We examine the pair entanglement in the ground state of finite dimerized spin-$s$ chains interacting through anisotropic $XY$ couplings immersed in a transverse magnetic field by means of a self-consistent pair mean-field approximation. The approach, which makes no a priori assumptions on the pair states, predicts, for sufficiently low coupling between pairs, $2s$ distinct dimerized phases for increasing fields below the pair factorizing field, separated by spin-parity-breaking phases. The dimerized phases lead to approximate magnetization and pair entanglement plateaus, while the parity-breaking phases are characterized by weak pair entanglement but non-negligible entanglement of the pair with the rest of the system. These predictions are confirmed by the exact results obtained in finite $s=1$ and $s=3/2$ chains. It is also shown that for increasing values of the spin $s$, the entanglement of an isolated pair, as measured by the negativity, rapidly saturates in the anisotropic $XY$ case but increases as $s^{1/2}$ in the $XX$ case, reflecting a distinct single-spin entanglement spectrum.

The external controllability of topological superconductors and Majorana fermions would be important both for fundamental and practical interests. Here we predict the electric-field control of Majorana fermions in two-dimensional topological superconductors utilizing a topological insulator thin-film proximity coupled to a conventional $s$-wave superconductor. With ferromagnetic ordering, the tunable structure inversion asymmetry by vertical electric field could induce topological quantum phase transition and realize a chiral topological superconductor state. A zero-energy Majorana bound state appears at the boundary of an applied electric-field spot, which can be observed by scanning tunneling microscopy. Furthermore, the structure inversion asymmetry could also enlarge the helical topological superconductor state in the phase diagram, making the realization of such an exotic state more feasible. The electrical control of topological phases could further apply to van der Waals materials such as two-dimensional transition-metal dichalcogenides.

We report recent investigations into the transition to turbulence in superfluid ${}^4\mathrm{He}$, realized experimentally by measuring the drag forces acting on two custom-made quartz tuning forks with fundamental resonances at 6.5 kHz and 55.5 kHz, in the temperature range 10 mK to 2.17 K. In pure superfluid in the zero temperature limit, three distinct critical velocities were observed with both tuning forks. We discuss the significance of all critical velocities and associate the third critical velocity reported here with the development of large vortical structures in the flow, which thus starts to mimic turbulence in classical fluids. The interpretation of our results is directly linked to previous experimental work with oscillators such as tuning forks, grids, and vibrating wires, focusing on the behavior of purely superfluid ${}^4\mathrm{He}$ at very low temperatures.

The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in $d=2+\varepsilon$ of a $U\left(N\right)$ Gross-Neveu model in the limit $N\to 0$. Unfortunately, this model is not multiplicatively renormalizable in $2+\varepsilon$ dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high-energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a $d=4-\varepsilon$ expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.

This study aims to unravel the mechanism of colossal magnetoresistance (CMR) observed in $n\text{−}\mathrm{type} {\mathrm{HgCr}}_2{\mathrm{Se}}_4$, in which low-density conduction electrons are exchange-coupled to a three-dimensional Heisenberg ferromagnet with a Curie temperature $T_C\approx 105$ K. Near room temperature the electron transport exhibits an ordinary semiconducting behavior. As temperature drops below $T^{*}\simeq 2.1T_C$, the magnetic susceptibility deviates from the Curie-Weiss law, and concomitantly the transport enters an intermediate regime exhibiting a pronounced CMR effect before a transition to metallic conduction occurs at $T<T_C$. Our results suggest an important role of spin correlations not only near the critical point but also for a wide range of temperatures $\left(T_C<T<T^{*}\right)$ in the paramagnetic phase. In this intermediate temperature regime the transport undergoes a percolation type of transition from isolated magnetic polarons to a continuous network when temperature is lowered or magnetic field becomes stronger.

The evolution of the structural and magnetic properties of Co doped ZnO has been investigated over an unprecedented concentration range above the coalescence limit. ZnO films with Co concentrations from 20% to 60% of the cationic lattice have been grown by reactive magnetron sputtering. The wurtzite crystal structure was maintained even for these high dopant concentrations. By measuring the x-ray absorption at the near edge and the linear and circular dichroism of the films at the Zn and Co $K$ edge, it could be shown that Co substitutes predominantly for Zn in the lattice. No indications of metallic Co have been found in the samples. At low Co concentrations, the films are paramagnetic, but with increasing Co content, the films become antiferromagnetically ordered with increasing order temperature. Uncompensated spins, coupled to the antiferromagnetic dopant configurations, lead to a vertical exchange-bias-like effect, which increases with increasing Co concentration. In parallel, the single-ion anisotropy is gradually lost.

We have performed transverse-field muon spin relaxation measurements on ambient-pressure-grown polycrystalline $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$. From these measurements, no signature of magnetic order is found down to 25 mK. The value of the magnetic penetration depth extrapolated to 0 K is 0.89 (5) $\mu \mathrm{m}$. The temperature dependence of superconducting penetration depth is best described by either a multigap $s+s$-wave model with ${\mathrm{\Delta }}_1=0.947 \left(7\right) \mathrm{meV}$ and ${\mathrm{\Delta }}_2=0.22$ (4) meV or the anisotropic $s$-wave model with $\mathrm{\Delta }\left(0\right)=0.776 \mathrm{meV}$ and anisotropic gap amplitude ratio ${\mathrm{\Delta }}_{\text{min}}/{\mathrm{\Delta }}_{\text{max}}=0.34$. Comparisons with other potentially multigap ${\mathrm{BiS}}_2$-based superconductors are discussed. We find that these ${\mathrm{BiS}}_2$-based superconductors, including ${\mathrm{Bi}}_4{\mathrm{O}}_4{\mathrm{S}}_3$ and the high-pressure synthesized $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$, generally conform to the Uemura relation.

We analyze the highly nonperturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory (DMFT) calculations at the two-particle level. By extending the results of Schäfer et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. By comparing our numerical data for the Hubbard model with analytical calculations for exactly solvable systems of increasing complexity [disordered binary mixture (BM), Falicov-Kimball (FK), and atomic limit (AL)], we have (i) identified two different kinds of divergence lines; (ii) classified them in terms of the frequency structure of the associated singular eigenvectors; and (iii) investigated their relation to the emergence of multiple branches in the Luttinger-Ward functional. In this way, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, single energy scale ${\nu }^{*}$ below which perturbation theory is no longer applicable, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the nonperturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

We calculate the photoluminescence spectrum of a single semiconductor quantum dot strongly coupled to a continuum as a function of light frequency, gate voltage, and magnetic field. The spectrum is dominated by the recombination of several excitonic states which can be considered as quantum quenches in which the many-body nature of the system is suddenly changed between initial and final states. This is associated with an Anderson orthogonality catastrophe with a power-law singularity at the threshold. We explain the main features observed experimentally in the region of stability of the trion $X^{-}$, the neutral exciton $X^0$, and the gate-voltage-induced transition between them.

A generalized version of the fidelity susceptibility of single-band and multiorbital Hubbard models is systematically studied using single-site dynamical mean-field theory in combination with a hybridization expansion continuous-time quantum Monte Carlo impurity solver. We find that the fidelity susceptibility is extremely sensitive to changes in the state of the system. It can be used as a numerically inexpensive tool to detect and characterize a broad range of phase transitions and crossovers in Hubbard models, including (orbital-selective) Mott metal-insulator transitions, magnetic phase transitions, high-spin to low-spin transitions, Fermi-liquid to non-Fermi-liquid crossovers, and spin-freezing crossovers.

Dirac points in two-dimensional electronic structures are a source for topological electronic states due to the $\pm \pi$ Berry phase that they sustain. Here we show that two rutile multilayers [namely ${\left({\mathrm{WO}}_2\right)}_2/{\left({\mathrm{ZrO}}_2\right)}_n$ and ${\left({\mathrm{PtO}}_2\right)}_2/{\left({\mathrm{ZrO}}_2\right)}_n$], where an active bilayer is sandwiched by a thick enough ($n=6$ is sufficient) band insulating substrate, show semimetallic Dirac dispersions with a total of four Dirac cones along the $\mathrm{\Gamma }-M$ direction. These become gapped upon the introduction of spin-orbit coupling, giving rise to an insulating ground state comprising four edge states. We discuss the origin of the lack of topological protection in terms of the valley spin-Chern numbers and the multiplicity of Dirac points. We show with a model Hamiltonian that mirror-symmetry breaking would be capable of creating a quantum phase transition to a strong topological insulator, with a single Kramers pair per edge.

We analyze the linear thermoelectric transport properties of devices with three quantum dots in a star configuration. A central quantum dot is tunnel-coupled to source and drain electrodes and to two additional quantum dots. For a wide range of parameters, in the absence of an external magnetic field, the system is a singular Fermi liquid with a nonanalytic behavior of the electric transport properties at low energies. The singular behavior is associated with the development of a ferromagnetic or an underscreened Kondo effect, depending on the parameter regime. A magnetic field drives the system into a regular Fermi liquid regime and leads to a large peak $\left(\sim k_B/\left|e\right|\right)$ in the spin thermopower as a function of the temperature, and to a $\sim 100\%$ spin polarized current for a wide range of parameters due to interference effects. We find a qualitatively equivalent behavior for systems with a larger number of side-coupled quantum dots, with the maximum value of the spin thermopower decreasing as the number of side-coupled quantum dots increases.

Can topological quantum entanglement between anyons in one topological medium “stray” into a different, topologically distinct medium? In other words, can quantum information encoded nonlocally in the combined state of non-Abelian anyons be shared between two distinct topological media? For one-dimensional topological superconductors with Majorana bound states at the end of system, the quantum information store in those Majorana bound states can be transfered by directly coupling nearby Majorana bound states. However, coupling of two one-dimensional Majorana states will produce a gap, indicating that distinct topological regions of one-dimensional wires unite into a single topological region through the information transfer process. In this paper, we consider a setup with two two-dimensional $p$-wave superconductors of opposite chirality adjacent to each other. Even two comoving chiral modes at the domain wall between them cannot be gapped through interactions; we demonstrate that information encoded in the fermionic parity of two Majorana zero modes, originally within the same superconducting domain, can be shared between the domains or moved entirely from one domain to another provided that vortices can tunnel between them in a controlled fashion.

We study the properties of dipolar wave propagation in linear chains of isotropic particles with independent electric and magnetic response, embedded in vacuum. It is shown that the chain can support simultaneously right-handed modes (RHMs) and left-handed modes (LHMs) of transverse polarization. The LHMs are supported by the structure even if the chain's particles possess positive polarizabilities and no Bi isotropy; the needed structural Bi isotropy is provided by the propagator instead of by the particle's local properties. In contrast to the transverse modes in chains that consist of purely electric particles that are inherently RHM, the LHM dispersion lacks the light-line branch since the dipolar features are not aligned with the electric and magnetic fields of a right-handed plane-wave solution in free space. Furthermore, it is shown that the spatial width of the LHM is significantly smaller than that of the RHM. Excitation theory is developed, and it is shown that the chain possesses modal and excitation asymmetries that can be used to eliminate reflections from the chain's termination.

We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high temperature and, at large $U$, they are featureless with characteristic widths of the order of the lattice hopping parameter $t$. In the infinite-$d$ limit, we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime, which applies for $T\gtrsim (1-n)D$, the Brinkman-Rice scale. The resistivity increases linearly in $T$ at high temperature without saturation. This results from the $1/T$ behavior of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturates at high $T$. We find that $\sigma (n,T)\approx (1-n)\sigma (n=0,T)$ to a very good approximation for all $n$, with $\sigma (n=0,T)\propto t/T$ at high temperatures. The saturation at small $n$ occurs due to a compensation between the density dependence of the effective number of carriers and that of the scattering time. The $T$ dependence of the resistivity displays a kneelike feature which signals a crossover to the intermediate-temperature regime where the diffusion constant (or scattering time) starts increasing with decreasing $T$. At high temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$. The relevance of our calculations to experiments probing high-temperature transport in materials with strong electronic correlations or ultracold atomic gases in an optical lattice is briefly discussed.

We investigate the anomalous Hall effect (AHE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities, and find topologically nontrivial and trivial mechanisms simultaneously contributing to the Hall conductivity. In the topologically nontrivial mechanism, the impurities gap the surface spectrum and result in a half-integer quantized intrinsic Hall conductivity in units $e^2/h$, while in the topologically trivial mechanism, the half-integer quantized plateau is modified by impurity-induced localized states via a gap-filling process. The nonmagnetic charge potential itself, though participating in the gap-filling process, cannot induce the AHE. In the presence of a finite magnetic potential, the charge potential would destroy the symmetric distribution of the Hall conductivity by redistributing the localized levels. More interestingly, the sign of the Hall conductivity is tunable by changing the strength of the charge potential.

The charge transport properties of individual InSb nanowires based transistors are studied at 4.2 K in the quasiballistic regime. The energy level separations at zero magnetic field are extracted from a bias voltage spectroscopy. The magnetoconductance under a magnetic field applied perpendicularly to the nanowire axis is investigated up to 50 T. Owing to the magnetic reduction of the backscattering, the electronic states of the quasi-one-dimensional electron gas are revealed by Landauer-Büttiker conductance quantization. The results are compared to theoretical predictions revealing the spin and orbital degeneracy lifting. At sufficiently high magnetic field the measurements show the evolution to the quantum Hall effect regime with the formation of Landau orbits and conducting edge states.

In this work the Casimir-Polder interaction energy between a rubidium atom and a disordered graphene sheet is investigated beyond the Dirac cone approximation by means of accurate real-space tight-binding calculations. As a model of defected graphene, we consider a tight-binding model of $\pi$ electrons on a honeycomb lattice with a small concentration of vacancies. The optical response of the graphene sheet is evaluated with full spectral resolution by means of exact Chebyshev polynomial expansions of the Kubo formula in large lattices in excess of 10 million atoms. At low temperatures, the optical response of defected graphene is found to display two qualitatively distinct behaviors with a clear transition around finite (nonzero) Fermi energy. In the vicinity of the Dirac point, the imaginary part of optical conductivity is negative for low frequencies while the real part is strongly suppressed. On the other hand, for high doping, it has the same features found in the Drude model within the Dirac cone approximation, namely, a Drude peak at small frequencies and a change of sign in the imaginary part above the interband threshold. These characteristics translate into a nonmonotonic behavior of the Casimir-Polder interaction energy with very small variation with doping in the vicinity of the neutrality point while having the same form of the interaction calculated with Drude's model at high electronic density.