Dept. of Physics
http://hdl.handle.net/2142/8858
Sun, 19 Apr 2015 09:30:32 GMT2015-04-19T09:30:32ZClassical hydrodynamics of Calogero-Sutherland models
http://hdl.handle.net/2142/73044
Classical hydrodynamics of Calogero-Sutherland models
The Calogero Sutherland model is system of particle moving on a line and interacting with long-range
forces. In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions.
We show numerically that the spinful system also exhibits localized solutions with the soliton property. This
is a strong evidence that the continuum spin-Calogero model is exactly integrable.
spin; hydrodynamics; Calogero; soliton; integrability
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/730442015-01-21T00:00:00ZThermal transport in graphene-based nanostructures and other two-dimensional materials
http://hdl.handle.net/2142/72987
Thermal transport in graphene-based nanostructures and other two-dimensional materials
Heat conduction in nanomaterials is an important area of study, with both fundamental and technological implications. However, little is known about heat flow in two-dimensional (2D) materials or devices with dimensions comparable to the phonon mean free path (MFP). Here, we investigated thermal transport in graphene-based nanostructures and several other 2D materials.
First, we measured heat conduction in nanoscale graphene by a substrate-supported thermometry platform. Short, quarter-micron graphene samples reach ~35% of the ballistic thermal conductance limit (Gball) up to room temperature, enabled by the relatively large phonon MFP (~100 nm) in SiO2 substrate-supported graphene. In contrast, patterning similar samples into nanoribbons leads to a diffusive heat flow regime that is controlled by ribbon width and edge disorder. These results show how manipulation of device dimensions on the scale of the phonon MFP can be used to achieve full control of their heat-carrying properties, approaching fundamentally limited upper or lower bounds.
We also examined the possibility of using this supported platform to measure other materials through finite element simulations and uncertainty analysis. The smallest thermal sheet conductance that can be sensed by this method within a 50% error is ~25 nW/K at room temperature, indicating this platform can be applied to most thin films like polymer and nanotube networks, as well as nanomaterials like nanotube or nanowire arrays, even a single Si nanowire. Moreover, the platform can be extended to plastic substrates, not limited to the SiO2/Si substrate.
Last, we calculated in-plane (for monolayer and bulk) and cross-plane (for bulk) ballistic thermal conductances Gball of graphene/graphite, h-BN, MoS2, and WS2, based on full phonon dispersions from first-principles approach. Then, a rigorous and proper average of phonon mean free path, λ was simply obtained in terms of Gball and the diffusive thermal conductivity. Moreover, length-dependent thermal conductivity (k) was estimated using a ballistic-diffusive model, which agrees with available experimental data and shows increasing k with length until ~100λ before convergence. This indicates that, to observe theoretically predicted k divergence in low-dimensional systems, simulations and experiments should extend beyond length ~100λ.
Our work provides a comprehensive study of thermal conduction in 2D layered materials in micro- and nanoscale with an emphasis on ballistic conduction and size effects. The findings extend our understanding of thermal conduction and how to tune it to reach the requirements for potential applications like thermal management and thermoelectric conversion.
Layered Materials; Graphene; Nanoscale Heat Transport; Thermal Conductivity; Mean Free Path; Ballistic; Diffusive; Phonon Dispersion; Scattering; Thermometry
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/729872015-01-21T00:00:00ZExploring the interplay between topological order, magnetism and superconductivity
http://hdl.handle.net/2142/72933
Exploring the interplay between topological order, magnetism and superconductivity
This thesis presents a theoretical study of topological insulators coupled with superconductor and magnet. We discuss different physics due to these novel couplings and the topological properties.
Chapter 2 describes the background of the research projects. We present different Quantum Hall systems, discuss their topological properties. Also we provide some basic formulas in Luttinger liquid theory, which will be used heavily in this thesis.
Chapter 3 presents different phases we discovered in 2D topological insulators. We explore the phases exhibited by an interacting quantum spin Hall edge state in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature of the edge state gives rise to orders that are expected to be absent in non-chiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wavevector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. We find that finite spin imbalance favors a finite current carrying groundstate that is not condensed in the absence of interactions and is superconducting for attractive interactions. This state is characterized by FFLO-type oscillations where the Cooper pairs obtain a finite center of mass momentum.
Chapter 4 describes the new spin Josephson effect. We explore a spin Josephson effect in a system of two ferromagnets coupled by a tunnel junction formed of 2D time-reversal invariant topological insulators. In analogy with the more commonly studied instance of the Josephson effect for charge in superconductors, we investigate properties of the phase-coherent {\it spin} current resulting from the misalignment of the in-plane magnetization angles of the two ferromagnets. We show that the topological insulating barrier offers the exciting prospect of hosting a {\it fractional} spin Josephson effect mediated by bound states at the ferromagnet-topological insulator interface. We provide multiple perspectives to understand the $4\pi$ periodic nature of this effect. We discuss several measurable consequences, such as, the generation of a transverse voltage signal which allows for purely electrical measurements, an inverse of this effect where an applied voltage gives rise to a transverse spin-current, and a fractional AC spin-Josephson effect.
Chapter 5 presents the inverse spin pumping effect. We study the dynamics of a quantum spin Hall edge coupled to a magnet with its own
dynamics. Using spin transfer torque principles, we analyze the interplay between
spin currents in the edge state and dynamics of the axis of the magnet, and draw parallels with circuit analogies.
As a highlighting feature, we show that while coupling to a magnet typically renders the edge state insulating
by opening a gap, in the presence of a small potential bias, spin-transfer torque can restore perfect
conductance by transferring angular momentum to the magnet. In the presence of interactions within the edge
state, we employ a Luttinger liquid treatment to show that the edge, when subject to a small voltage bias, tends to
form a unique dynamic rotating spin wave state that naturally couples into the dynamics of the magnet.
We briefly discuss realistic physical parameters and constraints for observing this interplay between quantum
spin Hall and spin-transfer torque physics.
Chapter 6 discusses possible mass terms in 3D topological insulators. We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized fractional charge, also taking into account interaction effects for the 2D case. We show that the effects of tunneling are topologically equivalent to a certain deformation or folding of the sample geometry. Our key advance is the realization that the quantum Hall or fractional charge physics can appear in the presence of only a \emph{single} magnet unlike previous proposals which involve magnetic domain walls on the surface or edges of topological insulators respectively. We give illustrative topological folding arguments to prove our results and show that for the 2D case our results are robust even in the presence of interactions.
topological insulator; superconductor; magnet; fractional charge
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/729332015-01-21T00:00:00ZMagnetic domain formation in La1-xSrxMnO3 nanowires studied with resonant soft x-ray scattering
http://hdl.handle.net/2142/72899
Magnetic domain formation in La1-xSrxMnO3 nanowires studied with resonant soft x-ray scattering
Phase separation and nanoscale fluctuation in strongly correlated systems are known to exist around their phase transitions. They are directly connected to the ordering mechanisms that cause magnetic orders, density waves, or superconductivity. These orders likely have their origins rooted in the differences in the correlation lengths of the underlying competing orders. Therefore studying materials in size that is comparable to these fluctuations can disentangle the complexity of the mechanism. To serve this purpose, we studied magnetic domain formation in La(1-x)Sr(x)MnO3 (LSMO) nanowires. In theory, a 1D ferromagnetic wire is not capable of forming a single domain without an applied field. Therefore, it is meaningful to study how the spatial confinement contributes towards magnetic domain formation. In particular, how its phase transition differs from that of the bulk, how magnetization density distributes inside the nanowires, and what the domain sizes are inside the nanowires. For this purpose, we fabricated arrays of nanowires 30nm tall, 80nm wide from LSMO thin films using e-beam lithography. Magnetization measurements performed on these wires showed an anomalous increase in the magnetization at temperatures far below the Curie point of the bulk material. Around this temperature, coexisting phase separated domains were observed with transport measurements. To understand these observations, resonant soft x-ray scattering studies were performed on Mn L-absorption-edge with an applied field and varying polarization at different temperatures. Our results suggest nontrivial magnetic domain formation inside the nanowires that may be phase separated at low temperature. In the end, we suggest a phase retrieval model to reconstruct the real space evolution of the magnetization density in nanowires to better understand the magnetic systems measured with resonant soft x-ray scattering.
phase separation; nanowires; colossal magnetoresistive (CMR) manganite; resonant soft x-ray scattering
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/728992015-01-21T00:00:00ZQuantitative all-atom and coarse-grained molecular dynamics simulation studies of DNA
http://hdl.handle.net/2142/72871
Quantitative all-atom and coarse-grained molecular dynamics simulation studies of DNA
The remarkable molecule that encodes genetic information for all life on earth—DNA—is a polymer with unusual physical properties. The mechanical and electrostatic properties of DNA are utilized extensively by cells in the replication, regular maintenance, and expression of their genetic material. This can be illustrated by considering the journey of a typical gene regulating protein, the lac repressor, which recognizes a particular gene and prevents its expression. First, the large electrostatic charge density of DNA provides an energetic track that guides the repressor’s search for its target binding site. Next, as the protein moves along the DNA, it attempts to deform the DNA. The repressor is only able to form an active complex with DNA that has the right sequence-dependent ﬂexibility. Finally, the repressor is believed to form a very small DNA loop that prevents the gene from being expressed. The stability of the loop can be expected to depend sensitively on the global ﬂexibility of DNA. Thus, the key to understanding the some of the most important cellular processes lies in understanding the physical properties of DNA. Single-molecule experiments allow direct observation of the behavior of individual DNA molecules, but act on length and timescales that are often too large and fast to observe underlying DNA and DNA–protein dynamics. Acting on length and timescales that complement single-molecule experiments, molecular dynamics simulations provide a high-resolution glimpse into the mechanics of a biomolecular world. Here, several simulation studies are presented, each of which quantiﬁed one or more properties of DNA. Speciﬁcally, the repulsive forces between parallel duplex DNA molecules were measured; the short-ranged, attractive end-to-end stacking energy was obtained; a single-stranded DNA model was developed that reproduced experimental measurements of its extension upon applied force; and ﬁnally the nature of single-stranded DNA binding to a single-stranded DNA binding protein was investigated. These works represent important steps towards larger simulations of more biologically complete DNA–protein systems.
DNA; all-atom molecular dynamics; coarse-grained molecular dynamics; single-stranded DNA binding protein
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/728712015-01-21T00:00:00ZSources of noise in niobium-based superconducting quantum circuits
http://hdl.handle.net/2142/72869
Sources of noise in niobium-based superconducting quantum circuits
Quantum computation is a fascinating field that combines novel physics with improvements in computation times and has been rapidly growing in the past few years. Using superconductors to form the qubits has the potential for large-scale computing, if the decoherence inherent in these devices can be understood and reduced. Two-level fluctuators due to defects in the materials are thought to cause changes to the Josephson critical current or the flux through the superconducting loop of a flux qubit, which leads to decoherence in the qubit. Alternatively, defects in the crystal lattice give rise to electron localization which in turn traps spins with random orientations at the substrate/metal interface, again producing decoherence.
My work studied the proposed noise mechanisms by using Molecular Beam Epitaxy to fabricate single-crystal niobium-based Josephson junctions. Using RHEED, AFM, and TEM/STEM, I studied the epitaxy of the niobium film at the substrate interface to reduce noise due to crystal defects. I then measured flux noise in these films; the noise in the epitaxial films is lower than the comparative polycrystalline films. Further measurements using ex-situ Josephson junctions and epitaxial niobium loops resulted in the lowest reported flux noise measurements to date. Additionally, EELS measurements made in the course of the STEM analysis of the crystal structure reveal oxygen depletion from the substrate at elevated growth temperatures. This depletion leads to oxygen vacancies in the aluminum oxide substrate, which can in turn lead to charge traps at the substrate/metal interface and hence to decoherence in the qubit.
Critical current noise was investigated by changing the oxidation dose of the alumina barrier in more than 50 separate Josephson junctions. Films which were grown with lower oxidation doses have a non-ideal critical current temperature dependence as well as higher critical current noise values, suggesting that insufficient oxygen is being incorporated into these junctions.
Finally, I studied the effect of surface cleaning after fabrication for resonators and transmons. Microscopy shows that an oxygen ash and BOE dip together removes all photoresist residue from the chip. Internal-Q measurements do not show a marked improvement due to this cleaning, but the coherence times do improve upon the cleaning step.
superconducting; quantum computing; Superconducting QUantum Interference Devices (SQUIDs); Josephson junction; niobium; decoherence; quantum information; molecular beam epitaxy (MBE); transmon; flux qubit; quantum noise
Wed, 21 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2142/728692015-01-21T00:00:00ZFinite temperature contributions to the thermodynamic properties of a normal fermi liquid
http://hdl.handle.net/2142/55618
Finite temperature contributions to the thermodynamic properties of a normal fermi liquid
Landau Fermi liquid theory and microscopic theory are used to investigate finite-temperature contributions to the thermodynamic properties of a normal Fermi liquid . The contribution from long wavelength spin and density fluctuations to the total energy is expressed in terms of the energy of interaction of a quasiparticle and a quasihole with small total momentum. The interaction energy is related to the scattering amplitude , which is known in terms of Landau parameters . By functional differentiation of the expression for the total energy the quasiparticle energy and the Landau quasiparticle interaction are calculated . It is shown that for small q the spin-symmetric quasiparticle interaction fs p, p+q has a term varying as (p x q)^2 which gives rise to a T^3ln(T) term in the specific heat. The coefficient of this T^3lnT term is then evaluated in terms of Landau parameters . We also calculate the spin-antisymmetric quasiparticle interaction f^a p, p+q and show that, for the case when Fo^s and Fo^a are the only nonzero Landau paremeters, there are no T^2ln(T) terms in the magnetic susceptibility.
Starting from the expression for the thermodynamic potential as a functional of the renormalized single particle propagator we derive microscopic expressions for the thermodynamic functions. From this we obtain the entropy as the sum of a "dynamical quasi particle contribution", plus a correction term. When the width of the single particle states can be neglected the dynamical quasiparticle contribution to the entropy is identical to the entropy of a system of independent quasiparticles whose energies are given by the poles of the single particle propagator. We discuss the correction term, which comes from terms in perturbation theory having vanishing energy denominators, and develop methods for evaluating the leading contributions to it at low temperatures. We show that the microscopic calculations give results identical to the Landau theory calculations, and also discuss the difference between the statistical quasiparticle energy, defined as a functional derivative, and the dynamical quasiparticle energy, given by the pole of the single-particle propagator.
Fermi liquids
Mon, 01 Jan 1973 00:00:00 GMThttp://hdl.handle.net/2142/556181973-01-01T00:00:00ZTopics in fluid phase transitions
http://hdl.handle.net/2142/55617
Topics in fluid phase transitions
Dynamic critical point phenomena in fluid systems are studied first by means of models and then with the aid of the scaling laws for critical exponents. Two models whose equilibrium distribution functions reduce to the standard Ising model density matrices and whose time dependences are governed by master equations are introduced. The first model gives spin and heat diffusion and a proof similar to that of Kawasaki that the transport coefficients are finite near the critical point holds. The second model, which gives sound waves and heat and transverse momentum diffusion, admits the possibility of infinite transport coefficients. A perturbation theory for the determination of transport coefficients near the critical point if presented. This perturbation theory is based upon processes in which one transport mode decays into several low wave-number modes. Scaling law concepts are used to calculate the order of magnitude of the matrix elements and frequency denominators which appear in this theory. This permits the estimation of the order of magnitude of the transport coefficients near the critical point. The perturbation theory is applied to estimating the anomalous part of the transport coefficients of a liquid-gas near its critical point and of a binary liquid mixture near its consolute temperature. Specific predictions of the singularities in the transport coefficients are given in terms of the critical exponents which describe the behavior of thermodynamic and static correlation functions. The connection between these reactions and the scaling of frequencies is discussed.
Fluid Systems
Mon, 01 Jan 1968 00:00:00 GMThttp://hdl.handle.net/2142/556171968-01-01T00:00:00ZField theory of electrons and phonons
http://hdl.handle.net/2142/55616
Field theory of electrons and phonons
Electrons in an alkali metal are allowed to interact by multiple processes, including direct coulomb interactions and retarded phonon exchanges, by including in the Hamiltonian both coulomb interaction and electron-phonon interaction terms. Corrections to low temperature one-electron properties are discussed for actual metallic densities by obtaining expressions for the electron self-energy, Sigma(p), in terms of single-particle Green's functions. The phonon terms, including Umklapp processes, are handled by means of Bardeen's matrix elements for the electron-phonon interaction, using longitudinal coupling and subjecting all directionally dependent quantities to a spherical averaging procedure. A criterion is developed to determine when phonon terms are comparable in magnitude to coulomb terms, and when they are negligible. Migdal has shown that phonon processes often contribute small terms proportional to factors of sqrt(m/M) (where m is electron mass and M is ion mass). In fact, phonon terms are of the same size as coulomb terms only for transitions lying within a narrow band of energies about the Fermi surface, whose width is of the order of the longitudinal phonon frequency, omega q. This leads to the general result that physical quantities depending upon Sigma(p), such as correlation energy or paramagnetic susceptibility, should show no phonon contribution to order sqrt(m/M), while quantities such as specific heat, which depend on (dsigma / dp)p = pf (density of states at the Fermi surface), show phonon contributions comparable to the coulomb contributions. A calculation of the phonon contribution to the linear electronic specific heat for sodium is made using the Nozieres-Pines interpolation scheme. Adding this to Silverstein's calculation of the coulomb terms yields a net enhancement over the free-electron value of 21 percent. Actually, for small wave-number vectors q, q less than or equal to sqrt(m/M) pf, it is shown that the electron-phonon interaction becomes just large enough to exactly cancel the divergences in the coulomb interaction perturbation series. This result depends upon the use of "bare," or unrenormalized, quantities, and makes strong use of the longitudinal sum rule for phonon frequencies. A new "combined" form of perturbation series is proposed which consists of keeping coulomb and phonon terms together in any integration process, and which depends, for consistency, on a certain contour in the complex energy-transfer plane, chosen to avoid phonon poles. The series does not use any infinite sums (screening) and has the advantage of being consistently defined for all q (no interpolation) in the region of actual metallic densities. A first order specific heat calculation predicts an enhancement of 32 percent over the free-electron value for sodium.
Electrons; Phonons
Tue, 01 Jan 1963 00:00:00 GMThttp://hdl.handle.net/2142/556161963-01-01T00:00:00ZEmission and capture of electrons at sulfur centers in silicon
http://hdl.handle.net/2142/55615
Emission and capture of electrons at sulfur centers in silicon
Some new techniques have been used to study the physical properties of sulfur centers in silicon. These techniques make use of the effects of the sulfur centers on the depletion region properties of a reverse-biased P-N junction.
This study indicates that sulfur acts as a double donor in silicon. The ionization energy of electrons from neutral sulfur centers was found to be 0.275 eV, and the ionization energy of electrons from singly ionized sulfur centers was found to be 0.53 eV.
The thermal emission rate of electrons from sulfur centers was found to be much greater than the thermal emission rate of holes. A least square fit of the measured electron emission rates to T^2 exp(-deltaE/kT) gave 1.64E10 (T/300)^2 exp(-0.276/kT) for the emission rate of electrons from neutral sulfur centers and 1.03E12 (T/300)^2 exp(-0.528/kT) for the emission rate of electrons from single ionized sulfur centers.
The thermal electron emission rates were found to be quite field dependent. As the electric field was increased from 2E4 V/cm to 10^5 V/cm, the emission rate of electrons at 130 degrees K from neutral sulfur centers increased by a factor of approximately 1.5 while the emission rate of electrons at 200 degree K from singly ionized sulfur centers increased by a factor of 3.0.
The photoionization cross-section of electrons from sulfur centers was found to be much greater than the photoionization cross-section of holes. In the photon energy range of 0.70 to 1.00 eV the photoionization cross-section of electrons from neutral sulfur centers is approximately 2E-16 cm^2, and the photoionization cross-section of electrons from singly ionized sulfur centers is approximately 10^16 cm^2. The spectral dependence of the photoionization cross-section of electrons from neutral sulfur centers fits a Lucovsky delta function potential model much better than a scaled hydrogenic model. For photon energies above threshold there was no observable field dependence or temperature dependence. As the field is increased from 2.14E4 V/cm to 1.11E5 V/cm, the threshold is lowered by approximately 0.01 eV. This reduction in the threshold is much lower than predicted by a Poole-Frenkel barrier lowering model. The photoionization cross-section of electrons from singly ionized sulfur centers was found to be very temperature dependent for photon energies near the absorption edge.
The capture rate of electrons by doubly ionized sulfur centers was measured as 5E-7 cm^3/sec at a field of 3E4 V/cm and decreased to approximately 10^-7 cm^3 /sec at a field of 10^5 V/cm. Little if any temperature dependence was observed. The capture rate of electrons by singly ionized sulfur centers was found to be approximately two orders of magnitude smaller than that of the doubly ionized sulfur center.
Silicon diodes
Thu, 01 Jan 1970 00:00:00 GMThttp://hdl.handle.net/2142/556151970-01-01T00:00:00Z