Insulating State and Breakdown of Fermi Liquid Description in Molecular-Scale Single-Crystalline Wires of Gold

Electrical transport measurements on ultrathin single-crystalline Au nanowires, synthesized via a wet chemical route, show an unexpected insulating behavior. The linear response electrical resistance exhibits a power-law dependence on temperature. In addition, the variation of current over a wide range of temperature and voltage obeys a universal scaling relation that provides compelling evidence for a non-Fermi liquid behavior. Our results demonstrate that the quantum ground state In ultrathin nanowires of simple metallic systems can be radically different from their bulk counterparts and can be described In terms of a Tomonaga-Luttinger liquid (TLL), in the presence of remarkably strong electron-electron interactions.

Pareamento BCS em um Líquido de Luttinger em 1D

In this work we investigate the effect of a BCS-type pairing term for free spinless fermions, with a propensity to form a condensate of pairs in a 1+1 dimension. Using the of bosonization technique we explore the possible condition of existence of quasiparticles in a superconducting state. Although there is no spontaneous breaking of chiral symmetry the propagator of one-particle fermion is massive and, in fact, resembles the one-particle Green s function of conventional quasiparticles

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

Characterisation of multi wall carbon nanotube–polymer composites for strain sensing applications

Carbon nanotubes (CNTs) have excellent electrical, mechanical and electromechanical properties. When CNTs are incorporated into polymers, electrically conductive composites with high electrical conductivity at very low CNT content (often below 1% wt CNT) result. Due to the change in electrical properties under mechanical load, carbon nanotube/polymer composites have attracted significant research interest especially due to their potential for application in in-situ monitoring of stress distribution and active control of strain sensing in composite structures or as strain sensors. To sucessfully develop novel devices for such applications, some of the major challenges that need to be overcome include; in-depth understanding of structure-electrical conductivity relationships, response of the composites under changing environmental conditions and piezoresistivity of different types of carbon nanotube/polymer sensing devices. In this thesis, direct current (DC) and alternating current (AC) conductivity of CNT-epoxy composites was investigated. Details of microstructure obtained by scanning electron microscopy were used to link observed electrical properties with structure using equivalent circuit modeling. The role of polymer coatings on macro and micro level electrical conductivity was investigated using atomic force microscopy. Thermal analysis and Raman spectroscopy were used to evaluate the heat flow and deformation of carbon nanotubes embedded in the epoxy, respectively, and related to temperature induced resistivity changes. A comparative assessment of piezoresistivity was conducted using randomly mixed carbon nanotube/epoxy composites, and new concept epoxy- and polyurethane-coated carbon nanotube films. The results indicate that equivalent circuit modelling is a reliable technique for estimating values of the resistance and capacitive components in linear, low aspect ratio-epoxy composites. Using this approach, the dominant role of tunneling resistance in determining the electrical conductivity was confirmed, a result further verified using conductive-atomic force microscopy analysis. Randomly mixed CNT-epoxy composites were found to be highly sensitive to mechanical strain and temperature variation compared to polymer-coated CNT films. In the vicinity of the glass transition temperature, the CNT-epoxy composites exhibited pronounced resistivity peaks. Thermal and Raman spectroscopy analyses indicated that this phenomenon can be attributed to physical aging of the epoxy matrix phase and structural rearrangement of the conductive network induced by matrix expansion. The resistivity of polymercoated CNT composites was mainly dominated by the intrinsic resistivity of CNTs and the CNT junctions, and their linear, weakly temperature sensitive response can be described by a modified Luttinger liquid model. Piezoresistivity of the polymer coated sensors was dominated by break up of the conducting carbon nanotube network and the consequent degradation of nanotube-nanotube contacts while that of the randomly mixed CNT-epoxy composites was determined by tunnelling resistance between neighbouring CNTs. This thesis has demonstrated that it is possible to use microstructure information to develop equivalent circuit models that are capable of representing the electrical conductivity of CNT/epoxy composites accurately. New designs of carbon nanotube based sensing devices, utilising carbon nanotube films as the key functional element, can be used to overcome the high temperature sensitivity of randomly mixed CNT/polymer composites without compromising on desired high strain sensitivity. This concept can be extended to develop large area intelligent CNT based coatings and targeted weak-point specific strain sensors for use in structural health monitoring.

Nonlinear transport in semiconducting polymers at high carrier densities

Conducting and semiconducting polymers are important materials in the development of printed, flexible, large-area electronics such as flat-panel displays and photovoltaic cells. There has been rapid progress in developing conjugated polymers with high transport mobility required for high-performance field-effect transistors (FETs), beginning(1) with mobilities around 10(-4) cm(2) V-1 s(-1) to a recent report(2) of 1 cm(2) V-1 s(-1) for poly(2,5-bis(3-tetradecylthiophen-2-yl) thieno[3,2-b] thiophene) (PBTTT). Here, the electrical properties of PBTTT are studied at high charge densities both as the semiconductor layer in FETs and in electrochemically doped films to determine the transport mechanism. We show that data obtained using a wide range of parameters (temperature, gate-induced carrier density, source-drain voltage and doping level) scale onto the universal curve predicted for transport in the Luttinger liquid description of the one-dimensional `metal'.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Power dissipation for systems with junctions of multiple quantum wires

We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi-liquid leads) or noninteracting electrons. We show that for a given matrix M, the eigenvalues of (MM)-M-T characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M matrix whose entries depends on the tunneling amplitudes between the different edges.

Tunability of electronic states in ultrathin gold nanowires

The electronic state in ultrathin gold nanowires is tuned by careful engineering of the device architecture via a chemical methodology. The electrons are localized to an insulating state (showing variable range hopping transport) by simply bringing them close to the substrate, while the insertion of an interlayer leads to a Tomonaga Luttinger liquid state.

Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Effects of electron-electron interactions on the electronic Raman scattering of graphite in high magnetic fields

We report the observation of strongly temperature (T)-dependent spectral lines in electronic Raman-scattering spectra of graphite in a high magnetic field up to 45 T applied along the c axis. The magnetic field quantizes the in-plane motion, while the out-of-plane motion remains free, effectively reducing the system dimension from 3 to 1. Optically created electron-hole pairs interact with, or shake up, the one-dimensional Fermi sea in the lowest Landau subbands. Based on the Tomonaga-Luttinger liquid theory, we show that interaction effects modify the spectral line shape from (ω-Δ)-1/2 to (ω-Δ)2α-1/2 at T = 0. At finite T, we predict a thermal broadening factor that increases linearly with T. Our model reproduces the observed T-dependent line shape, determining the electron-electron interaction parameter α to be ∼0.05 at 40 T. © 2014 American Physical Society.

Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

Crystal Growth and Characterization of Li0.9Mo6O17

Purple bronze Li0.9Mo6O17 has attracted researchers for its low dimensionality and corresponding properties. Although it has been studied for nearly two decades, there are still some unsolved puzzles with this unique material. Single crystals of Li0.9Mo6O17 were grown using the temperature gradient flux technique in this research. The crystal growth was optimized by experimenting different conditions and good quality crystals were obtained. X-ray diffraction results have confirmed the right phase of the crystals. Resistivity measurements and magnetic susceptibility measurements were carried out, and anomalous electronic behaviors were found. All of the samples showed the metal-insulator transition near 20K, followed by behavior that differs from sample to sample: either superconducting, metallic or insulating behavior was observed below 2K. Li0.9Mo6O17 was considered as a quasi-one-dimensional crystal and also a superconducting crystal, which implies a dimensional crossover may occur at the metal-insulator transition. A two-band scenario of the Luttinger liquid model was used to fit the resistivity data and excellent results were achieved, suggesting that the Luttinger theory is a very good candidate for the explanation of the anomalous behavior of Li0.9Mo6O17. In addition, the susceptibility measurements showed Curie paramagnetism and some temperature independent paramagnetism at low temperature. The absence of any anomalous magnetic feature near 20K where the resistivity upturn takes place, suggests that a charge density wave mechanism, which has been proposed by some researchers, is not responsible for the unique properties of Li0.9Mo6O17.

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Physik der Elektronen in Nanostrukturen und niedrigdimensionalen Systemen - Studie zweier Beispiele

Als Beispiele für die vielfältigen Phänomene der Physik der Elektronen in niedrigdimensionalen Systemen wurden in dieser Arbeit das Cu(110)(2x1)O-Adsorbatsystem und die violette Li0.9Mo6O17-Bronze untersucht. Das Adsorbatsystem bildet selbstorganisierte quasi-eindimensionale Nanostrukturen auf einer Kupferoberfläche. Die Li-Bronze ist ein Material, das aufgrund seiner Kristallstruktur quasi-eindimensionale elektronische Eigenschaften im Volumen aufweist. Auf der Cu(110)(2x1)O-Oberfläche kann durch Variation der Sauerstoffbedeckung die Größe der streifenartigen CuO-Domänen geändert werden und damit der Übergang von zwei Dimensionen auf eine Dimension untersucht werden. Der Einfluss der Dimensionalität wurde anhand eines unbesetzten elektronischen Oberflächenzustandes studiert. Dessen Energieposition (untere Bandkante) verschiebt mit zunehmender Einschränkung (schmalere CuO-Streifen) zu größeren Energien hin. Dies ist ein bekannter quantenmechanischer Effekt und relativ gut verstanden. Zusätzlich wurde die Lebensdauer des Zustandes auf der voll bedeckten Oberfläche (zwei Dimensionen) ermittelt und deren Veränderung mit der Breite der CuO-Streifen untersucht. Es zeigt sich, dass die Lebensdauer auf schmaleren CuO-Streifen drastisch abnimmt. Dieses Ergebnis ist neu. Es kann im Rahmen eines Fabry-Perot-Modells als Streuung in Zustände außerhalb der CuO-Streifen verstanden werden. Außer den gerade beschriebenen Effekten war es möglich die Ladungsdichte des diskutierten Zustandes orts- und energieabhängig auf den CuO-Streifen zu studieren. Die Li0.9Mo6O17-Bronze wurde im Hinblick auf das Verhalten der elektronischen Zustandsdichte an der Fermikante untersucht. Diese Fragestellung ist besonders wegen der Quasieindimensionalität des Materials interessant. Die Messungen von STS-Spektren in der Nähe der Fermienergie zeigen, dass die Elektronen in der Li0.9Mo6O17-Bronze eine sogenannte Luttingerflüssigkeit ausbilden, die anstatt einer Fermiflüssigkeit in eindimensionalen elektronischen Systemen erwartet wird. Bisher wurde Luttingerflüssigkeitsverhalten erst bei wenigen Materialien und Systemen experimentell nachgewiesen, obschon die theoretischen Voraussagen mehr als 30 Jahre zurückliegen. Ein Charakteristikum einer Luttingerflüssigkeit ist die Abnahme der Zustandsdichte an der Fermienergie mit einem Potenzgesetz. Dieses Verhalten wurde in STS-Spektren dieser Arbeit beobachtet und quantitativ im Rahmen eines Luttingerflüssigkeitsmodells beschrieben. Auch die Temperaturabhängigkeit des Phänomens im Bereich von 5K bis 55K ist konsistent mit der Beschreibung durch eine Luttingerflüssigkeit. Generell zeigen die Untersuchungen dieser Arbeit, dass die Dimensionalität, insbesondere deren Einschränkung, einen deutlichen Einfluss auf die elektronischen Eigenschaften von Systemen und Materialien haben kann.

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

By means of nuclear spin-lattice relaxation rate T-1(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)(2) and the spin-ladder system (C5H12N)(2)CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T-1(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T-1(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.