Two-channel Kondo physics in odd impurity chains

We study odd-membered chains of spin-(1/2) impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong inter-impurity coupling, a residual chain spin-(1/2) moment experiences a renormalized effective coupling to the leads; while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models where the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even-fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is non-zero and determined solely by the `excess' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where inter-lead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of these problems.Comment: 21 pages, 19 figure

Two-channel Kondo physics in two-impurity Kondo models

We consider the non-Fermi liquid quantum critical state of the spin-S two-impurity Kondo model, and its potential realization in a quantum dot device. Using conformal field theory (CFT) and the numerical renormalization group (NRG), we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin-S. Distinct conductance signatures are shown to arise as a function of device asymmetry; with the `smoking gun' square-root behavior, commonly believed to arise at low-energies, dominant only in certain regimes.Comment: 4.5 pages (with 3 figures) + 9 pages (with 4 figures) supplementary materia

The History of Air Quality in Utah: A Narrative Review

Utah has a rich history related to air pollution; however, it is not widely known or documented. This is despite air quality being a top issue of public concern for the state’s urban residents and acute episodes that feature some of the world’s worst short-term particulate matter exposure. As we discuss in this narrative review, the relationship between air pollution and the state’s residents has changed over time, as fuel sources shifted from wood to coal to petroleum and natural gas. Air pollution rose in prominence as a public issue in the 1880s as Utah’s urban areas grew. Since then, scientific advances have increased the understanding of air quality impacts on human health, groups of concerned citizens worked to raise public awareness, policy makers enacted legislation to improve air quality, and courts upheld rights to clean air. Utah’s air quality future holds challenges and opportunities and can serve as useful case for other urbanizing regions struggling with air quality concerns. Population growth and changing climate will exacerbate current air quality trends, but economically viable clean energy technologies can be deployed to reduce air pollution, bringing substantial public health and economic benefits to the state’s residents and other settings with similar public health concerns

Generalized Wilson Chain for solving multichannel quantum impurity problems

The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a simple generalization of the Wilson Chain, which improves the scaling of computational cost with the number of channels/bands, bringing new problems within reach. The method is applied to calculate the t-matrix of the three-channel Kondo model at T=0, which shows universal crossovers near non-Fermi liquid critical points. A non-integrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening/overscreening mechanisms.Comment: 5 pages + 5 pages supplementary materia

Conductance fingerprint of Majorana fermions in the topological Kondo effect

We consider an interacting nanowire/superconductor heterostructure attached to metallic leads. The device is described by an unusual low-energy model involving spin-1 conduction electrons coupled to a nonlocal spin-1/2 Kondo impurity built from Majorana fermions. The topological origin of the resulting Kondo effect is manifest in distinctive non-Fermi-liquid (NFL) behavior, and the existence of Majorana fermions in the device is demonstrated unambiguously by distinctive conductance lineshapes. We study the physics of the model in detail, using the numerical renormalization group, perturbative scaling and abelian bosonization. In particular, we calculate the full scaling curves for the differential conductance in AC and DC fields, onto which experimental data should collapse. Scattering t-matrices and thermodynamic quantities are also calculated, recovering asymptotes from conformal field theory. We show that the NFL physics is robust to asymmetric Majorana-lead couplings, and here we uncover a duality between strong and weak coupling. The NFL behavior is understood physically in terms of competing Kondo effects. The resulting frustration is relieved by inter-Majorana coupling which generates a second crossover to a regular Fermi liquid.Comment: 17 pages, 8 figure

The late holocene atmospheric methane budget reconstructed from ice cores

Ice cores are considered the gold standard for recording past climate and biogeochemical changes. However, gas records derived from ice core analysis have until now been largely limited to centennial and longer timescales because sufficient temporal resolution and analytical precision have been lacking, except during rare times when atmospheric concentrations changed rapidly. In this thesis I used a newly developed methane measurement line to make high-resolution, high-precision measurements of methane during the late Holocene (2800 years BP to present). This new measurement line is capable of an analytical precision of 1500 discrete ice core methane measurements and construct the highest resolution records of methane available over the late Holocene. Ice core samples came from the recently completed West Antarctic Ice Sheet (WAIS) Divide ice core which has as one of its primary scientific objectives to produce the highest resolution records of greenhouse gases, and from the Greenland Ice Sheet Project (GISP2) ice core which is a proven paleoclimate archive. My thesis has the following three components. I first used a shallow ice core from WAIS Divide (WDC05A) to produce a 1000 year long methane record with a ~9 year temporal resolution. This record confirmed the existence of multidecadal scale variations that were first observed in the Law Dome, Antarctica ice core. I then explored a range of paleoclimate archives for possible mechanistic connections with methane concentrations on multidecadal timescales. In addition, I present a detailed description of the analytical methods used to obtain high-precision measurements of methane including the effects of solubility and a new chronology for the WDC05A ice core. I found that, in general, the correlations with paleoclimate proxies for temperature and precipitation were low over a range of geographic regions. Of these, the highest correlations were found from 1400-1600 C.E. during the onset of the Little Ice Age and with a drought index in the headwater region of the major East Asian rivers. Large population losses in Asia and the Americas are also coincident with methane concentration decreases indicating that anthropogenic activities may have been impacting multidecadal scale methane variability. In the second component I extended the WAIS Divide record back to 2800 years B.P. and also measured methane from GISP2D over this time interval. These records allowed me to examine the methane Inter-Polar Difference (IPD) which is created by greater northern hemispheric sources. The IPD provides an important constraint on changes in the latitudinal distribution of sources. We used this constraint and an 8-box global methane chemical transport model to examine the Early Anthropogenic Hypothesis which posits that humans began influencing climate thousands of years ago by increasing greenhouse gas emissions and preventing the onset of the next ice age. I found that most of the increase in methane sources over this time came from tropical regions with a smaller contribution coming from the extratropical northern hemisphere. Based on previous modeling estimates of natural methane source changes, I found that the increase in the southern hemisphere tropical methane emissions was likely natural and that the northern hemispheric increase in methane emissions was likely due to anthropogenic activities. These results also provide new constraints on the total magnitude of pre-industrial anthropogenic methane emissions, which I found to be between the high and low estimates that have been previously published in the literature. For the final component of my thesis I assembled a coalition of scientists to investigate the effects of layering on the process of air enclosure in ice at WAIS Divide. Air bubbles are trapped in ice 60-100m below the surface of an ice sheet as snow compacts into solid ice in a region that is known as the Lock-In Zone (LIZ). The details of this process are not known and in the absence of direct measurements previous researchers have assumed it to be a smooth process. This project utilized high-resolution methane and air content measurements as well as density of ice, δ¹⁵N of N₂, and bubble number density measurements to show that air entrapment is affected by high frequency (mm scale) layering in the density of ice within the LIZ. I show that previous parameterizations of the bubble closure process in firn models have not accounted for this variability and present a new parameterization which does. This has implications for interpreting rapid changes in trace gases measured in ice cores since variable bubble closure will impact the smoothing of those records. In particular it is essential to understand the details of this process as new high resolution ice core records from Antarctica and Greenland examine the relative timing between greenhouse gases and rapid climate changes

Quantum phase transition in quantum dot trimers

We investigate a system of three tunnel-coupled semiconductor quantum dots in a triangular geometry, one of which is connected to a metallic lead, in the regime where each dot is essentially singly occupied. Both ferro- and antiferromagnetic spin-1/2 Kondo regimes, separated by a quantum phase transition, are shown to arise on tuning the interdot tunnel couplings and should be accessible experimentally. Even in the ferromagnetically-coupled local moment phase, the Kondo effect emerges in the vicinity of the transition at finite temperatures. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of the problem.Comment: 5 pages, 5 figure