We study the symmetry-broken phases in two- and three-orbital Hubbard models with lifted orbital degeneracy using dynamical mean-field theory. On the technical level, we explain how symmetry relations can be exploited to measure the four-point correlation functions needed for the calculation of the lattice susceptibilities. In the half-filled two-orbital model with crystal-field splitting, we find an instability of the metallic phase to spin-orbital order with neither spin nor orbital moment. This ordered phase is shown to be related to the recently discovered fluctuating-moment induced spin-triplet superconducting state in the orbitally degenerate model with shifted chemical potential. In the three-orbital case, we consider the effect of a crystal-field splitting on the spin-triplet superconducting state in the model with positive Hund coupling, and the spin-singlet superconducting state in the case of negative Hund coupling. It is demonstrated that for certain crystal-field splittings the higher energy orbitals instead of the lower ones are relevant for superconductivity, and that $T_c$ can be slightly enhanced by the crystal-field effect. We comment on the implications of our results for the superconductivity in strontium ruthenates, and for the recently reported light-enhanced superconducting state in alkali-metal-doped fullerides.

We discuss the calculation of the double occupancy using dynamical mean-field theory in finite dimensions. The double occupancy can be determined from the susceptibility of the auxiliary impurity model or from the lattice susceptibility. The former method typically overestimates, whereas the latter underestimates the double occupancy. We illustrate this for the square-lattice Hubbard model. We propose an approach for which both methods lead to identical results by construction and which resolves this ambiguity. This self-consistent dual boson scheme results in a double occupancy that is numerically close to benchmarks available in the literature.

Transport and torque magnetometry measurements are performed at high magnetic fields and low temperatures in a series of p-type (Ca-doped) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals. The angular dependence of the Shubnikov-de Haas and de Haas-van Alphen quantum oscillations enables us to determine the Fermi surface of the bulk valence band states as a function of the carrier density. At low density, the angular dependence exhibits a downturn in the oscillations frequency between $0^{\circ }$ and ${90}^{\circ }$, reflecting a bag-shaped hole Fermi surface. The detection of a single frequency for all tilt angles rules out the existence of a Fermi surface with different extremal cross sections down to 24 meV. There is therefore no signature of a camelback in the valence band of our bulk samples, in accordance with the direct band gap predicted by $GW$ calculations.

The spin Hall effect creates a spin current in response to a charge current in a material that has strong spin-orbit coupling. The size of the spin Hall effect in many materials is disputed, requiring independent measurements of the effect. We develop a novel mechanical method to measure the size of the spin Hall effect, relying on the equivalence between spin and angular momentum. The spin current carries angular momentum, so the flow of angular momentum will result in a mechanical torque on the material. We determine the size and geometry of this torque and demonstrate that it can be measured using a nanomechanical device. Our results show that measurement of the spin Hall effect in this manner is possible and also opens possibilities for actuating nanomechanical systems with spin currents.

A superconducting wire described by a $p$-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.

We present a time-resolved terahertz spectroscopic study of the half-metallic ferromagnet ${\mathrm{CrO}}_2$. The ultrafast conductivity dynamics excited by an optical pump displays very short (several picoseconds) and a very long (several hundred picoseconds) characteristic time scales. We attribute the former to the electron-phonon relaxation and the latter to the spin-lattice relaxation. We use this distinction to quantify the relative contribution of the scattering by spin fluctuations to the resistivity of ${\mathrm{CrO}}_2$: We find that they contribute less than one half of all scattering events below room temperature. This contribution rises to $\sim 70\%$ as the temperature approaches $T_C=390$ K. The small effect of spin fluctuations on the resistivity is unexpected in light of the proposed double-exchange nature of the electronic and magnetic properties of ${\mathrm{CrO}}_2$.

The dynamical cluster approximation (DCA) and its ${\mathrm{DCA}}^{+}$ extension use coarse-graining of the momentum space to reduce the complexity of quantum many-body problems, thereby mapping the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. While it gives a more localized self-energy for a given cluster size, we show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which converge to the results obtained from the standard coarse-graining with increasing cluster size. Most importantly, the new coarse-graining reduces the severity of the fermionic sign problem of the underlying quantum Monte Carlo cluster solver and thus allows for calculations on larger clusters. This enables the treatment of correlations longer ranged than those accessible with the standard coarse-graining and thus can allow for the evaluation of the exact infinite cluster size result via finite size scaling. As a demonstration, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the extended ${\mathrm{DCA}}^{+}$ algorithm permits the determination of the superconducting $T_c$ on cluster sizes for which the results can be fit with a Kosterlitz-Thouless scaling law.

We present detailed theoretical predictions on the enhancement of the thermoelectric figure of merit by minority carrier blocking with heterostructure barriers in bulk narrow-band-gap semiconductors. Bipolar carrier transport, which is often significant in a narrow-band-gap material, is detrimental to the thermoelectric energy conversion efficiency as it suppresses the Seebeck coefficient and increases the thermal conductivity. When the minority carriers are selectively prevented from participating in conduction while the transport of majority carriers is relatively unaffected by one-sided heterobarriers, the thermoelectric figure of merit can be drastically enhanced. Thermoelectric transport properties such as Seebeck coefficient, electrical conductivity, and electronic thermal conductivity including the bipolar term are calculated with and without the barriers based on the near-equilibrium Boltzmann transport equations under the relaxation time approximation to investigate the effects of minority carrier barriers on the thermoelectric figure of merit. For this, we provide details of carrier transport modeling and fitting results of experimental data for three important material systems, $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$-based alloys, $\mathrm{M}{\mathrm{g}}_2\mathrm{S}{\mathrm{i}}_{1-x}\mathrm{S}{\mathrm{n}}_x$, and $\mathrm{S}{\mathrm{i}}_{1-x}\mathrm{G}{\mathrm{e}}_x$, that represent, respectively, near-room-temperature (300 K–500 K), midtemperature (600 K–900 K), and high-temperature ($>1000\mathrm{K}$) applications. Theoretical maximum enhancement of thermoelectric figure of merit that can be achieved by minority carrier blocking is quantified and discussed for each of these semiconductors.

We report on the structural and electronic properties of a single bismuth layer intercalated underneath a graphene layer grown on an Ir(111) single crystal. Scanning tunneling microscopy (STM) reveals a hexagonal surface structure and a dislocation network upon Bi intercalation, which we attribute to a $\sqrt{3}\times \sqrt{3}R{30}^{\circ }$ Bi structure on the underlying Ir(111) surface. Ab initio calculations show that this Bi structure is the most energetically favorable and illustrate that STM measurements are most sensitive to C atoms in close proximity to intercalated Bi atoms. Additionally, Bi intercalation induces a band gap ($E_{\mathrm{g}}=0.42$ eV) at the Dirac point of graphene and an overall $n$ doping $\left(\sim 0.39\mathrm{eV}\right)$ as seen in angular-resolved photoemission spectroscopy. We attribute the emergence of the band gap to the dislocation network which forms favorably along certain parts of the moiré structure induced by the graphene/Ir(111) interface.

We have used resonant inelastic x-ray scattering (RIXS) and dynamical susceptibility calculations to study the magnetic excitations in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ ($x=0$, 0.03, and 0.08). Despite a relatively low ordered magnetic moment, collective magnetic modes are observed in parent compounds ($x=0$) and persist in optimally ($x=0.03$) and overdoped ($x=0.08$) samples. Their magnetic bandwidths are unaffected by doping within the range investigated. High-energy magnetic excitations in iron pnictides are robust against doping and present irrespectively of the ordered magnetic moment. Nevertheless, Co doping slightly reduces the overall magnetic spectral weight, differently from previous studies on hole-doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, where it was observed constant. Finally, we demonstrate that the doping evolution of magnetic modes is different for the dopants being inside or outside the Fe-As layer.

The recently discovered ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ superconductor provides an alternative and ideal material base for investigating possible topological superconductivity. Here, we report that in ${\mathrm{Sr}}_{0.065}{\mathrm{Bi}}_2{\mathrm{Se}}_3$, the ambient superconducting phase is gradually depressed upon the application of external pressure. At high pressure, a second superconducting phase emerges at above 6 GPa, with a maximum $T_c$ value of $\sim 8.3$ K. The joint investigations of the high-pressure synchrotron x-ray diffraction and electrical transport properties reveal that the reemergence of superconductivity in ${\mathrm{Sr}}_{0.065}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ is closely related to the structural phase transition from an ambient rhombohedral phase to a high-pressure monoclinic phase around 6 GPa, and further to another high-pressure tetragonal phase above 25 GPa.

In this paper, we study an $\mathrm{su}\left(m\right)$-invariant open version of the Haldane-Shastry spin chain whose ground state can be obtained from the chiral correlator of the $c=m-1$ free boson boundary conformal field theory. We show that this model is integrable for a suitable choice of the chain sites depending on the roots of the Jacobi polynomial $P_N^{\beta -1,{\beta }^{\prime }-1}$, where $N$ is the number of sites and $\beta ,{\beta }^{\prime }$ are two positive parameters. We also compute in closed form the first few nontrivial conserved charges arising from the twisted Yangian invariance of the model. We evaluate the chain's partition function, determine the ground-state energy, and deduce a complete description of the spectrum in terms of Haldane's motifs and a related classical vertex model. In particular, this description entails that the chain's level density is normally distributed in the thermodynamic limit. We also analyze the spectrum's degeneracy, proving that it is much higher than for a typical Yangian-invariant model.

Narrow-band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy-fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs). Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping. In particular, we show how the imaginary gap, which serves as a proxy for band flatness, can be optimized by appealing to Rouché's theorem, a familiar result from complex analysis. This leads to an explicit construction which we illustrate through its application to two-band FCI models with nontrivial topology (i.e., nonzero Chern numbers). We show how the imaginary-gap perspective leads to an elegant geometric picture of how topological properties can obstruct band flatness in systems with finite-range hopping.

A complex few-layer $\mathrm{MoS}{\mathrm{e}}_2$/graphene oxide (GO) heterostructure with strong interlayer coupling was prepared by a facile hydrothermal method. In this strongly coupled heterostructure, we demonstrate a giant enhancement of two-photon absorption that is in stark contrast to the reverse saturable absorption of a weakly coupled $\mathrm{MoS}{\mathrm{e}}_2$/GO heterostructure and saturable absorption of isolated $\mathrm{MoS}{\mathrm{e}}_2$. Spectroscopic evidence of our study indicates that the optical signatures of isolated $\mathrm{MoS}{\mathrm{e}}_2$ and GO domains are significantly modified in the heterostructure, displaying a direct coupling of both domains. Furthermore, our first-principles calculations indicate that strong interlayer coupling between the layers dramatically suppresses the $\mathrm{MoS}{\mathrm{e}}_2$ excitonic bands. We envision that our findings provide a powerful tool to explore different optical functionalities as a function of interlayer coupling, which may be essential for the development of device technologies.

We propose an interferometry in graphene's reciprocal space without a magnetic field, employing strong ultrafast circularly polarized optical pulses. The reciprocal space interferograms contain information on the electronic spectra and topological properties of graphene and on the waveform and circular polarization of the excitation optical pulses. These can be measured using angle-resolved photoemission spectroscopy (ARPES) with attosecond ultraviolet pulses. The predicted effects provide unique opportunities in fundamental studies of two-dimensional topological materials and in applications to future petahertz light-wave-driven electronics.

Photoluminescence excitation measurements have been performed on single, unstrained oxide-embedded Si nanocrystals. Having overcome the challenge of detecting weak emission, we observe four broad peaks in the absorption curve above the optically emitting state. Atomistic calculations of the Si nanocrystal energy levels agree well with the experimental results and allow identification of some of the observed transitions. An analysis of their physical nature reveals that they largely retain the indirect band-gap structure of the bulk material with some intermixing of direct band-gap character at higher energies.

By recording low-noise energy-dispersive x-ray spectroscopy maps from crystalline specimens using aberration-corrected scanning transmission electron microscopy, it is possible to probe core-level electron orbitals in real space. Both the $1s$ and $2p$ orbitals of Sr and Ti atoms in $\mathrm{SrTi}{\mathrm{O}}_3$ are probed, and their projected excitation potentials are determined. This paper also demonstrates experimental measurement of the electronic excitation impact parameter and the delocalization of an excitation due to Coulombic beam-orbital interaction.

Recent applications of quantum Monte Carlo (QMC) technique to Fe-based superconductors opened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper [arXiv:1512.08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. The type of the orbital order found in QMC is different from the one found in earlier itinerant analysis. We report the results of our calculations within the itinerant scenario and argue that they are in perfect agreement with QMC.