Quantum wire networks with local Z2 symmetry

For a large class of networks made of connected loops, in the presence of an external magnetic field of half flux quantum per loop, we show the existence of a large local symmetry group, generated by simultaneous flips of the electronic current in all the loops adjacent to a given node. Using an ultra-localized single particle basis adapted to this local Z_2 symmetry, we show that it is preserved by a large class of interaction potentials. As a main physical consequence, the only allowed tunneling processes in such networks are induced by electron-electron interactions and involve a simultaneous hop of two electrons. Using a mean-field picture and then a more systematic renormalization-group treatment, we show that these pair hopping processes do not generate a superconducting instability, but they destroy the Luttinger liquid behavior in the links, giving rise at low energy to a strongly correlated spin-density-wave state.Comment: 16 pages, 9 figures, v.2 section IV D added,accepted for publication in PR

Study of disposable microdevices for DNA electrophoresis

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, September 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. [77]-[79]).A study was undertaken to determine if a microfluidic chip, made of economical plastic materials, is feasible. The chip was designed to perform gel electrophoresis, specifically of DNA fragments for either sequencing or identification purposes. With a disposable version of such a chip, constraints on the gel type are relaxed and lifetime issues become nonexistent. Such a chip was created using polydimethylsiloxane(PDMS) as the plastic material, with a cast molding process. The chip was subsequently sealed against a piece of PDMS, mounted on a glass slide for structural support. Fluidic and electrical interconnects were added to the chip. A polyacrylarnide solution was injected into the chip for use in DNA separations. The chip was then placed into an apparatus designed for laser induced fluorescence(LIF) detection. Several different samples were run on the chip, including polystyrene beads, organic dye molecules, and single tandem repeat (STR) allelic ladders. The chip demonstrated its electrophoretic efficiency, evincing a low, almost negligible amount of electroosmotic flow. The separation of the dye and DNA was accomplished with good fidelity, allowing for identification of the various substitutents of the loaded sample.(cont.) The PDMS chip, though demonstrably efficient at DNA separation, needs work before it can move out of the prototype phase. Substantial work on the fluidic interconnection, as well as the basic plastic formulation is needed to move this idea forward. However, the chip is sufficient for a clear proof of the principle of disposable chips use in electrophoretic separations.by Winston Timp.S.M

Study of cell-cell communication using 3D living cell microarrays

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 135-152).Cellular behavior is not dictated solely from within; it is also guided by a myriad of external cues. If cells are removed from their natural environment, apart from the microenvironment and social context they are accustomed to, it is difficult to study their behavior in any meaningful way. To that end, I describe a method for using optical trapping for positioning cells with submicron accuracy in three dimensions, then encapsulating them in hydrogel, in order to mimic the in vivo microenvironment. This process has been carefully optimized for cell viability, checking both prokaryotic and eukaryotic cells for membrane integrity and metabolic activity. To demonstrate the utility of this system, I have looked at a model "quorum sensing" system in Vibrio Fischeri, which operates by the emission and detection of a small chemical signal, an acyl-homoserine lactone. Through synthetic biology, I have engineered plasmids which express "sending" and "receiving" genes. Bacteria containing these plasmids were formed into complex 3D patterns, designed to assay signaling response. The gene expression of the bacteria was tracked over time using fluorescent proteins as reporters. A model for this system was composed using a finite element method to simulate signal transport through the hydrogel, and simple mass-action kinetic equations to simulate the resulting protein expression over time.by Winston Timp.Ph.D

Regular networks of Luttinger liquids

We consider arrays of Luttinger liquids, where each node is described by a unitary scattering matrix. In the limit of small electron-electron interaction, we study the evolution of these scattering matrices as the high-energy single particle states are gradually integrated out. Interestingly, we obtain the same renormalization group equations as those derived by Lal, Rao, and Sen, for a system composed of a single node coupled to several semi-infinite 1D wires. The main difference between the single node geometry and a regular lattice is that in the latter case, the single particle spectrum is organized into periodic energy bands, so that the renormalization procedure has to stop when the last totally occupied band has been eliminated. We therefore predict a strongly renormalized Luttinger liquid behavior for generic filling factors, which should exhibit power-law suppression of the conductivity at low temperatures E_{F}/(k_{F}a) > 1. Some fully insulating ground-states are expected only for a discrete set of integer filling factors for the electronic system. A detailed discussion of the scattering matrix flow and its implication for the low energy band structure is given on the example of a square lattice.Comment: 16 pages, 7 figure

Theory of Incompressible States in a Narrow Channel

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the charge-density profile of translationally invariant states. We derive a phase diagram which includes many of the stable odd-denominator states as well as a novel fractional quantum Hall state at lowest half-filled Landau level. The collective mode evaluated at the half-filled case is strikingly similar to that for an odd-denominator fractional quantum Hall state.Comment: 4 pages, REVTEX, and 4 .ps file

Observation of Resonant Tunneling in Silicon Inversion Layers

Measurements of the temperature and carrier-density dependence of the strongly localized conductance of short silicon inversion layers are reported. At the lowest temperatures we observe well-isolated, large conductance peaks whose width and temperature dependence are only consistent with resonant tunneling and are inconsistent with Mott hopping. Several new features are observed which we believe may be the result of Coulomb interactions

Finite Size Analysis of Luttinger Liquids with a source of 2k_f Scattering

Numerical analysis of the spectrum of large finite size Luttinger liquids (g<1) in the presence of a single source of 2k_f scattering has been made possible thanks to an effective integration of high degrees of freedom. Presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by g=1/2. Temperature dependence of conductance is shown to be dominated by hopping alone. Frequency dependence is affected by both irrelevant operators.Comment: 4 pages, LaTex (RevTex), 3 PostScript figures appende

Disorder suppression and precise conductance quantization in constrictions of PbTe quantum wells

Conductance quantization was measured in submicron constrictions of PbTe, patterned into narrow,12 nm wide quantum wells deposited between Pb$_{0.92}$Eu$_{0.08}$Te barriers. Because the quantum confinement imposed by the barriers is much stronger than the lateral one, the one-dimensional electron energy level structure is very similar to that usually met in constrictions of AlGaAs/GaAs heterostructures. However, in contrast to any other system studied so far, we observe precise conductance quantization in $2e^2/h$ units, {\it despite of significant amount of charged defects in the vicinity of the constriction}. We show that such extraordinary results is a consequence of the paraelectric properties of PbTe, namely, the suppression of long-range tails of the Coulomb potentials due to the huge dielectric constant.Comment: 7 pages, 6 figures, submitted to Phys. Rev.

Stretching and unzipping nucleic acid hairpins using a synthetic nanopore

We have explored the electromechanical properties of DNA by using an electric field to force single hairpin molecules to translocate through a synthetic pore in a silicon nitride membrane. We observe a threshold voltage for translocation of the hairpin through the pore that depends sensitively on the diameter and the secondary structure of the DNA. The threshold for a diameter 1.5 < d < 2.3 nm is V > 1.5 V, which corresponds to the force required to stretch the stem of the hairpin, according to molecular dynamics simulations. On the other hand, for 1.0 < d < 1.5 nm, the threshold voltage collapses to V < 0.5 V because the stem unzips with a lower force than required for stretching. The data indicate that a synthetic nanopore can be used like a molecular gate to discriminate between the secondary structures in DNA

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.