We examine the mechanical eigenmodes of a quartz tuning fork (QTF) for the purpose of facilitating its use as a probe for multifrequency atomic force microscopy (AFM). We perform simulations based on the three-dimensional finite element method and compare the observed motions of the beams with experimentally measured resonance frequencies of two QTF systems. The comparison enabled us to assign the first seven asymmetric eigenmodes of the QTF. We also find that a modified version of single beam theory can be used to guide the assignment of mechanical eigenmodes of QTFs. The usefulness of the QTF for multifrequency AFM measurements is demonstrated through photoinduced force microscopy measurements. By using the QTF in different configurations, we show that the vectorial components of the photoinduced force can be independently assessed and that lateral forces can be probed in true noncontact mode.

The Dirac semimetal phase found in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ is protected by a $C_4$ rotational symmetry derived from a corkscrew arrangement of systematic Cd vacancies in its complicated crystal structure. It is therefore surprising that no microscopic observation, direct or indirect, of these systematic vacancies has so far been described. To this end, we revisit the cleaved (112) surface of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ using a combined approach of scanning tunneling microscopy and ab initio calculations. We determine the exact position of the (112) plane at which ${\mathrm{Cd}}_3{\mathrm{As}}_2$ naturally cleaves, and describe in detail a structural periodicity found at the reconstructed surface, consistent with that expected to arise from the systematic Cd vacancies. This reconciles the current state of microscopic surface observations with those of crystallographic and theoretical models, and demonstrates that this vacancy superstructure, central to the preservation of the Dirac semimetal phase, survives the cleavage process and retains order at the surface.

Recently synthesized three-dimensional materials with Dirac spectrum exhibit peculiar electric transport qualitatively different from its two-dimensional analog, graphene. By neglecting impurity scattering, the real part of the conductivity is strongly frequency dependent, while the imaginary part is nonzero unlike in undoped, clean graphene. The Coulomb interaction between electrons is unscreened as in a dielectric and hence is long range. We demonstrate that the interaction correction renders the electrodynamics nonlocal on a mesoscopic scale. The longitudinal conductivity ${\sigma }_{\mathrm{L}}$ and the transverse conductivity ${\sigma }_{\mathrm{T}}$ are different in the long-wavelength limit and consequently the standard local Ohm's law description does not apply. This leads to several remarkable effects in optical response. The $p$-polarized light generates in these materials bulk plasmons as well as the transversal waves. At a specific frequency the two modes coincide, a phenomenon impossible in a local medium. For any frequency there is a Brewster angle where total absorption occurs, turning the Weyl semimetals opaque. The effect of the surface, including the Fermi arcs, is discussed.

Raman scattering spectra of the dimer-Mott insulator ${\beta }^{\prime }\text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{IC}{\mathrm{l}}_2$ [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene] under a static electric field are investigated. The application of the electric field induces two additional Raman peaks on both sides of the original peak position of the charge-sensitive Raman mode $\left({\nu }_2\right)$ in the spectra. At 10 kV/cm, the original peak almost disappears and only the newly emerging peaks are observed. The emergence of these peaks indicates the field-induced charge disproportionation within the dimer. The temporal change of the Raman signals with the inversion of the electric field suggests a macroscopic domain formation of the charge-disproportionate dimers. This picture is reinforced by the direct measurement of the polarization.

We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (Hückel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the Hückel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zigzag chains using the density-matrix renormalization group (DMRG) method. We check our numerical approach against analytic results for the Hückel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.

We present a simple method that allows us to calculate the electromagnetic response of noninteracting electrons in a strong magnetic field to arbitrary order in the gradients of external electric and magnetic fields. We illustrate the method on both nonrelativistic and massless Dirac electrons filling $N$ Landau levels. First, we derive an exact relation between the electromagnetic response of the nonrelativistic and Dirac electrons in the lowest Landau level. Next, we obtain a closed form expression for the polarization operator in the large-$N$ (or weak magnetic field) limit. We explicitly show that in the large-$N$ limit the random phase approximation (RPA) computation of the polarization tensor agrees—in leading and subleading order in $N$—with a Fermi liquid computation to all orders in the gradient expansion and for arbitrary value of the $\mathrm{g}$ factor. Finally, we show that in the large-$N$ limit the nonrelativistic polarization tensor agrees with Dirac's in the leading and subleading orders in $N$, provided that the Berry phase of the Dirac cone is taken into account via replacement $N⟶N+1/2$.

Topological insulators (TIs) and Weyl semimetals (WSMs) are two realizations of topological matter usually appearing separately in nature. However, they are directly related to each other via a topological phase transition. In this paper, we investigate the question whether these two topological phases can exist together at the same time, with a combined, hybrid surface state at the joint boundaries. We analyze effective models of a three-dimensional TI and an inversion symmetric WSM and couple them in a way that certain symmetries, like inversion, are preserved. A tunnel coupling approach enables us to obtain the hybrid surface state Hamiltonian analytically. This offers the possibility of a detailed study of its dispersion relation depending on the investigated couplings. For spin-symmetric coupling, we find that two Dirac nodes can emerge out of the combination of a single Dirac node and a Fermi arc. For spin-asymmetric coupling, the dispersion relation is gapped and the former Dirac node gets spin-polarized. We propose different experimental realization of the hybrid system, including compressively strained HgTe as well as heterostructures of TI and WSM materials.

We analyze quantum dot models used in current research for misconceptions that arise from the choice of basis states for the carriers. The examined models originate from semiconductor quantum optics, but the illustrated conceptional problems are not limited to this field. We demonstrate how the choice of basis states can imply a factorization scheme that leads to an artificial dependency between two, actually independent, quantities. Furthermore, we consider an open quantum dot-cavity system and show how the dephasing, generated by the dissipator in the von Neumann Lindblad equation, depends on the choice of basis states that are used to construct the collapse operators. We find that the Rabi oscillations of the $s$-shell exciton are either dephased by the dissipative decay of the $p$-shell exciton or remain unaffected, depending on the choice of basis states. In a last step we resolve this discrepancy by taking the full system-reservoir interaction Hamiltonian into account.

One crucial and important aspect to account for the nature of the quantum wires is the understanding of the effects associated to many-body interactions between confined electrons. The inclusion of such many-body forces in any theoretical framework is a difficult and computationally demanding task. Then one has to make use of coarse-grained descriptions that allow one to incorporate the contribution of all the electrons. In a simple physical picture, the interaction between two electrons can be considered screened due to the presence of the other ones. If the latter are homogeneously distributed inside the wire, the interaction between the former can then be assumed of the Yukawa form. In this contribution, we report on the lower energy states of $n$-doped GaAs circular-quantum wires with two electrons in the conduction band interacting through a repulsive Yukawa potential. By varying the length and the electronic density of the wire, quite different trends in the electronic distribution are observed. By changing the material parameters to InSb and InAs nanowires, we found that our results are consistent with available experimental data that have reported the formation of Wigner crystals.

We theoretically study the interaction of crystalline topological insulator (CTIs), characterized by surface quadratic gapless bands, with an ultrashort (few-femtosecond) optical pulse. The electron dynamics in such an optical pulse is determined by a strong lattice-momentum dependence of the interband dipole coupling, which is anisotropic and singular at the degeneracy point. The interband mixing induced by the ultrashort pulse results in a finite conduction band population, the distribution of which in the reciprocal space is correlated with the profile of the interband dipole matrix elements and has high contrast. The number of such high-contrast regions depends on the polarization direction of the optical pulse. The ultrashort pulse also causes an electrical current and a net charge transfer through the system in the direction of the maximum field. These findings open up roots to ultrafast optical-field control of the CTIs and petahertz-band optoelectronics.

The $\mathrm{S}{\mathrm{r}}_{1-x}\mathrm{B}{\mathrm{a}}_x\mathrm{Tc}{\mathrm{O}}_3$ ($x=0$, 0.1, 0.2) oxides were prepared and their solid-state and magnetic structure studied as a function of temperature by x-ray and neutron powder diffraction. The refined Tc moments at room temperature and Néel temperatures for $\mathrm{B}{\mathrm{a}}_{0.1}\mathrm{S}{\mathrm{r}}_{0.9}\mathrm{Tc}{\mathrm{O}}_3$ and $\mathrm{B}{\mathrm{a}}_{0.2}\mathrm{S}{\mathrm{r}}_{0.8}\mathrm{Tc}{\mathrm{O}}_3$ were $2.32\left(14\right){\mu }_{\beta }$ and $2.11\left(13\right){\mu }_{\beta }$ and $714{}^{\circ }\mathrm{C}$ and $702{}^{\circ }\mathrm{C}$, respectively. In contrast to expectations, the Néel temperature in the series $\mathrm{S}{\mathrm{r}}_{1-x}{A}_x\mathrm{Tc}{\mathrm{O}}_3$ decreases with increasing Ba content. This observation is consistent with previous experimental measurements for the two series $A\mathrm{M}{\mathrm{O}}_3$ ($M=\mathrm{Ru}$, Mn; $A=\mathrm{Ca}$, Sr, Ba) where the maximum magnetic ordering temperature was observed for $A=\mathrm{Sr}$. Taken with these previous results the current work demonstrates the critical role of the $A$-site cation in the broadening of the ${\pi }^{*}$ bandwidth and ultimately the magnetic ordering temperature.

Conventional magnetometry yields a low temperature bulk magnetic moment of about $4{\mu }_{\mathrm{B}}/\phantom{{\mu }_{\mathrm{B}}\mathrm{D}{\mathrm{y}}^{3+}}\mathrm{D}{\mathrm{y}}^{3+}$ in an applied field of ${\mu }_{0}H=9\mathrm{T}$ for thin and thick dysprosium nitride (DyN) films. This is significantly lower than the maximum possible value of $10{\mu }_{\mathrm{B}}/\phantom{10{\mu }_{\mathrm{B}}\mathrm{D}{\mathrm{y}}^{3+}}\mathrm{D}{\mathrm{y}}^{3+}.$ Ion-assisted deposition was used to grow 5.7-μm-thick rare earth nitride DyN films on organic Kapton® substrates. ${}^{161}\mathrm{Dy}$ Mössbauer spectroscopy (with its time scale on the order of nanoseconds) indicates thermal relaxation between fully stretched $\pm 10{\mu }_{\mathrm{B}}$ levels of a low-lying Kramers doublet, which is inconsistent with the $\mathrm{D}{\mathrm{y}}^{3+}$ site's ideal cubic symmetry. However, a small tetragonal distortion $\left[\epsilon \approx -0.024\left(10\right)\right]$ observed using x-ray powder diffraction is compatible with an additional rank 2 crystal field term, $B_2^0\approx -1.0\left(4\right)\mathrm{K}$, approaching the magnitude estimated to bring this about. The observed magnetic behavior can then be described using a two-level, molecular field model with ${\theta }_{\mathrm{C}}$ set to $\approx 6–8\mathrm{K},$ which is substantially smaller than the accepted ordering temperature of $T_{\mathrm{C}}\approx 17–26\mathrm{K}$.

Magnetic structures of metastable perovskites ${\mathrm{ScCrO}}_3, {\mathrm{InCrO}}_3$, and ${\mathrm{TlCrO}}_3$, stabilized under high-pressure and high-temperature conditions, have been studied by neutron powder diffraction. Similar to the other orthochromites ${\mathrm{LnCrO}}_3$ (Ln = lanthanide or Y), these materials crystallize into the orthorhombic structure with $Pnma{1}^{\prime }$ symmetry. The spin configuration of the metastable perovskites has been found to be $C$ type, contrasting with the $G$-type structure usually observed in ${\mathrm{LnCrO}}_3$. First-principles calculations demonstrate that the $C$-type structure found in ${\mathrm{ScCrO}}_3$ and ${\mathrm{InCrO}}_3$ is attributed to a ferromagnetic (FM) nearest-neighbor interaction, while in ${\mathrm{TlCrO}}_3$, this type of magnetic ordering is stabilized by a strong next-nearest-neighbor antiferromagnetic (AFM) exchange. The spins in the $C$-type magnetic structure line up along the orthorhombic $b$ axis, yielding the $Pnma$ magnetic symmetry. The dominant mechanism controlling this spin direction has been concluded to be the single ion anisotropy imposed by a uniaxial distortion of ${\mathrm{CrO}}_6$ octahedra.

Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized model converge toward the ones of the continuous model when the number of states of the discretized model increases. We answer this question for the XY model and its discretization, the $q$-state clock model, in the mean-field setting provided by random graphs. It is found that the convergence of physical observables is exponentially fast in the number $q$ of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states. Furthermore, such an exponential convergence is found to be independent from the disorder distribution used. Only at $T=0$, the convergence is slightly slower (stretched exponential). Thanks to the analytical solution to the $q$-state clock model, we compute accurate phase diagrams in the temperature versus disorder strength plane. We find that, at zero temperature, spontaneous replica symmetry breaking takes place for any amount of disorder, even an infinitesimal one. We also study the one step of replica symmetry breaking (1RSB) solution in the low-temperature spin glass phase.

We use spatially-resolved transport techniques to investigate the superconducting properties of single crystals ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$. We find a superconducting transition temperature $T_{cs}$ associated with the $ab$-plane surface region which is considerably higher than the bulk $T_c$. The effect is pronounced in the region of charge carrier doping $x$ with strong spin-charge stripe correlations, reaching $T_{cs}=36$ K or $1.64T_c$.

A recent claim of superfluid behavior of parahydrogen adsorbed inside armchair carbon nanotubes [M. Rossi and F. Ancilotto, Phys. Rev. B 94, 100502 (2016)] is disproven by means of first-principles computer simulations. Conclusive numerical evidence shows that the low-temperature equilibrium thermodynamic phase of parahydrogen adsorbed inside a $(10,10)$ armchair nanotube features a crystalline shell adsorbed on the inner surface of the tube, and a well-separated quasi-one-dimensional central column showing no evidence of possible fluid or superfluid behavior. Rather, the system is quasicrystalline and nonsuperfluid; its physical character is qualitatively identical to that observed in similar confined settings extensively studied in the past. The incorrect prediction of superfluidity stems from the erroneous use of an effective one-dimensional interaction potential that does not describe parahydrogen at the center of the nanotube.

We study surface superconductivity involving the “drumhead” surface states of (doped) Weyl loop materials. The leading weak-coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with $p+ip$ symmetry. We show that the surface SC state is “topological” as long as it is fully gapped, and the system traps Majorana modes wherever a vortex line enters or exits the bulk. In contrast to true two-dimensional $p+ip$ superconductors, these Majorana zero modes arise even in the “strong pairing” regime where the chemical potential is entirely above/below the drumhead. We also consider conventional $s$-wave pairing, and show that in this case the surface hosts a flat band of charge neutral Majorana fermions, whose momentum range is given by the projection of the bulk Fermi surface. Weyl loop materials thus provide access to new forms of topological superconductivity.

Standard Landau theory coupled to infinitesimal strain allows a concise description of the temperature-driven ferroelectric tetragonal-to-cubic phase transition in ${\mathrm{PbTiO}}_3$ at ambient pressure. Unfortunately, it fails to cover its high-pressure counterpart at ambient temperature. For example, the experimental transition pressure is vastly underestimated, and neither the change from first to second order with increasing pressure nor the unusual pressure dependence of the tetragonal unit cell parameters observed in experiment are reproduced. Here we demonstrate that a combination of density functional theory and a recently constructed finite-strain extension of Landau theory provides a natural mechanism for resolving these discrepancies between theory and experiment. Our approach also allows us to determine the full tetragonal-cubic phase boundary in the $(P,T)$ plane including an estimate of the tricritical point. We show that a careful analysis of the thermal elastic baseline is an essential ingredient to the success of this theory.