both Cu and O atoms as a function of doping. For purely repulsive interactions, using bosonization, we find significant differences with the single-orbital case: a completely massless quantum critical regime is obtained for a finite range of carrier concentration. In a broad region of the phase diagram, the ground state consists of a pattern of orbital currents plus a density wave. NMR properties of the Cu and O nuclei are presented for the various phases.
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