We demonstrate few-charge occupation of electron and hole quantum dots in silicon via charge sensing. We have fabricated quantum dot (QD) devices in a silicon metal-oxide-semiconductor heterostructure comprising a single-electron transistor next to a single-hole transistor. Both QDs can be tuned to simultaneously sense charge transitions of the other one. We further detect the few-electron and few-hole regimes in the QDs of our device by active charge sensing.

Two-dimensional monolayers consisting of a single element have attracted considerable interest due to their intriguing properties, which can be fundamentally different from the bulk counterparts. However, their large-scale synthesis often remains challenging owing to the nonlayered nature of the respective bulk crystal structures. In this Rapid Communication we show that the noble metal silver can be confined into the monolayer limit via intercalation between silicon carbide and epitaxial buffer layer graphene. Using angle-resolved photoelectron spectroscopy we reveal the formation of a silver-related valence band whose dispersion can be described by a simple, triangular-lattice tight-binding model. Interestingly, the synthesized silver monolayer is semiconducting as opposed to the prototype $sp$ bulk metal. The intercalation process further yields an $n$-type doped quasi-free-standing graphene monolayer, thereby realizing a two-dimensional metal/semiconductor heterostructure. Our results demonstrate the potential of epitaxial graphene on silicon carbide as a functional platform for the wafer-scale synthesis of monoelemental monolayers with unique attributes.

We investigate quantum quenches and the Loschmidt echo in the two-dimensional, three-band $\alpha -T_3$ model, a close descendant of the dice lattice. By adding a chemical potential to the central site, the integral of the Berry curvature of the bands in different valleys is continously tunable by the ratio of the hopping integrals between the sublattices. By investigating one and two filled bands, we find that dynamical quantum phase transition (DQPT), i.e., nonanalytical temporal behavior in the rate function of the return amplitude, occurs for a certain range of parameters, independent of the band filling. By focusing on the effective low-energy description of the model, we find that DQPTs happen not only in the time derivative of the rate function, which is a common feature in two-dimensional models, but also in the rate function itself. This feature is not related to the change of topological properties of the system during the quench but rather follows from population inversion for all momenta. This is accompanied by the appearance of dynamical vortices in the time-momentum space of the Pancharatnam geometric phase. The positions of the vortices form an infinite vortex ladder, i.e., a macroscopic phase structure, which allows us to identify the dynamical phases that are separated by the DQPT.

We report the superconducting properties of single unit cell FeSe prepared on ${\mathrm{SrTiO}}_3\left(\mathrm{STO}\right)\left(001\right)\text{−}c(6\times 2)$ using scanning tunneling microscopy/spectroscopy (STM/STS). A surface superstructure of $c(6\times 2)$ was obtained by annealing the substrate under an oxygen atmosphere. A $3\times 1$ periodicity, which corresponds to the topmost Ti atoms of the substrate, was observed in high-resolution STM images, and the superconducting gap size was $11.5\pm 2.5\mathrm{meV}$. A nonsuperconducting region with additional $\sqrt{2}\times \sqrt{2}$ periodicity was also found, and this originates from the difference in the arrangement of the Sr and Ti atoms at the surface. We conclude that there is a universal superconducting dome structure in the (electron-doping level)—(superconducting gap size) phase diagram by comparing with previous results that controlled the surface of the substrate/film and the gap size can be maximized/minimized by selecting the appropriate STO surface superstructure.

We investigate theoretically the noise and the full counting statistics of electrons that are emitted from a superconductor into two spatially separated quantum dots by the splitting of Cooper pairs and further on collected in two normal-state electrodes. With negatively biased drain electrodes and a large superconducting gap, the dynamics of the Cooper pair splitter can be described by a Markovian quantum master equation. Using techniques from full counting statistics, we evaluate the electrical currents, their noise power spectra, and the power-power correlations in the output leads. The current fluctuations can be attributed to the competition between Cooper pair splitting and elastic cotunneling between the quantum dots via the superconductor. In one regime, these processes can be clearly distinguished in the cross-correlation spectrum with peaks and dips appearing at characteristic frequencies associated with elastic cotunneling and Cooper pair splitting, respectively. We corroborate this interpretation by analyzing the charge transport fluctuations in the time domain, specifically by investigating the $g^{\left(2\right)}$ function of the output currents. Our work identifies several experimental signatures of the fundamental transport processes involved in Cooper pair splitting and provides specific means to quantify their relative strengths. As such, our results may help guide and interpret future experiments on current fluctuations in Cooper pair splitters.

Strong interactions between excitons are a characteristic feature of two-dimensional (2D) semiconductors, determining important excitonic properties, such as exciton lifetime, coherence, and photon-emission efficiency. Rhenium disulfide ($\mathrm{Re}{\mathrm{S}}_2$), a member of the 2D transition-metal dichalcogenide (TMD) family, has recently attracted great attention due to its unique excitons that exhibit excellent polarization selectivity and coherence features. However, an in-depth understanding of exciton-exciton interactions in $\mathrm{Re}{\mathrm{S}}_2$ is still lacking. Here we used ultrafast pump-probe spectroscopy to study exciton-exciton interactions in monolayer (1L), bilayer (2L), and triple layer $\mathrm{Re}{\mathrm{S}}_2$. We directly measure the rate of exciton-exciton annihilation, a representative Auger-type interaction between excitons. It decreases with increasing layer number, as observed in other 2D TMDs. However, while other TMDs exhibit a sharp weakening of exciton-exciton annihilation between 1L and 2L, such behavior was not observed in $\mathrm{Re}{\mathrm{S}}_2$. We attribute this distinct feature in $\mathrm{Re}{\mathrm{S}}_2$ to the relatively weak interlayer coupling, which prohibits a substantial change in the electronic structure when the thickness varies. This work not only highlights the unique excitonic properties of $\mathrm{Re}{\mathrm{S}}_2$ but also provides novel insight into the thickness dependence of exciton-exciton interactions in 2D systems.

We report systematic theoretical studies of the inverse Faraday effect in materials with massless Dirac fermions, both in two dimensions such as graphene and surface states in topological insulators, and in three dimensions such as Dirac and Weyl semimetals. Both semiclassical and quantum theories are presented, with dissipation and finite-size effects included. We find that the magnitude of the effect can be much stronger in Dirac materials as compared to conventional semiconductors. Analytic expressions for the optically induced magnetization in the low-temperature limit are obtained. Strong inverse Faraday effect in Dirac materials can be used for the optical control of magnetization, all-optical modulation, and optical isolation.

$3d\text{−}4f$ intermetalic compounds with heavy rare-earth elements show first-order phase transitions in high magnetic fields due to the competition between the exchange interaction and the magnetocrystalline anisotropy. However, the microscopic picture of the field-induced noncollinear magnetic structures remains elusive. Here we report the direct experimental observation of the coherent stepwise rotation of the $3d$ and $4f$ magnetic moments of the uniaxial hard ferrimagnet ${\mathrm{TmFe}}_5{\mathrm{Al}}_7$ by using soft x-ray magnetic circular dichroism in pulsed magnetic fields up to 25 T. The element- and shell-selective moments show a transition from the collinear ferrimagnet toward the forced ferromagnetic state via a canted phase, which is explained by a two-sublattice model.

When light is absorbed in solids, electrical conductivity is usually enhanced through generation of photodoped conductive carriers, known as photoconduction. Here we show UV-light absorption restrains photoconduction, but markedly enhances dielectric permittivity in a ceramic sample of $\mathrm{LaAl}{\mathrm{O}}_3$ with defects introduced deliberately by reduction synthesis. Using systematic dielectric measurements under photoirradiation combined with computational studies for defect formation energies, we explain this unconventional photoinduced phenomenon in terms of photoexcited dipoles: The photoexcited electrons are trapped in in-gap states introduced by oxygen vacancies whereas photoexcited holes are localized in a valence-band maximum. Thus the created electron-hole pair acts as an electric dipole to enhance the dielectric permittivity. This unprecedented photoelectric effect does not only provide an alternative functionality for dielectric materials, but also paves the way for next-generation photoelectronic devices.

Self-field imaging of current distribution in the $\mathrm{B}{\mathrm{a}}_{0.6}{\mathrm{K}}_{0.4}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ superconductor is used to study the effect of drive on the low-field vortex solid to liquid melting phase transformation. At low fields, the current-induced drive on the vortices aids in thermally destabilizing the low field glassy vortex (solid) phase, thereby shifting the low-field melting phase boundary. We show that the current-induced drive shifts solid-liquid boundaries and prepones the vortex melting phenomenon compared to the equilibrium situation. The analysis shows that, for currents above 50 mA, Joule heating effects shift the melting line whereas, below 50 mA, an effective temperature concept for the driven system viz., a drive-dependent shaking temperature, explains the shift. The observation of a transformation from inhomogeneous to homogeneous current flow in the sample at low fields as a function of the driving force is reconciled via an inverse dependence of the shaking temperature on vortex velocity.

We demonstrate the emergence of antichiral edge states in a Heisenberg ferromagnet with Dzyaloshinskii-Moriya interaction (DMI) on a honeycomb lattice with inequivalent sublattices, using both Schwinger-boson mean field theory and Holstein-Primakoff transformation. The DMI, which acts between atoms of the same species, differs in magnitude for the two sublattices, resulting in a shifting of the energy of the magnon bands (or bands in each spinon sector) in opposite directions at the two Dirac points. The chiral symmetry is broken and, for sufficiently strong asymmetry, the band shifting leads to antichiral edge states (in addition to the normal chiral edge states) in a rectangular strip where the magnon (or up or down spinon) current propagates in the same direction along the two edges. This is compensated by a counterpropagating bulk current that is enabled by the broken chiral symmetry. We analyze the resulting magnon (spinon) current profile across the width of the system in details and suggest realistic experimental probes to detect them. Finally, we discuss possible materials that can potentially exhibit such antichiral edge states.

We perform large-scale density-functional calculations using the real-space finite-difference scheme endorsed by the Gordon Bell prize in 2011 that reveal detailed atomic and electronic structures of atomic steps on silicon carbide (SiC) polar surfaces for the first time. The accurate structural optimization elucidates characteristic atomic reconstruction among the upper and lower edge atoms, which is peculiar to compound semiconductors having both covalent and ionic nature. The calculated formation energies of all the possible atomic steps lead us to unequivocally identify the abundant atomic steps on the Si-face SiC polar surfaces. The energetics thus obtained for the atomic steps provides a natural and persuasive microscopic reason for the difference in the step morphology observed experimentally, i.e., the meandering and straight step edges depending on the inclined direction on the polar vicinal SiC surfaces. Electron states caused by those atomic steps are also calculated, which assists in the identification of the atomic steps by future experiments.

In a recent study of the transport properties in the Aubry-André-Harper model [Phys. Rev. B 100, 195143 (2019)], the authors point out the failure of the Hellmann-Feynman theorem (HFT) in the case of degenerate states. They try to support such a statement from earlier papers that prove exactly the opposite. It appears that the application of the HFT to degenerate states has not been well understood. For this reason, in this Comment we illustrate the correct application of the HFT to the model just mentioned.

In a recent paper [Phys. Rev. B 99, 155124 (2019)], the spectrum of a regularized Coulomb charge was studied in gapped pseudospin-1 systems generated by an $\alpha -{\mathcal{T}}_3$ lattice. The electronic spectrum was studied as a function of the impurity strength $Z\alpha$. However, the results and conclusions on the behavior of the flatband states as a function of the impurity strength are incomplete. In this Comment, I argue that because of the dispersionless nature of the flatband, the states spread out under the influence of a charged impurity forming a continuous band of states. I support my arguments with explicit numerical calculations which show the emergence of a continuum of states.

${\mathrm{MnV}}_2{\mathrm{O}}_4$ in the spinel structure is known to exhibit coupled orbital and spin ordering and its Raman spectra show interesting anomalies in its low-temperature phase. With a goal to explain this behavior involving coupled spins and phonons, we determine here the spin-phonon couplings in ${\mathrm{MnV}}_2{\mathrm{O}}_4$ from a theoretical analysis of its phonon spectra and their dependence on spin ordering and electron correlations, obtained from first-principles density functional theoretical calculations. Using these in an analysis based on a Landau-like theory, we uncover the mechanism governing the Raman anomalies observed in its low-temperature phase.

Magnetic torque measurements have been performed to investigate the phase transitions of the metallic pyrochlore compound $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$, in which a spin-orbit (SO) interaction leads to unique multipole orders associated with an inversion symmetry breaking. We find that the magnetic torque signals with a fourfold symmetry (${\tau }_4\propto H^4$) as well as a twofold symmetry (${\tau }_2\propto H^2$) are significantly enhanced at low temperatures below a structural phase transition temperature (∼200 K). The analyses of the torque curve symmetries show that the ${\tau }_4$ term arises from an even-parity order parameter (OP) with the irreducible representation $E_{\mathrm{g}}$, whereas the ${\tau }_2$ term from an odd-parity OP with $E_{\mathrm{u}}$, $T_{1\mathrm{u}}$ or $T_{2\mathrm{u}}$. The parity mixing of the primary OPs shows a peculiar phase transition in the SO coupled $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$. The coexistence of the two OPs provides important insights into the origin of the multipole orders induced by the SO interaction.

Relativistic massless Weyl and Dirac fermions exhibit the isotropic and linear dispersion relations to preserve the Pioncaré symmetry, the most fundamental symmetry in high energy physics. In solids, the counterparts of the Pioncaré symmetry are crystallographic symmetries, and hence, it is natural to explore generalizations of Dirac and Weyl fermions compatible with their crystallographic symmetries and then the new physics coming along with them. Here, we study an important kind of generalization, namely massless Dirac fermions with higher-order dispersion relations protected by crystallographic symmetries in three-dimensional nonmagnetic systems. We perform a systematic search over all 230 space groups with time-reversal symmetry and spin-orbit coupling considered. We find that the order of dispersion cannot be higher than three, i.e., only the quadratic and cubic Dirac points (QDPs and CDPs) are possible. We discover previously unknown classes of higher-order Dirac points, including the chiral QDPs with Chern numbers of $\pm 4$ and the QDPs/CDPs without centrosymmetry. Especially the chiral QDPs feature four extensive surface Fermi arcs and four chiral Landau bands and hence leads to observable signatures in spectroscopic and transport experiments. We further show that these higher-order Dirac points represent parent phases for other exotic topological structures. Via controlled symmetry breaking, QDPs and CDPs can be transformed into double Weyl points, triple Weyl points, charge-2 Dirac points or Weyl loops. Using first-principles calculations, we also identify possible material candidates, including $\alpha \text{−}{\mathrm{TeO}}_2$ and ${\mathrm{YRu}}_4{\mathrm{B}}_4$, which realize the predicted nodal structures.

We calculate the lattice-driven in-plane $\left({\kappa }_{\parallel }\right)$ and out-of-plane $\left({\kappa }_{\perp }\right)$ thermal conductivities of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ bulk, and of films of different thicknesses, using the Boltzmann equation with phonon scattering times obtained from anharmonic third order density functional perturbation theory. We compare our results for the lattice component of the thermal conductivity with published data for ${\kappa }_{\parallel }$ on bulk samples and with our room-temperature thermoreflectance measurements of ${\kappa }_{\perp }$ on films of thickness ($L$) ranging from 18 nm to 191 nm, where the lattice component has been extracted via the Wiedemann-Franz law. Ab initio theoretical calculations on bulk samples, including an effective model to account for finite sample thickness and defect scattering, compare favorably both for the bulk case (from literature) and thin films (new measurements). In the low-$T$ limit the theoretical in-plane lattice thermal conductivity of bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ agrees with previous measurements by assuming the occurrence of intercalated ${\mathrm{Bi}}_2$ layer defects. The measured thermal conductivity monotonically decreases by reducing $L$; its value is ${\kappa }_{\perp }\approx 0.39\pm 0.08\mathrm{W}/\mathrm{m}\mathrm{K}$ for $L=18\mathrm{nm}$ and ${\kappa }_{\perp }=0.68\pm 0.14\mathrm{W}/\mathrm{m}\mathrm{K}$ for $L=191\mathrm{nm}$. We show that the decrease of room-temperature ${\kappa }_{\perp }$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films as a function of sample thickness can be explained by the incoherent scattering of out-of-plane momentum phonons with the film surface. Our work outlines the crucial role of sample thinning in reducing the out-of-plane thermal conductivity.

Whether there is a minimal conductivity in the $\alpha \text{−}{T}_3$ model or not is still in debate. By considering the evanescent modes contributing to the zero-energy conductivity, we showed that the conductivity of a large sample vanishes in the clean limit but it can rise up swiftly to the same magnitude of order of ${\sigma }_0=4e^2/h\pi$ when either a mass term of Dirac electrons or a weak disorder is introduced into the system. Both methods can render a nonzero minimal conductivity that is continuous upon the parameter $\alpha$. The mass term can cause the conductivity smaller than ${\sigma }_0$ depending on $\alpha$, while the static disorder can make it approach to ${\sigma }_0$ for $\alpha \to 0$ and be a little larger than ${\sigma }_0$ for $\alpha \to 1$ in a mesoscopic sample. It is also found that the recovered minimal conductivity is quite stable against a moderate disorder strength.