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## Scholarly Works (293 results)

We investigate the edge properties of Abelian topological phases in two spatial dimensions. We discover that many of them support multiple fully chiral edge phases, with surprising and measurable experimental consequences. Using the machinery of conformal field theory and integral quadratic forms we establish that distinct chiral edge phases correspond to genera of positive-definite integral lattices. This completes the notion of bulk-boundary correspondence for topological phases. We establish that by tuning inter-channel interactions the system can be made to transition between the different edge phases without closing the bulk gap.

Separately we construct a family of one-dimensional models, called Perfect Metals, with no relevant mass-generating operators. These theories describe stable quantum critical phases of interacting fermions, bosons or spins in a quantum nanowire. These models rigorously answer a long-standing question about the existence of stable metallic phases in one and two spatial dimensions in the presence of generic disorder. Separately, they are the first example of a stable phase of an infinite parallel array of coupled Luttinger liquids.

We perform a detailed study of the transport properties of Perfect Metals and show that in addition to violating the Wiedemann-Franz law, they naturally exhibit low power-law dependence of electric and thermal conductivities on temperature all the way to zero temperature. We dub this phenomenological set of properties a hyperconductor because in some sense, hyperconductors are better conductors that superconductors, which may have thermal conductivities that are exponentially small in temperature.

The Herschel Space Observatory recently detected the presence of water vapor in observations of Ceres, bringing it into the crosshairs of the search for the building blocks of life in the solar system. I present a mission concept designed in collaboration with the NASA Ames Research Center for a two-probe mission to the dwarf planet Ceres, utilizing a pair of small low-cost spacecraft. The primary spacecraft will carry both a mass and an infrared spectrometer to characterize the detected vapor. Shortly after its arrival a second and largely similar spacecraft will impact Ceres to create an impact ejecta “plume” timed to enable a rendezvous and sampling by the primary spacecraft. This enables additional subsurface chemistry, volatile content and material characterization, and new science complementary to the Dawn spacecraft, the first to arrive at Ceres. Science requirements, candidate instruments, rendezvous trajectories, spacecraft design and comparison with Dawn science are detailed.

Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators.

Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design.

We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.

While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.

The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.

Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

The quantum Hall effect is recognized as one of the earliest examples of a topological phase of matter. Yet, thirty-five years after its initial discovery, there remain many open questions, especially surrounding states that may host fractional excitations and exotic statistics. Through the bulk-edge correspondence, many questions can be answered by studying the low-energy edge excitations. In this thesis, we investigate analytically certain aspects of the edge excitations using Chern-Simons-Landau-Ginzburg theory. The results include some surprises: our microwave absorption proposal leads to an interferometer whose read-out is first order in the tunneling amplitude; tunneling current across a quantum point contact is affected by the presence of a neutral mode; and the bulk-edge correspondence for chiral Abelian phases can be one-to-many. We now describe these investigations in more detail.

We start by proposing an experiment to measure the microwave absorption spectrum of a quantum Hall droplet. We show that the number and velocities of charged edge modes can be directly measured from a droplet of known shape. In contrast to standard transport measurements, different edge equilibration regimes can be accessed in the same device. If there is a quantum point contact, then quasiparticle properties, including braiding statistics, can be observed. Their effects are manifested as modulations of the spectrum that are, notably, first-order in the tunneling amplitude at the point contact.

We next consider transport through a quantum point contact in states with counter-propagating neutral edge modes. We show that both the noise and the average transmitted current are affected by downstream perturbations within the standard edge state model. We argue that the change in transmitted current should be observable in experiments that have observed increased noise.

Finally, we investigate the bulk-edge correspondence for chiral Abelian quantum Hall phases. We show that the same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. This can happen for both integer and fractional quantum Hall states. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. We find that edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many.

This thesis is concerned with phases of matter, one of the central notions in condensed matter physics. Traditionally, condensed matter physics has been concerned with phases of matter in thermal equilibrium, which means it is coupled to a heat bath. The main interest of this thesis, however, is isolated systems, in which the system is allowed to reach a steady state on its own, without interacting with a heat bath. In such a context it is possible for the steady state to be non-thermal in character, leading to many new phenomena.

A main interest of this thesis will be Floquet systems, which are systems that are periodically driven, for example by a time-oscillatory electric field. In this thesis, we will identify and charcterize phases of matter occuring in Floquet systems that are entirely new, in the sense that they have no analog in equilibrium.

We introduce a “Floquet equivalence principle”, which states that Floquet topological phases with symmetry G are in one-to-one correspondence with stationary topological phases with additional symmetry. This allows us to leverage the existing literature on topological phases with symmetries to understand Floquet topological phases. Such phases can be stabilized in driven strongly disordered systems through the phenomenon of “many-body localization” (MBL). We discuss properties of Floquet phases such as the “pumping” of lower-dimensional topological phases onto the boundary at each time cycle.

We then turn to spontaneous symmetry-breaking phases. We show that in Floquet systems, there is a striking new kind of such phase: the Floquet time crystal, in which the symmetry that is spontaneously broken is discrete time-translation symmetry. Such systems, though driven at frequency \omega, respond at a fractional frequency \omega/n. We show using analytical arguments and numerical evidence that such phases can be stabilized in driven strongly disordered systems through the phenomenon of “many-body localization” (MBL).

Next, we show that both Floquet time crystals and Floquet topological phases can be stabilized even without disorder. We establish a new scenario for “pre-thermalization”, a phenomenon where the eventual thermalization of the system takes place at a rate that is exponentially small in a parameter. In the intermediate regime, before pre-thermalization, there is a quasi-stationary pre-thermal regime in which Floquet phases can be stabilized.

In a slight digression, we then develop a systematic theory of stationary topological phases with discrete spatial symmetries (as opposed to the discrete temporal symmetry characterizing Floquet phases), showing that they also satisfy a “crystalline

equivalence principle” relating phases of matter with spatial symmetry to phases of matter with internal symmetry. Our arguments are based on notions of “gauging spatial symmetries” as well as a viewpoint based on topological quantum field theory (TQFT).

Finally, we put the Floquet equivalence principle on a systematic footing, and unify it with the crystalline equivalence principle for stationary topological phases, by invoking a powerful homotopy-theoretic viewpoint on phases of matter. The end result is a general theory of strongly correlated phases of matter with space-time symmetries.

This dissertation presents a detailed analysis of recorded seismic waves in terms of their source and their propagation through the Earth in multiple scenarios. First, I investigate the source mechanisms of some highly unusual seismic events associated with the formation of a large sinkhole at Napoleonville salt dome, Assumption Parish, Louisiana in August 2012. I implemented a grid-search approach for automatic detection, location and moment tensor inversion of these events. First, the effectiveness of this technique is demonstrated using low frequency (0.1-0.2 Hz) displacement waveforms and two simple 1D velocity models for the salt dome and the surrounding sedimentary strata for computation of Green’s functions in the preliminary analysis. In the revised, and more detailed analysis, I use Green’s functions computed using a finite-difference wave propagation method and a 3D velocity model that incorporates the currently known approximate geometry of the salt dome and the overlying anhydrite-gypsum cap rock, and features a large velocity contrast between the high velocity salt dome and low velocity sediments overlying and surrounding it. I developed a method for source-type-specific inversion of moment tensors utilizing long-period complete waveforms and first-motion polarities, which is useful for assessing confidence and uncertainties in the source-type characterization of seismic events. I also established an empirical method to rigorously assess uncertainties in the centroid location, MW and the source type of the events at the Napoleonville salt dome through changing network geometry, using the results of synthetic tests with real seismic noise. During 24-31 July 2012, the events with the best waveform fits are primarily located at the western edge of the salt dome at most probable depths of ~0.3-0.85 km, close to the horizontal positions of the cavern and the future sinkhole. The data are fit nearly equally well by opening crack moment tensors in the high velocity salt medium or by isotropic volume-increase moment tensors in the low velocity sediment layers. The addition of more stations further constrains the events to slightly shallower depths and to the lower velocity media just outside the salt dome with preferred isotropic volume-increase moment tensor solutions. I find that Green’s functions computed with the 3D velocity model generally result in better fit to the data than Green’s functions computed with the 1D velocity models, especially for the smaller amplitude tangential and vertical components, and result in better resolution of event locations and event source type. The dominant seismicity during 24- 31 July 2012 is characterized by the steady occurrence of seismic events with similar locations and moment tensor solutions at a near-characteristic inter-event time. The steady activity is sometimes interrupted by tremor-like sequences of multiple events in rapid succession, followed by quiet periods of little of no seismic activity, in turn followed by the resumption of seismicity with a reduced seismic moment-release rate. The dominant volume- increase moment tensor solutions and the steady features of the seismicity indicate a crack- valve-type source mechanism possibly driven by pressurized natural gas.

Accurate and properly calibrated velocity models are essential for the recovery of correct seismic source mechanisms. I retrieved empirical Green’s functions in the frequency range ~ 0.2–0.9 Hz for interstation distances ranging from ~1 to ~30 km (~0.22 to ~6.5 times the wavelength) at The Geysers geothermal field, northern California, from cross-correlation of ambient seismic noise recorded by a wide variety of sensors. I directly compared noise- derived Green’s functions with normalized displacement waveforms of complete single-force synthetic Green’s functions computed with various 1D and 3D velocity models using the frequency-wavenumber integration method, and a 3D finite-difference wave propagation method, respectively. These comparisons provide an effective means of evaluating the suitability of different velocity models to different regions of The Geysers, and assessing the quality of the sensors and the noise cross-correlations. In the T-Tangential, R-Radial, Z- Vertical reference frame, the TT, RR, RZ, ZR and ZZ components (first component: force direction, second component: response direction) of noise-derived Green’s functions show clear surface-waves and even body-wave phases for many station pairs. They are also broadly consistent in phase and relative inter-component amplitudes with the synthetic Green’s functions for the known local seismic velocity structure that was derived primarily from body wave travel-time tomography, even at interstation distances less than one wavelength. I also found anomalous large amplitudes in TR, TZ, RT and ZT components of noise-derived Green’s functions at small interstation distances (≲4 km) that can be attributed to ~10°-30° sensor misalignments at many stations inferred from analysis of longer period teleseismic waveforms. After correcting for sensor misalignments, significant residual amplitudes in these components for some longer interstation distance (≳ 8 km) paths are better reproduced by the 3D velocity model than by the 1D models incorporating known values and fast axis directions of crack-induced shear-wave anisotropy in the geothermal field. I also analyzed the decay of Fourier spectral amplitudes of the TT component of the noise-derived Green’s functions at 0.72 Hz with distance in terms of geometrical spreading and attenuation. While there is considerable scatter in the amplitudes of noise-derived Green’s functions, the average decay is consistent with the decay expected from the amplitudes of synthetic Green’s functions and with the decay of tangential component local-earthquake ground-motion amplitudes with distance at the same frequency.