Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles

Conventional models of Josephson junction dynamics rely on the absence of low energy quasiparticle states due to a large superconducting gap. With this assumption the quasiparticle degrees of freedom become "frozen out" and the phase difference becomes the only free variable, acting as a fictitious particle in a local in time Josephson potential related to the adiabatic and non-dissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low energy quasiparticles interacting non-adiabatically with the phase degree of freedom. Such quasiparticle states exist generically in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Furthermore, recent experiments have revealed the existence of spurious low energy in-gap states in tunnel junctions of conventional superconductors - a system for which the adiabatic assumption typically is assumed to hold. We show that the resonant interaction with such low energy states rather than the Josephson potential defines nonlinear Josephson dynamics at small amplitudes.Comment: 9 pages, 1 figur

Josephson effect in ballistic graphene

We solve the Dirac-Bogoliubov-De-Gennes equation in an impurity-free superconductor-normal-superconductor (SNS) junction, to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result is determined by the superconducting gap and by the aspect ratio of the junction (length L, small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result in which the Fermi wave length takes over from L. The product of critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.Comment: 4 pages, 2 figure

Resolving transition metal chemical space: feature selection for machine learning and structure-property relationships

Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships between the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently-available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20x higher errors from feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5x smaller than RAC-155 produce sub- to 1-kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 {\AA} MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.Comment: 43 double spaced pages, 11 figures, 4 table

Electron-electron interactions in antidot-based Aharonov-Bohm interferometers

We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in the Hartree approximation, which indicate pinning and correlation of the single-particle states at the Fermi energy as well as charge oscillation when antidot-bound states depopulate. We have also found interesting phenomena of anti-resonance reflection of the Fano type.Comment: 12 pages, 8 figure

Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U

Approximate density functional theory (DFT) suffers from many-electron self- interaction error, otherwise known as delocalization error, that may be diagnosed and then corrected through elimination of the deviation from exact piecewise linear behavior between integer electron numbers. Although paths to correction of energetic delocalization error are well- established, the impact of these corrections on the electron density is less well-studied. Here, we compare the effect on density delocalization of DFT+U, global hybrid tuning, and range- separated hybrid tuning on a diverse test set of 32 transition metal complexes and observe the three methods to have qualitatively equivalent effects on the ground state density. Regardless of valence orbital diffuseness (i.e., from 2p to 5p), ligand electronegativity (i.e., from Al to O), basis set (i.e., plane wave versus localized basis set), metal (i.e., Ti, Fe, Ni) and spin state, or tuning method, we consistently observe substantial charge loss at the metal and gain at ligand atoms (ca. 0.3-0.5 e or more). This charge loss at the metal is preferentially from the minority spin, leading to increasing magnetic moment as well. Using accurate wavefunction theory references, we observe that a minimum error in partial charges and magnetic moments occur at higher tuning parameters than typically employed to eliminate energetic delocalization error. These observations motivate the need to develop multi-faceted approximate-DFT error correction approaches that separately treat density delocalization and energetic errors in order to recover both correct density and magnetization properties.Comment: 34 pages, 11 figure

Reduced leakage current in Josephson tunnel junctions with codeposited barriers

Josephson junctions were fabricated using two different methods of barrier formation. The trilayers employed were Nb/Al-AlOx/Nb on sapphire, where the first two layers were epitaxial. The oxide barrier was formed either by exposing the Al surface to O2 or by codepositing Al in an O2 background. The codeposition process yielded junctions that showed the theoretically predicted subgap current and no measurable shunt conductance. In contrast, devices with barriers formed by thermal oxidation showed a small shunt conductance in addition to the predicted subgap current.Comment: 3 pages, 4 figure

Transport Processes in Metal-Insulator Granular Layers

Tunnel transport processes are considered in a square lattice of metallic nanogranules embedded into insulating host to model tunnel conduction in real metal/insulator granular layers. Based on a simple model with three possible charging states ($\pm$, or 0) of a granule and three kinetic processes (creation or recombination of a $\pm$ pair, and charge transfer) between neighbor granules, the mean-field kinetic theory is developed. It describes the interplay between charging energy and temperature and between the applied electric field and the Coulomb fields by the non-compensated charge density. The resulting charge and current distributions are found to be essentially different in the free area (FA), between the metallic contacts, or in the contact areas (CA), beneath those contacts. Thus, the steady state dc transport is only compatible with zero charge density and ohmic resistivity in FA, but charge accumulation and non-ohmic behavior are \emph{necessary} for conduction over CA. The approximate analytic solutions are obtained for characteristic regimes (low or high charge density) of such conduction. The comparison is done with the measurement data on tunnel transport in related experimental systems.Comment: 10 pages, 11 figures, 1 reference corrected, acknowlegments adde

Universal Finite Temperature Properties of a Three Dimensional Quantum Antiferromagnet in the Vicinity of a Quantum Critical Point

We consider a 3-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter g. Starting from the magnetically ordered phase, the N{\'e}el temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behaviour near the QCP. We compare our results with available data for TlCuCl_

Josephson effect in graphene SBS junctions

We study Josephson effect in graphene superconductor- barrier- superconductor junctions with short and wide barriers of thickness $d$ and width $L$, which can be created by applying a gate voltage $V_0$ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width $d$ and the applied gate voltage $V_0$. We also demonstrate that in the thin barrier limit, where $V_0 \to \infty$ and $d \to 0$ keeping $V_0 d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac-Bogoliubov-de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.Comment: 7 Pg., 6 Figs, extended version submitted to PR

Direct Observation of Early-stage Quantum Dot Growth Mechanisms with High-temperature Ab Initio Molecular Dynamics

Colloidal quantum dots (QDs) exhibit highly desirable size- and shape-dependent properties for applications from electronic devices to imaging. Indium phosphide QDs have emerged as a primary candidate to replace the more toxic CdSe QDs, but production of InP QDs with the desired properties lags behind other QD materials due to a poor understanding of how to tune the growth process. Using high-temperature ab initio molecular dynamics (AIMD) simulations, we report the first direct observation of the early stage intermediates and subsequent formation of an InP cluster from separated indium and phosphorus precursors. In our simulations, indium agglomeration precedes formation of In-P bonds. We observe a predominantly intercomplex pathway in which In-P bonds form between one set of precursor copies while the carboxylate ligand of a second indium precursor in the agglomerated indium abstracts a ligand from the phosphorus precursor. This process produces an indium-rich cluster with structural properties comparable to those in bulk zinc-blende InP crystals. Minimum energy pathway characterization of the AIMD-sampled reaction events confirms these observations and identifies that In-carboxylate dissociation energetics solely determine the barrier along the In-P bond formation pathway, which is lower for intercomplex (13 kcal/mol) than intracomplex (21 kcal/mol) mechanisms. The phosphorus precursor chemistry, on the other hand, controls the thermodynamics of the reaction. Our observations of the differing roles of precursors in controlling QD formation strongly suggests that the challenges thus far encountered in InP QD synthesis optimization may be attributed to an overlooked need for a cooperative tuning strategy that simultaneously addresses the chemistry of both indium and phosphorus precursors.Comment: 40 pages, 9 figures, submitted for publicatio