Condensed Matter

The specific heat Cp and other properties of glasses (ranging from amorphous solids to disordered crystals) at low temperatures, are well known to be markedly different from those in fully-ordered crystals. For decades, this qualitative, and even quantitative, universal behavior of glasses has been thoroughly studied. However, a clear understanding of its origin and microscopic nature, needless to say a closed theory, is still lacking. To shed light on this matter, I review the situation in this work, mainly by compiling and discussing measured low-temperature Cp data of many glasses and disordered crystals, as well as highlighting a few exceptions to that "universality rule". Thus, one can see that, in contrast to other low-temperature properties of glasses, the magnitude of the "glassy" Cp excess at low temperature is far from being universal. Even worse, some molecular crystals without a clear sign of disorder exhibit linear coefficients in Cp larger than those found in many amorphous solids, whereas a few of the latter show negligible values.

We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. {We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets}. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.

The current critical review aims to be more than a simple summary and reproduction of previously published work. Many comprehensive reviews and collections can be found in the literature. The main intention is to provide an account of the progress made in selected aspects of photoinduced phenomena in non-crystalline chalcogenides, presenting the current understanding of the mechanisms underlying such effects. An essential motive for the present review article has been to assess critically published experimental work in the field.

Cycling of a metallic glass between ambient and cryogenic temperatures can induce higher-energy states characteristic of glass formation on faster cooling. This rejuvenation, unexpected because it occurs at small macroscopic strains and well below the temperatures of thermally induced structural change, is important, for example, in improving plasticity. Molecular-dynamics simulations elucidate the mechanisms by which thermal cycling can induce relaxation (reaching lower energy) as well as rejuvenation. Thermal cycling, over tens of cycles, drives local atomic rearrangements progressively erasing the initial glass structure. This arises mainly from the heating stage in each thermal cycle, linked to the intrinsic structural heterogeneity in metallic glasses. Although, in particular, the timescales in MD simulations are shorter than in physical experiments, the present simulations reproduce many physically observed effects, suggesting that they may be useful in optimizing thermal cycling for tuning the properties of metallic glasses and glasses in general.

Spin qubits in quantum dots are a compelling platform for fault-tolerant quantum computing due to the potential to fabricate dense two-dimensional arrays with nearest neighbour couplings, a requirement to implement the surface code. However, due to the proximity of the surface gate electrodes, cross-coupling capacitances can be substantial, making it difficult to control each quantum dot independently. Increasing the number of quantum dots increases the complexity of the calibration process, which becomes impractical to do heuristically. Inspired by recent demonstrations of industrial-grade silicon quantum dot bilinear arrays, we develop a theoretical framework to mitigate the effect of cross-capacitances in 2x2 arrays of quantum dots, that can be directly extended to 2xN arrays. The method is based on extracting the gradients in gate voltage space of different charge transitions in multiple two-dimensional charge stability diagrams to determine the system's virtual voltages. To automate the process, we train an ensemble of regression models to extract the gradients from a Hough transformation of a stability diagram and validate the algorithm on simulated and experimental data of a 2x2 quantum dot array. Our method provides a completely automated tool to mitigate the effect of cross capacitances, which could be used to study cross capacitance variability across QDs in large bilinear arrays

Polarization dynamics in ferroelectric materials are explored via the automated experiment in Piezoresponse Force Spectroscopy. A Bayesian Optimization framework for imaging is developed and its performance for a variety of acquisition and pathfinding functions is explored using previously acquired data. The optimized algorithm is then deployed on an operational scanning probe microscope (SPM) for finding areas of large electromechanical response in a thin film of PbTiO3, with metrics showing gains of ~3x in the sampling efficiency. This approach opens the pathway to perform more complex spectroscopies in SPM that were previously not possible due to time constraints and sample stability, tip wear, and/or stochastic sample damage that occurs at specific, a priori unknown spatial positions. Potential improvements to the framework to enable the incorporation of more prior information and improve efficiency further are discussed.

Existing theoretical works differ on whether three-dimensional Dirac and Weyl semimetals are stable to a short-range-correlated random potential. Numerical evidence suggests the semimetal to be unstable, while some field-theoretic instanton calculations have found it to be stable. The differences go beyond method: the continuum field-theoretic works use a single, perfectly linear Weyl cone, while numerical works use tight-binding lattice models which inherently have band curvature and multiple Weyl cones. In this work, we bridge this gap by performing exact numerics on the same model used in analytic treatments, and we find that all phenomena associated with rare regions near the Weyl node energy found in lattice models persist in the continuum theory: The density of states is non-zero and exhibits an avoided transition. In addition to characterizing this transition, we find rare states and show that they have the expected behavior. The simulations utilize sparse matrix techniques with formally dense matrices; doing so allows us to reach Hilbert space sizes upwards of 10 7 states, substantially larger than anything achieved before.

We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and vanishes toward the critical strength of disorder, hence becoming the order parameter. The obtained critical behavior of the speed of the wave packets is consistent with that predicted by the scaling conjecture.

We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising p -spin Model with p=3 and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers and trapping times on sub-sequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various trap models finding the best agreement with the step model when the p -spin configurations are constrained to be uncorrelated.

We study the one-dimensional nearest neighbor tight binding model of electrons with independently distributed random hopping and no on-site potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to sub-lattice symmetry, for each realization). For non-singular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states ρ(E)∼1/|E ln 3 |E|| and of the localization length ξ(E)∼|ln|E|| , near the band center E=0 . (This singular behavior is also applicable to random XY and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain). Simultaneously, the state at E=0 shows a universal, sub-exponential decay at large distances ∼exp[− r/ r 0 − − − − √ ] . In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small t is of the form ∼1/[t ln λ+1 (1/t)] , characterized by a single, continuously tunable parameter λ>0 . We find, using a combination of analytic and numerical methods, that while the universal result applies for λ>2 , it no longer holds in the interval 0<λ<2 . In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the non-universal parameter λ ; simultaneously, the localization length shows a less divergent form at low energies, and ceases to diverge below λ=1 . For λ<2 , the fall-off of the E=0 state at large distances also deviates from the universal result, and is of the form ∼exp[−(r/ r 0 ) 1/λ ] , which decays faster than an exponential for λ<1 .