This thesis delves into a study of phases of strongly correlated quantum matter confined to two spatial dimensions. The thesis can broadly be divided into three parts. In the first part, comprising of chapters 2 and 3, we investigate some interesting aspects of symmetry breaking and quantum criticality in the superconducting phase of the iron-based superconductors. In particular, motivated by tunneling microscopy measurements on FeSe, in chapter 2 we study the effect of spontaneously broken rotational symmetry on the structure of the superconducting vortex. In chapter 3, we study the critical singularities associated with the superfluid-density at a wide class of symmetry-breaking and topological phase transitions in a clean superconductor. Inspired by experiments on BaFe$_2$(As$_{1-x}$P$_x$)$_2$, we also analyze the effect of quenched disorder on the superfluid-density in the vicinity of magnetic quantum critical points. The second part of this thesis, consisting of chapters 4 and 5, is devoted to a study of the pseudogap phase in the underdoped cuprates. In chapter 4 we study the effect of thermal fluctuations of various competing order parameters, including preformed superconductivity and short-ranged charge-density wave, on the electronic excitations. In chapter 5 we analyze the feedback of pairing fluctuations on the landscape of various competing charge-density wave order parameters within the framework of fermi-liquid theory. In the final part of the thesis, consisting of chapters 6 and 7, we propose an alternative picture for describing the pseudogap metal. In chapter 6, we study a quantum-disordered phase of matter---the fractionalized fermi-liquid (FL*)---where the electrons are coupled to the fractionalized excitations of a strongly fluctuating antiferromagnet and propose it to be a candidate state for the pseudogap. We investigate instabilities of the FL* to density-wave order and compare with experiments. In chapter 7, we describe a framework for describing a novel quantum phase transition without any broken-symmetries---a Higgs transition---that describes a transition from a conventional fermi-liquid to a parent phase of the FL* state via an intermediate non-fermi liquid. We discuss its possible connection to the optimal doping critical point in the cuprates. / Physics

This thesis explains how extreme superheating and single bubble nucleation can be achieved in an electrolytic solution within a solid state nanopore. A highly focused ionic current, induced to flow through the pore by modest voltage biases, leads to rapid Joule heating of the electrolyte in the nanopore. At sufficiently high current densities, temperatures near the thermodynamic limit of superheat are achieved, ultimately leading to nucleation of a vapor bubble within the nanopore. A mathematical model for Joule heating of an electrolytic solution within a nanopore is presented. This model couples the electrical and thermal dynamics responsible for rapid and extreme superheating of the electrolyte within the nanopore. The model is implemented numerically with a finite element calculation, yielding a time and spatially resolved temperature distribution in the nanopore region. Temperatures near the thermodynamic limit of superheat are predicted to be attained just before the explosive nucleation of a vapor bubble is observed experimentally. Knowledge of this temperature distribution is used to evaluate related phenomena including bubble nucleation kinetics, relaxation oscillation, and bubble dynamics. In particular, bubble nucleation is shown to be homogeneous and highly reproducible. These results are consistent with experimental data available from electronic and optical measurements of Joule heating and bubble nucleation in a nanopore. / Engineering and Applied Sciences - Applied Physics

Solid-state nanopores are a nanofluidic platform with unique advantages for single-molecule analysis and filtration applications. However, significant improvements in device performance and scalable fabrication methods are needed to make nanopore devices competitive with existing technologies. This dissertation investigates the potential advantages of ultra-thin nanopores in which the thickness of the membrane is significantly smaller than the nanopore diameter. Novel, scalable fabrication methods were first developed and then utilized to examine device performance for water filtration and single molecule sensing applications. Fabrication of nanometer-thin pores in silicon nitride membranes was achieved using a feedback-controlled ion beam method in which ion sputtering is arrested upon detection of the first few ions that drill through the membrane. Performing fabrication at liquid nitrogen temperatures prevents surface atom rearrangements that have previously complicated similar processes. A novel cross-sectional imaging method was also developed to allow careful examination of the full nanopore geometry. Atomically-thin graphene nanopores were fabricated via an electrical pulse method in which sub-microsecond electrical pulses applied across a graphene membrane in electrolyte solution are used to create a defect in the membrane and controllably enlarge it into a nanopore. This method dramatically increases the accuracy and reliability of graphene nanopore production, allowing consistent production of single nanopores down to subnanometer sizes. In filtration applications in which nanopores are used to selectively restrict the passage of dissolved contaminants, ultra-thin nanopores minimize the flow resistance, increasing throughput and energy-efficiency. The ability of graphene nanopores to separate different ions was characterized via ionic conductance and reversal potential measurements. Graphene nanopores were observed to conduct cations preferentially over anions with selectivity ratios of 100 or higher for pores as large as 20 nm in diameter, suggesting that porous graphene membranes can be used to create highly effective cation exchange membranes for electrodialysis filtration. These surprisingly high selectivities cannot be explained by current models of ionic conduction in graphene nanopores, motivating the development of a new model in which elevated concentrations of mobile cations near the graphene surface generate additional ion selectivity. / Engineering and Applied Sciences - Applied Physics

A central goal in the study of modern condensed matter physics is the characterization of the dynamical properties of quantum systems. Many decades of effort towards this goal, studying a diverse range of (near-equilibrium) quantum matter, from Fermi liquids, to quantum two-level systems, to interacting spin models, and more, has revealed a remarkable pervasiveness of the simple dynamical description of these complex systems in terms of quasi-particles that carry spin, charge, and heat, and that are generally able to equilibrate systems. This thesis is an examination of some exceptions to this rule. Specifically, we study a number of instances of quantum matter where equilibration phenomena happens at rather long time scales, or does not occur at all. Particular emphasis is laid on the role of dimensionality, disorder, and dissipation in engendering such novel dynamical behavior. First, we consider non-equilibrium dynamics in one-dimensional quasi-condensates. Low dimensionality inhibits scattering in these systems, and low-energy excitations are long-lived phase fluctuations that exhibit an enriched conformal symmetry. Utilizing this symmetry, we generalize sudden quenches typically used to study non-equilibrium dynamics to quenches along general relativistic and conformal trajectories. Gases never truly equilibrate after such a quench; instead, they evolve into a `prethermal' state with thermal-looking correlations and a chiral asymmetry. We then study the problem of the dynamical transition driven by disorder, from an ergodic to a non-ergodic phase, in one-dimensional quantum spin chains. In particular, in XXZ chains with on-site disorder, we find a unique intermediate phase straddling the boundary of the dynamical phase transition, wherein rare-region effects lead to long-time tails in equilibration and vanishing DC conduction before the onset of non-ergodicity. We propose generalizations of such `Griffiths' behavior to arbitrary dimensions. We also study the dynamics of random-bond Heisenberg chains by developing a strong-disorder renormalization group protocol for these systems. We discuss how magnetic noise from such disordered systems contains signatures of their anomalous dynamical properties. Next, we re-examine the phenomenological theory of two-level systems in amorphous materials in the light of new experimental evidence that these states have large electric/magnetic dipole moments. We propose and justify an interpretation of the model as one of tunneling electrons slowed down by a large phonon drag and discuss the dynamical consequences of such polaronic effects. Finally, we discuss how magnetic noise measurements can be used to non-invasively access the anomalous properties of systems such as those discussed above. In particular, we examine how scattering properties of isolated magnetic impurities and non-local transport in a variety of two-dimensional materials can be probed experimentally using NV centers as noise magnetometers. / Physics

The potential of interface engineering to enhance electronic properties is exemplified in a single atomic layer of FeSe grown on SrTiO$_3$, which exhibits an order-of-magnitude increase in its superconducting transition temperature ($T_c$ up to 110 K) compared to bulk ($T_c$ = 8 K). Since this discovery in 2012, efforts to reproduce, understand, and extend this finding continue to draw both excitement and scrutiny. In this thesis, we report the use of a combined molecular beam epitaxy (MBE) and scanning tunneling microscopy (STM) system to grow and image films of superconducting FeSe/SrTiO$_3$. In particular, we investigate and harness atomic defects in as-grown films to derive microscopic insights in two directions. First, we image quasiparticle interference (QPI) patterns generated around defects in order to reconstruct the electronic structure of the unperturbed system, and uncover pieces of the puzzle of high-$T_c$ superconductivity in a monolayer of FeSe. Second, we characterize the atomic structure of defects using density functional theory (DFT), with possible implications on film quality and nanostructuring. / Physics

In recent years, two-dimensional electron systems have played an integral role at the forefront of discoveries in condensed matter physics. These include the integer and fractional quantum Hall effects, massless electron physics in graphene, the quantum spin and quantum anomalous Hall effects, and many more. Investigation of these fascinating states of matter brings with it surprising new results, challenges us to understand new physical phenomena, and pushes us toward new technological capabilities. In this thesis, we describe a set of experiments aimed at elucidating the behavior of two such two-dimensional systems: the quantum Hall effect, and the quantum spin Hall effect. The first experiment examines electronic behavior at the edge of a two-dimensional electron system formed in a GaAs/AlGaAs heterostructure, under the application of a strong perpendicular magnetic field. When the ratio between the number of electrons and flux quanta in the system is tuned near certain integer or fractional values, the electrons in the system can form states which are respectively known as the integer and fractional quantum Hall effects. These states are insulators in the bulk, but carry gapless excitations at the edge. Remarkably, in certain fractional quantum Hall states, it was predicted that even as charge is carried downstream along an edge, heat can be carried upstream in a neutral edge channel. By placing quantum dots along a quantum Hall edge, we are able to locally monitor the edge temperature. Using a quantum point contact, we can locally heat the edge and use the quantum dot thermometers to detect heat carried both downstream and upstream. We find that heat can be carried upstream when the edge contains structure related to the $\nu=2/3$ fractional quantum Hall state. We further find that this fractional edge physics can even be present when the bulk is tuned to the $\nu=1$ integer quantum Hall state. Our experiments also demonstrate that the nature of this fractional reconstruction can be tuned by modifying the sharpness of the confining potential at the edge. In the second set of experiments, we focus on an exciting new two-dimensional system known as a quantum spin Hall insulator. Realized in quantum well heterostructures formed by layers of HgTe and HgCdTe, this material belongs to a set of recently discovered topological insulators. Like the quantum Hall effect, the quantum spin Hall effect is characterized by an insulating bulk and conducting edge states. However, the quantum spin Hall effect occurs in the absence of an external magnetic field, and contains a pair of counter propagating edge states which are the time-reversed partners of one another. It was recently predicted that a Josephson junction based around one of these edge states could host a new variety of excitation called a Majorana fermion. Majorana fermions are predicted to have non-Abelian braiding statistics, a property which holds promise as a robust basis for quantum information processing. In our experiments, we place a section of quantum spin Hall insulator between two superconducting leads, to form a Josephson junction. By measuring Fraunhofer interference, we are able to study the spatial distribution of supercurrent in the junction. In the quantum spin Hall regime, this supercurrent becomes confined to the topological edge states. In addition to providing a microscopic picture of these states, our measurement scheme generally provides a way to investigate the edge structure of any topological insulator. In further experiments, we tune the chemical potential into the conduction band of the HgTe system, and investigate the behavior of Fraunhofer interference as a magnetic field is applied parallel to the plane of the quantum well. By theoretically analyzing the interference in a parallel field, we find that Cooper pairs in the material acquire a tunable momentum that grows with the magnetic field strength. This finite pairing momentum leads to the appearance of triplet pair correlations at certain locations within the junction, which we are able to control with the external magnetic field. Our measurements and analysis also provide a method to obtain information about the Fermi surface properties and spin-orbit coupling in two-dimensional materials. / Physics

In this thesis, we have presented the experimental investigations on the crystal-liquid transitions in a colloidal system. Colloids behave as big atoms, thus they are good model systems to study the dynamics of condensed matter. Their phases are determined by the particle concentration which can be controlled by external forces. We studied the transitions such as crystallization and melting in a controlled way. With a confocal microscopy, we were able to obsserve the transitions at single particle level in three-dimension. In Chapters 2-3, we introduced the electric bottle setup which played a significant role to induce the transitions in this thesis. The electric bottle was designed to generate inhomogeneous electric fields, and we were able to employ dielectrophoresis to manipulate the particle concentration using this setup. The colloidal suspension we used here is composed of PMMA particles (Ɛp=2.3), the mixture of cis-decalin and tetrachloroethylene (Ɛm = 2.6$), and surfactant AOT molecules to give repulsive interaction between the particles. We also introduced analysis methods to obtain particle location information from the raw confocal images and to distinguish between the crystal and liquid phases by using their different structures. In Chapters 4-6, we investigated the crystal-liquid transitions and a crystal-crystal transition. We studied the growth kinetics in crystallization and melting in a system which is covalent to the collision-limited growth of pure metals. We measured the attachment and detachment rates, which can be denoted as jump rates. It was found that the process is governed by the Brownian motion of the particles which is dealing with the random walk. The free energy difference between the two phases gives bias to the random walk, thus we insist that the growth process is a biased random walk. We also studied the equilibrated interfaces in a BCC crystal-liquid system. We measured the equilibrium fluctuations of the interface, which gives an interfacial stiffness of the interface. Although the orientation of the interface plane doesn't have high-rotational symmetry, the stiffness was observed to be isotropic in a long wavelength limit. The last transition we observed is the one between crystals, BCC and FCC crystals. We explored the crystal-liquid transitions at single particle level using the combination of the electric bottle and colloids. Instead having multiple samples to study the phase behaviors as a function of volume fraction, we were able to obtain a concentration-dependent phase diagram in a single electric bottle sample. The design of the sample cell can be further developed to induce the various kinds of density gradient. Also, many other phase behaviors resulted from different type of interactions can be studied. / Engineering and Applied Sciences - Engineering Sciences

<p> While the electrical transport characteristics of organic electronic devices are generally inferior to their inorganic counterparts, organic materials offer many advantages over inorganics. The materials used in organic devices can often be deposited using cheap and simple processing techniques such as spincoating, inkjet printing, or roll-to-roll processing; allow for large-scale, flexible devices; and can have the added benefits of being transparent or biodegradable.</p><p> In this manuscript, we examine the role of solvents in the performance of pentacene-based devices using the ferroelectric copolymer polyvinylidene fluoride-trifluoroethylene (PVDF-TrFe) as a gate insulating layer. High dipole moment solvents, such as dimethyl sulfoxide, used to dissolve the copolymer for spincoating increase the charge carrier mobility in field-effect transistors (FETs) by nearly an order of magnitude as compared to lower dipole moment solvents. The polarization in Al/PVDF-TrFe/Au metal-ferroelectric-metal devices also shows an increase in remnant polarization of ~20% in the sample using dimethyl sulfoxide as the solvent for the ferroelectric. Interestingly, at low applied electric fields of ~100 MV/m a remnant polarization is seen in the high dipole moment device that is nearly 3.5 times larger than the value observed in the lower dipole moment samples, suggesting that the degree of dipolar order is higher at low operating voltages for the high dipole moment device.</p><p> We will also discuss the use of peptide-based nanostructures derived from natural amino acids as building blocks for biocompatible devices. These peptides can be used in a bottom-up process without the need for expensive lithography. Thin films of L,L-diphenylalanine micro/nanostructures (FF-MNSs) were used as the dielectric layer in pentacene-based FETs and metal-insulator-semiconductor diodes both in bottom-gate and top-gate structures. It is demonstrated that the FFMNSs can be functionalized for detection of enzyme-analyte interactions. This work opens up a novel and facile route towards scalable organic electronics using peptide nanostructures as scaffolding and as a platform for biosensing. </p><p>

<p> Active nematics are a class of nonequilibrium systems which have received much attention in the form of continuum models in recent years. For the dense, highly ordered case which is of particular interest, these models focus almost exclusively on suspensions of active particles in which the flow of the medium plays a key role in the dynamical equations. Many active nematics, however, reside at an interface or on a surface where friction excludes the effects of long-range flow. In the following pages we shall construct a general model which describes these systems with overdamped dynamical equations. Through numerical and analytical investigation we detail how many of the striking nonequilibrium behaviors of active nematics arise in such systems. </p><p> We shall first discuss how the activity in these systems gives rise to an instability in the nematic ordered state. This instability leads to phase-separation in which bands of ordered active nematic are interspersed with bands of the disordered phase. We expose the factors which control the density contrast and the stability of these bands through numerical investigation. </p><p> We then turn to the highly ordered phase of active nematic materials, in which striking nonequilibrium behaviors such as the spontaneous formation, self-propulsion, and ordering of charge-half defects occurs. We extend the overdamped model of an active nematic to describe these behaviors by including the advection of the director by the active forces in the dynamical equations. We find a new instability in the ordered state which gives rise to defect formation, as well as an analog of the instability which is seen in models of active nematic suspensions. Through numerical investigations we expose a rich phenomenology in the neighborhood of this new instability. The phenomenology includes a state in which the orientations of motile, transient defects form long-range order. This is the first continuum model to contain such a state, and we compare the behavior seen here with similar states seen in the experiments and simulations of Stephen DeCamp and Gabriel Redner et. al. [1] </p><p> Finally, we propose the measurement of defect shape as a mechanism for the comparison between continuum theories of active nematics and the experimental and simulated realiza- tions of these systems. We present a method for making these measurements which allows for averaging and statistical analysis, and use this method to determine how the shapes of defects depend on the parameters of our continuum theory. We then compare these with the shapes of defects which we measure in the experiments and simulations mentioned above in order to place these systems in the parameter space of our model. It is our hope that this mechanism for comparison between models and realizations of active nematics will provide a key to pairing the two more closely.</p><p>

<p> A two-dimensional electron system exposed to a strong perpendicular magnetic field at low temperatures (usually below one Kelvin) forms a new state of matter that exhibits the fractional quantum Hall effect. This phenomenon has been observed in graphene, a naturally occurring two-dimensional electron system. The theoretical understanding of the FQHE in graphene is complicated by the fact the electrons have valley and spin degrees of freedom. As a result, the different single-particle energy levels (Landau levels) of the electrons can mix with each other. This Landau level mixing is intrinsic to graphene and must be considered in any realistic theoretical treatment. Recently, an effective model Hamiltonian which includes Landau level mixing has been formulated in terms of Haldane pseudopotentials: this model includes emergent three-body interactions in addition to renormalizing the two-body interactions. We construct an effective real-space two-body interaction potential using a closed form expression found in the literature that can model various realistic effects including Landau level mixing. Our method will allow us to fully tackle the physics of the fractional quantum Hall effect in graphene and provide a method for extending our studies to realistic models of semiconductor heterostructure systems as well.</p><p>