The linear dependence on temperature $\left(\gamma T\right)$ of the heat capacity at low temperatures $(T<15\mathrm{K})$ is traditionally attributed to conduction electrons in metals; however, many insulators also exhibit a linear dependence that has been attributed to a variety of other physical properties. The property most commonly used to justify the presence of this linear dependence is lattice vacancies, but a correlation between these two properties has never been shown, to our knowledge. We have devised a theory that justifies a linear heat capacity as a result of lattice vacancies, and we provide measured values and data from the literature to support our arguments. We postulate that many small Schottky anomalies are produced by a puckering of the lattice around these vacancies, and variations in the lattice caused by position or proximity to some form of structure result in a distribution of Schottky anomalies with different energies. We present a mathematical model to describe these anomalies and their distribution based on literature data that ultimately results in a linear heat capacity. From these calculations, a quantitative relationship between the linear term and the concentration of lattice vacancies is identified, and we verify these calculations using values of $\gamma$ and vacancy concentrations for several materials. We have compiled many values of $\gamma$ and vacancy concentrations from the literature which show several significant trends that provide further evidence for our theory.

Individual highly pure single-crystalline silver nanowires (Ag NWs) were investigated with regard to the electrical conductivity $\sigma$, the thermal conductivity $\lambda$, and the Seebeck coefficient $S$ as a function of the temperature $T$ between $1.4\mathrm{K}$ and room temperature (RT). Transmission electron microscopy was performed subsequently to the thermoelectric characterization of the Ag NWs, so that their transport properties can be correlated with the structural data. The crystal structure, surface morphology and the rare occurrence of kinks and twinning were identified. The thermoelectric properties of the Ag NWs are discussed in comparison to the bulk: $S_{\mathrm{Ag},\mathrm{Pt}}\left(T\right)$ was measured with respect to platinum and is in agreement with the bulk, while $\sigma \left(T\right)$ and $\lambda \left(T\right)$ showed reduced values with respect to the bulk. The latter are both notably dominated by surface scattering caused by an increased surface-to-volume ratio. By lowering $T$, the electron mean free path strongly exceeds the NW's diameter of 150 nm so that the transition from diffusive transport to quasiballistic one-dimensional transport is observed. An important result of this work is that the Lorenz number $L\left(T\right)$ turns out to be independent of surface scattering. Instead, the characteristic of $L\left(T\right)$ is determined by the material's purity. Moreover, $\sigma \left(T\right)$ and $L\left(T\right)$ can be described by the bulk Debye temperature of silver. A detailed discussion of the temperature dependence of $L\left(T\right)$ and the scattering mechanisms is given.

We study normal transport and the subgap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance: Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (helical leads), but not in the central region. Conversely, a helical central region between nonhelical leads exhibits helical gaps of half-quantum conductance, with superimposed helical Fabry-Perot oscillations. These normal features translate into distinct subgap states when the leads become superconducting. In particular, Fabry-Perot resonances within the helical gap become parity-protected zero-energy states (parity crossings), well below the critical field $B_c$ at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these zero modes oscillate around zero energy, forming characteristic loops, which evolve continuously into Majorana bound states as $B$ exceeds $B_c$. The relation with the physics of parity crossings of Yu-Shiba-Rusinov bound states is discussed.

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist ${\omega }_4$ of $G$'s cohomology group ${\mathcal{H}}^4(G,\mathbb{R}/\mathbb{Z})$ in three-dimensional space and one-dimensional time $(3+1\mathrm{D})$. We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The $3+1\mathrm{D}$ twisted gauge theory can be characterized by a representation of a modular transformation group, $\mathrm{SL}(3,\mathbb{Z})$. We express the $\mathrm{SL}(3,\mathbb{Z})$ generators ${\mathsf{S}}^{xyz}$ and ${\mathsf{T}}^{xy}$ in terms of the gauge group $G$ and the 4-cocycle ${\omega }_4$. As we compactify one of the spatial directions $z$ into a compact circle with a gauge flux $b$ inserted, we can use the generators ${\mathsf{S}}^{xy}$ and ${\mathsf{T}}^{xy}$ of an $\mathrm{SL}(2,\mathbb{Z})$ subgroup to study the dimensional reduction of the 3D topological order ${\mathcal{C}}^{3\mathrm{D}}$ to a direct sum of degenerate states of 2D topological orders ${\mathcal{C}}_b^{2\mathrm{D}}$ in different flux $b$ sectors: ${\mathcal{C}}^{3\mathrm{D}}={\oplus }_b{\mathcal{C}}_b^{2\mathrm{D}}$. The 2D topological orders ${\mathcal{C}}_b^{2\mathrm{D}}$ are described by 2D gauge theories of the group $G$ twisted by the 3-cocycle ${\omega }_{3\left(b\right)}$, dimensionally reduced from the 4-cocycle ${\omega }_4$. We show that the $\mathrm{SL}(2,\mathbb{Z})$ generators, ${\mathsf{S}}^{xy}$ and ${\mathsf{T}}^{xy}$, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Charge fluctuations in the quasi-one-dimensional material ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ are analyzed based on a multiorbital extended Hubbard model. A charge-ordering transition induced by Coulomb repulsion is found with a particular charge-ordering pattern. The metallic phase is characterized by the presence of a charge collective mode which softens signaling the proximity to the charge order transition. We argue that the scattering between electrons mediated by these charge fluctuations can lead to non-Fermi liquid behavior in a quasi-one-dimensional system consistent with the unconventional metallic behavior observed above the superconducting transition in ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$.

Motivated by experimental evidence for mixed-valence correlations affecting the neutralization of strontium ions on gold surfaces, we set up an Anderson-Newns model for the Sr:Au system and calculate the neutralization probability $\alpha$ as a function of temperature. We employ quantum-kinetic equations for the projectile Green functions in the $\mathrm{finite}\text{−}U$ noncrossing approximation. Our results for $\alpha$ agree reasonably well with the experimental data as far as the overall order of magnitude is concerned, showing in particular the correlation-induced enhancement of $\alpha$. The experimentally found nonmonotonous temperature dependence, however, could not be reproduced. Instead of an initially increasing and then decreasing $\alpha$, we find over the whole temperature range only a weak negative temperature dependence. It arises, however, clearly from a mixed-valence resonance in the projectile's spectral density and thus supports qualitatively the interpretation of the experimental data in terms of a mixed-valence scenario.

We address the origin of beadlike edge states observed by scanning tunneling microscopy (STM) in moiré patterns of graphite. Low-bias STM measurements indicate these edge states are centered around $AB$ stacking sites, contrary to the common assumption of them being at $AA$ sites. This shift in the beads intensity with respect to the bulk moiré pattern has been corroborated by a tight-binding calculation of the edge states in bilayer flakes. Our results are valid not only for graphite, but also for few-layer graphene where these states have also been recently observed.

A Mott transition in granular Al films is observed by probing the increase of the spin-flip scattering rate of conduction electrons as the nanosize metallic grains are being progressively decoupled. The presence of free spins in granular Al films is directly demonstrated by $\mu \mathrm{SR}$ measurements. Analysis of the magnetoresistance in terms of an effective Fermi energy shows that it becomes of the order of the grains electrostatic charging energy at a room temperature resistivity ${\rho }_{300\mathrm{K}}\approx 50000\mu \Omega \mathrm{cm}$, at which a metal to insulator transition is known to exist. As this transition is approached the magnetoresistance exhibits a heavy-fermion-like behavior, consistent with an increased electron effective mass.

We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with projected entangled pair states (PEPS) as a function of the bond dimension ($D$), temperature (${\beta }^{-1}$), and system size ($N$). First, we introduce a compression method in which the bond dimension scales as $D=e^{O({log}_2^2(N/\epsilon ))}$ if $\beta <O\left({log}_{2}N\right)$. Second, building on the work of Hastings [M. B. Hastings, Phys. Rev. B 73, 085115 (2006)], we derive a polynomial scaling relation, $D={(N/\epsilon )}^{O\left(\beta \right)}$. This implies that the manifold of PEPS forms an efficient representation of Gibbs states of local quantum Hamiltonians. From those bounds it also follows that ground states can be approximated with $D=N^{O\left({log}_{2}N\right)}$ whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.

Using large-scale kinetic Monte Carlo (KMC) simulations, we investigate the nonequilibrium surface growth of the fullerene ${\text{C}}_{60}$. Recently we have presented a self-consistent set of energy barriers that describes the nucleation and multilayer growth of ${\text{C}}_{60}$ for different temperatures and adsorption rates in quantitative agreement with experiments [Bommel et al., Nat. Commun. 5, 5388 (2014)]. We found that ${\text{C}}_{60}$ displays lateral diffusion resembling colloidal systems, however it has to overcome an atomlike energetic step-edge barrier for interlayer diffusion. Here we focus on the particle-resolved dynamics, and the interplay between surface morphology and particle dynamics during growth. Comparing ${\text{C}}_{60}$ growth with an atomlike system, we find significant differences in the evolution of the surface morphology, as well as the single-particle dynamics on the growing material landscape. By correlating the mean-squared displacement of particles with their current neighborhood, we can identify the influence of the different time scales that compete during growth and can pinpoint the differences between the two systems.

Terahertz spectroscopy experiments at magnetic fields and low temperatures were carried out on samples of different gate shapes processed on a high electron mobility GaAs/AlGaAs heterostructure. For a given radiation frequency, multiple magnetoplasmon resonances were observed with a dispersion relation described within a local approximation of the magnetoconductivity tensor. The second harmonic of the cyclotron resonance was observed and its appearance was interpreted as resulting from a high-frequency, inhomogeneous electromagnetic field on the border of a two-dimensional electron gas with a metallic gate and/or an ohmic contact.

We report on current-induced domain wall motion in $\mathrm{Ta}/\mathrm{C}{\mathrm{o}}_{20}\mathrm{F}{\mathrm{e}}_{60}{\mathrm{B}}_{20}/\mathrm{MgO}$ nanowires. Domain walls are observed to move against the electron flow when no magnetic field is applied, while a field along the nanowires strongly affects the domain wall motion velocity. A symmetric effect is observed for up-down and down-up domain walls. This indicates the presence of right-handed domain walls, due to a Dzyaloshinskii-Moriya interaction (DMI) with a DMI coefficient $D=+0.06\mathrm{mJ}/{\mathrm{m}}^2$. The positive DMI coefficient is interpreted to be a consequence of B diffusion into the Ta buffer layer during annealing, which was observed by chemical depth profiling measurements. The experimental results are compared to one-dimensional model simulations including the effects of pinning. This modeling allows us to reproduce the experimental outcomes and reliably extract a spin-Hall angle ${\theta }_{\mathrm{SH}}=\text{–}0.11$ for Ta in the nanowires, showing the importance of an analysis that goes beyond the model for perfect nanowires.

The mesoscale allows a new probe of spin glass dynamics. Because the spin glass lower critical dimension $d_l>2$, the growth of the correlation length $\xi (t,T)$ can change the nature of the spin glass state at a crossover time $t_{\text{co}}$ when $\xi (t_{\text{co}},T)=\ell$, a minimum characteristic sample length (e.g., film thickness for thin films and crystallite size for bulk samples). For thin films, and times $t<t_{\text{co}}$ such that $\xi (t,T)<\ell$, conventional three-dimensional dynamics is observed. When $t>t_{\text{co}}$, a crossover to $d=2$ behavior takes place. The parallel correlation length, associated with a $T_g=0$ transition, increases in time from the saturated value of the perpendicular correlation length $\ell$ to an equilibrium value of the parallel correlation length proportional to $T^{-\nu }$. This results in a pancakelike correlated state, with a thickness $\ell$ and a temperature-dependent in-plane radius that increases with decreasing temperature. Activated dynamics is associated with these states. Measurements on Cu:Mn thin films are analyzed quantitatively within this framework. We extract a temperature-dependent activation energy from a fit to the frequency dependence of the dynamic susceptibility. The extrapolated temperature at which the activation energy would become large is close to the extrapolated glass transition temperature from ac susceptibility measurements. All known relevant experimental data are consistent with this approach. For polycrystalline materials, there is a distribution of length scales $\mathcal{P}\left(\ell \right)$. For sufficiently broad distributions, a logarithmic time dependence is derived for the time decay of the thermoremanent magnetization $M_{\text{TRM}}(t,T)$ using an approach originally derived by Ma. Properties dependent upon an effective waiting time $t_w^{\mathrm{eff}}$ are derived that are consistent with experiment, and further measurements are suggested.

In this study the magnetic order of the spin-1/2 XXZ chain system ${\mathrm{Cs}}_2{\mathrm{CoCl}}_4$ in a temperature range from 50 mK to 0.5 K and in applied magnetic fields up to 3.5 T is investigated by high-resolution measurements of the thermal expansion and the specific heat. Applying magnetic fields along $a$ or $c$ suppresses $T_{\mathrm{N}}$ completely at about 2.1 T. In addition, we find an adjacent intermediate phase before the magnetization saturates close to 2.5 T. For magnetic fields applied along $b$, a surprisingly rich phase diagram arises. Two additional transitions are observed at critical fields ${\mu }_0{H}_{SF1}\simeq 0.25\mathrm{T}$ and ${\mu }_0{H}_{SF2}\simeq 0.7\mathrm{T}$, which we propose to arise from a two-stage spin-flop transition.

Among the widely studied superconducting iron-pnictide compounds belonging to the Ln1111 family (with Ln a lanthanide), a systematic investigation of the crossover region between the superconducting and the antiferromagnetic phase for the Ln = Nd case has been missing. We fill this gap by focusing on the intermediate doping regime of ${\mathrm{NdFeAsO}}_{1-x}{\mathrm{F}}_x$ by means of dc-magnetometry and muon-spin spectroscopy ($\mu \mathrm{SR}$) measurements. The long-range order we detect at low fluorine doping is replaced by short-range magnetic interactions at $x=0.08$, where also superconductivity appears. In this case, longitudinal-field $\mu \mathrm{SR}$ experiments show clear evidence of slow magnetic fluctuations that disappear at low temperatures. This fluctuating component is ascribed to the glassy-like character of the magnetically ordered phase of NdFeAsO at intermediate fluorine doping.

Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here, we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean-field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin $\frac{1}{2}$ appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion $U$ that could in principle be used to determine experimentally the value of $U$.

We study noninteracting systems with a power-law quasiparticle dispersion ${\xi }_{\mathbf{k}}\propto k^{\alpha }$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$, there exists a critical disorder strength (set by the bandwidth), at which the system exhibits a disorder-driven quantum phase transition at the bottom of the band that lies in a universality class distinct from the Anderson transition. In contrast to the conventional wisdom, it manifests itself in, e.g., the disorder-averaged density of states. For systems in symmetry classes that permit localization, the striking signature of this transition is a nonanalytic behavior of the mobility edge, which is pinned to the bottom of the band for subcritical disorder and grows for disorder exceeding a critical strength. Focusing on the density of states, we calculate the critical behavior (exponents and scaling functions) at this novel transition, using a renormalization group, controlled by an $\varepsilon =d-2\alpha$ expansion. We also apply our analysis to Dirac materials, e.g., Weyl semimetals, where this transition takes place in physically interesting three dimensions.

In order to find the right support to form assemblies of superatoms with useful magnetic properties, adsorption of the magnetic superatom ${\mathrm{FeCa}}_8$ on different types of substrates is studied using first-principles electronic structure methods. ${\mathrm{FeCa}}_8$ interacts strongly with oxide and metal substrates and its structure and magnetic properties are destroyed. Interaction between ${\mathrm{FeCa}}_8$, and graphene and hexagonal BN (h-BN) are weak, and its structure is retained on these substrates. Dimers of ${\mathrm{FeCa}}_8$ are also found to be stable on both h-BN and graphene. While the magnetic interaction between two ${\mathrm{FeCa}}_8$ units deposited on h-BN involves only direct exchange, substrate mediated RKKY interaction also plays a role on graphene. Consequences of these for the magnetic properties of the assemblies are discussed.

We present an atomistic description of the electronic and optical properties of ${\text{In}}_{0.25}{\text{Ga}}_{0.75}\mathrm{N}/\mathrm{GaN}$ quantum wells. Our analysis accounts for fluctuations of well width, local alloy composition, strain and built-in field fluctuations as well as Coulomb effects. We find a strong hole and much weaker electron wave function localization in InGaN random alloy quantum wells. The presented calculations show that while the electron states are mainly localized by well-width fluctuations, the holes states are already localized by random alloy fluctuations. These localization effects affect significantly the quantum well optical properties, leading to strong inhomogeneous broadening of the lowest interband transition energy. Our results are compared with experimental literature data.