The power of the $GW$ formalism is, to a large extent, based on the explicit treatment of dynamical correlations in the self-energy. This dynamics is taken into account by calculating the energy dependence of the screened Coulomb interaction $W$, followed by a convolution with the Green's function $G$. In order to obtain the energy dependence of $W$ the prevalent methods are plasmon-pole models and numerical integration techniques. In this paper, we discuss an alternative approach, in which the energy-dependent screening is calculated by determining the resolvent, which is set up from a matrix representation of the dielectric function. On the one hand, this refrains from a numerical energy convolution and allows one to actually write down the energy dependence of $W$ explicitly (like in the plasmon-pole models). On the other hand, the method is at least as accurate as the numerical approaches due to its multipole nature. We discuss the theoretical setup in some detail, give insight into the computational aspects, and present results for Si, C, GaAs, and LiF. Finally, we argue that the analytic representability is not only useful for educational purposes but may also be of avail for the development of theory that goes beyond $GW$.

Bilayer graphene (BLG) offers a rich platform for broken-symmetry states stabilized by interactions. In this work, we study the phase diagram of BLG in the quantum Hall regime at filling factor $\nu =0$ within the Hartree-Fock approximation. In the simplest noninteracting situation, this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer polarized, canted antiferromagnetic, Kekule, a “spin-valley entangled” state, and a “broken U(1) $\times$ U(1)” phase. This last phase involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias $D$ and perpendicular magnetic field $B_{\perp }$ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed.

Phonons strongly influence the optical control of semiconductor quantum dots. When modeling the electron-phonon interaction in several theoretical approaches, the quantum dot geometry is approximated by a spherical structure, though typical self-assembled quantum dots are strongly lens-shaped. By explicitly comparing simulations of a spherical and a lens-shaped dot using a well-established correlation expansion approach, we show that, indeed, lens-shaped dots can be exactly mapped to a spherical geometry when studying the phonon influence on the electronic system. We also give a recipe to reproduce spectral densities from more involved dots by rather simple spherical models. On the other hand, breaking the spherical symmetry has a pronounced impact on the spatiotemporal properties of the phonon dynamics. As an example we show that for a lens-shaped quantum dot, the phonon emission is strongly concentrated along the direction of the smallest axis of the dot, which is important for the use of phonons for the communication between different dots.

We consider a dilute fluorinated graphene nanoribbon as a spin-active element. The fluorine adatoms introduce a local spin-orbit Rashba interaction that induces spin precession for electron passing by. The spin precession involving a single adatom is infinitesimal and accumulation of the spin-precession events with many electron passages under adatoms is necessary to accomplish a spin flip. In order to arrange for this accumulation, a circular $n\text{−}p$ junction can be introduced to the ribbon by, e.g., potential of the tip of an atomic force microscope. Alternatively, a fluorinated quantum ring can be attached to the ribbon. We demonstrate that the spin-flip probability can be increased in this manner by as much as three orders of magnitude. The Zeeman interaction introduces spin dependence of the Fermi wave vectors which changes the electron paths within the disordered system depending on the spin orientation. The effect destroys the accumulation of the spin-precession events in the $n\text{−}p$ junction. For side-attached quantum rings, however, for which the electron path is determined by the confinement within the channel, the accumulation of the spin precession is robust against the Zeeman spin splitting.

The ballistic point contact (BPC) with zigzag edges in graphene is a main candidate for a valley filter, in which the polarization of the valley degree of freedom can be selected by using a local gate voltage. Here, we propose to detect the valley filtering effect by Andreev reflection. By using both scattering matrix analysis and numerical simulation, we show that Andreev reflection is strongly suppressed as the incident electron and reflected hole propagate through different bands of BPC with opposite chirality. The conductance as a function of both the incident energy of electron and the local gate voltage at the BPC is obtained, with which the parametric region for a perfect valley filter and the direction of the valley polarization can be determined. As the length of the BPC increases, the conductance exhibits an oscillatory decay behavior, indicating a negative correlation between Andreev reflection and valley polarization.

The dependence of the anti-Stokes Raman intensity on the excitation laser energy in carbon nanotubes is studied by resonant Raman spectroscopy. The complete resonant anti-Stokes and Stokes Raman profiles of the high-energy longitudinal phonon ($G^{+}$) are obtained for (8,3), (7,5), (6,4), and (6,5) single chirality enriched samples. A high asymmetry between the intensity of the incoming and outgoing resonance is observed in the resonant Raman profiles. In contrast to Stokes scattering, anti-Stokes scattering is more intense at the outgoing resonance then at the incoming resonance. The resonance profiles are explained by a Raman process that includes the phonon-mediated interactions with the dark excitonic state. The chirality dependence of the Raman profiles is due to the variation in the exciton-phonon matrix elements, in agreement with tight-binding calculations. Based on the asymmetric Raman profiles we present the resonance factors for the Stokes/anti-Stokes ratios in carbon nanotubes.

We investigate the surface stress of solid-liquid diffusive interfaces at equilibrium using the phase field crystal model in two dimensions. To analytically study the surface energy dependence on elastic strains, we employ the amplitude equation formalism and recast the free energy functional in terms of strains and amplitudes of density waves to examine the intricate coupling between them. For planar interfaces, the surface stress and its anisotropy are explored using the phase field crystal model and its amplitude equations. The anisotropy of surface stress is shown to be closely related to the anisotropic density waves across the interface, and a stronger anisotropy is observed in the surface stress than that in the surface energy. In addition, to investigate the curvature effect, we examine resultant strain fields at equilibrium within nanoparticles of various sizes subjected to their surface stresses. The measured strains are compared with the classical sharp interface model. The discrepancy in strain fields arises as the size of nanoparticles becomes smaller which suggests a curvature dependent surface stress for diffusive interfaces. We construct the effective surface stress using the measured strain fields and classical linear elasticity theory. The overall magnitude of the effective surface stress decreases with the radius of the nanoparticle, and the effective surface stress is shown to be more isotropic for small nanoparticles.

A fully quantum-mechanical description of the precessional damping of a Pt/Co bilayer is presented in the framework of the Keldysh Green's function approach using ab initio electronic structure calculations. In contrast to previous calculations of classical Gilbert damping (${\alpha }_{\mathrm{GD}}$), we demonstrate that ${\alpha }_{\mathrm{GD}}$ in the quantum case does not diverge in the ballistic regime due to the finite size of the total spin $S$. In the limit of $S\to \infty$ we show that the formalism recovers the torque correlation expression for ${\alpha }_{\mathrm{GD}}$ which we decompose into spin-pumping and spin-orbital torque correlation contributions. The formalism is generalized to take into account a self-consistently determined dephasing mechanism which preserves the conservation laws and allows the investigation of the effect of disorder. The dependence of ${\alpha }_{\mathrm{GD}}$ on Pt thickness and disorder strength is calculated, and the spin-diffusion length of Pt and the spin mixing conductance of the bilayer are determined and compared with experiments.

We fabricated electric-field-effect transistor structures with a channel layer of an itinerant ferromagnet ${\mathrm{SrRuO}}_3$ (SRO) heterostructured with a cap layer of ${\mathrm{BaTiO}}_3$ and investigated the electric field effects on the anomalous Hall effect (AHE) in SRO. We show that by applying positive and negative gate voltages ($V_{\mathrm{G}}$), the anomalous Hall conductivity in the heterostructured SRO increases and decreases, respectively, regardless of its sign, while no change in the magnetic easy axis direction is observed. The results indicate that the observed $V_{\mathrm{G}}$-induced modulations of the AHE do not simply originate from changes in the magnetization and magnetic anisotropy and indicate that $V_{\mathrm{G}}$-induced changes in an integral of the Berry curvature over the filled electronic states play a key role in the observed electric field effects on the AHE in SRO. We also found that $V_{\mathrm{G}}$-induced modulations on the AHE are negligibly small for transistor structures with a SRO channel having no BTO cap layer. This implies that the cap-layer-induced modifications in the Ru-O-Ru bond angles in the channel affect the Berry phase, enhancing the electric field effects on the AHE in SRO.

Layered ${\mathrm{LnOBiS}}_2$ (where Ln represents a lanthanide element) compounds with Ln = La, Ce, Pr, Nd, and Yb can be rendered conducting and superconducting via two routes, substitution of F for O or the tetravalent ions Ti, Zr, Hf, and Th for trivalent Ln ions. Electrical resistivity measurements on nonfluorinated ${\mathrm{La}}_{0.80}{\mathrm{Ti}}_{0.20}{\mathrm{OBiS}}_2$ and ${\mathrm{La}}_{0.85}{\mathrm{Th}}_{0.15}{\mathrm{OBiS}}_2$ superconductors were performed between $\sim 1.5$ and 300 K and under pressure up to 2.4 GPa. For both compounds, the superconducting transition temperature $T_c$, which is $\sim 2.9\mathrm{K}$ at ambient pressure, gradually increases with pressure to 3.2–3.7 K at $\sim 1\mathrm{GPa}$, above which it is suppressed and the superconducting transitions become very broad. Measurements of the normal-state electrical resistivity of the two compounds reveal discontinuous changes in the resistivity as a function of pressure at $\sim 0.6\mathrm{GPa}$. Surprisingly, above 1.3 GPa, semiconductinglike behavior reappears in ${\mathrm{La}}_{0.80}{\mathrm{Ti}}_{0.20}{\mathrm{OBiS}}_2$. This paper reveals a new high-pressure phase of ${\mathrm{La}}_{1-x}{M}_x{\mathrm{OBiS}}_2$ containing the tetravalent ions $M=\mathrm{Ti}$, Th which does not favor superconductivity. In contrast, application of pressure to fluorinated ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ produces an abrupt tetragonal-monoclinic transition to a metallic phase with an enhanced $T_c$. These results demonstrate that the response of the normal and superconducting properties of ${\mathrm{LaOBiS}}_2$-based compounds depends strongly on the atomic site where the electron donor ions are substituted.

In this study, the superconducting gap symmetry of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$ is elucidated through specific heat measurements with one single crystal of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$. A clear jump is observed at 3.95 K in ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}\mathrm{BiSSe}$, suggesting bulk superconductivity. From specific heat measurements, $\mathrm{\Delta }{C}_{\mathrm{e}}/\gamma T_{\mathrm{c}}$ and $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{c}}$ are obtained as 2.31 and 4.5. These values indicate strong electron-phonon coupling superconductivity. The temperature $\left(T\right)$ and magnetic-field $\left(H\right)$ dependence of the electronic specific heat $C_{\mathrm{e}}(T,H)$ suggests that superconductivity is fully gapped. Our handmade system successfully elucidates superconducting gap symmetry of the ${\mathrm{BiS}}_2$-based compound with a small single crystal.

We address the superconducting singlet state of anisotropic Dirac fermions that disperse linearly in one direction and parabolically in the other. For systems that have uniaxial anisotropy, we show that the electromagnetic response to an external magnetic flux is extremely anisotropic near the quantum critical point of the superconducting order. In the quantum critical regime and above a critical magnetic field, we show that the superconductor may form an exotic smectic state, with a stripe pattern of flux domains.

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

Time-resolved magneto-optical imaging reveals that the dynamics of the helicity-dependent all-optical switching (HD-AOS) of Co/Pt ferromagnetic multilayers occurs on the time scales from nanoseconds to seconds. We find HD-AOS proceeds by two stages. First, for an optimized laser fluence, the ultrashort laser pulse demagnetizes the film to 25% of the initial magnetization. Subsequent laser pulses aids nucleation of small reversed domains. The observed nucleation is stochastic and independent of the helicity of laser light. At the second stage circularly polarized light breaks the degeneracy between the magnetic domains promoting a preferred direction of domain wall motion. One circular polarization results in a collapse of the reversed magnetic domains. The other polarization causes the growth of reversed magnetic domain from the nucleation sites, via deterministic displacement of the domain wall resulting in magnetization reversal. This mechanism is supported by further imaging studies of deterministic laser-induced displacement of the domain walls when excited by circularly polarized optical pulses.

We have studied the local structure of superconducting ${\mathrm{Ca}}_{10}{\mathrm{Pt}}_4{\mathrm{As}}_8{\left({\mathrm{Fe}}_2{\mathrm{As}}_2\right)}_5$ (Pt10418) and ${\mathrm{Ca}}_{10}{\mathrm{Ir}}_4{\mathrm{As}}_8{\left({\mathrm{Fe}}_2{\mathrm{As}}_2\right)}_5$ (Ir10418) iron arsenides, showing different transition temperatures $(T_c=38$ and 16 K, respectively), by polarized Fe $K$-edge extended x-ray absorption fine-structure measurements. Despite the similar average crystal structures, the local structures of the ${\mathrm{FeAs}}_4$ tetrahedra in the two compounds are found to be very different. The ${\mathrm{FeAs}}_4$ in Pt10418 is close to a regular tetrahedron, while it deviates largely in Ir10418. The Fe-Fe correlations in the two compounds are characterized by similar bond-length characteristics; however, the static disorder in Pt10418 is significantly lower than that in Ir10418. The results suggest that the optimized local structure and reduced disorder are the reasons for higher $T_c$ and well-defined electronic states in Pt10418 unlike Ir10418 showing the coexistence of glassy and normal electrons at the Fermi surface, and hence provide direct evidence of the local-structure-driven optimization of the electronic structure and superconductivity in iron arsenides.

We investigate the magnetic breakdown (MB) phenomena by means of the recently proposed magnetic-field-containing relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B 91, 075122 (2015)]. In the MFRTB method, the MB phenomena can be described as the electron hopping between adjacent semiclassical orbits. It is shown that a set of magnetic energy bands is generated by the MB in the cluster that corresponds to the semiclassical energy level. It is also found that magnetic energy bands originating from the MB and those originating from the semiclassical orbit lying on the constant energy surface are hybridized to each other. Such hybridization leads to various subclusters that correspond to energy states of the so-called forbidden orbits. Magnetic oscillations related to the MB occur when the subcluster changes from the occupied state to unoccupied one and vice versa.

Semiconductor quantum dots are potential building blocks for scalable qubit architectures. Efficient control over the exchange interaction and the possibility of coherently manipulating electron states are essential ingredients towards this goal. We studied experimentally the shuttling of electrons trapped in serial quantum dot arrays isolated from the reservoirs. The isolation hereby enables a high degree of control over the tunnel couplings between the quantum dots, while electrons can be transferred through the array by gate voltage variations. Model calculations are compared with our experimental results for double, triple, and quadruple quantum dot arrays. We are able to identify all transitions observed in our experiments, including cotunneling transitions between distant quantum dots. The shuttling of individual electrons between quantum dots along chosen paths is demonstrated.

We study electric transport along an integer quantum Hall edge where the proximity effect is induced due to a coupling to a superconductor. Such an edge exhibits two Majorana-Weyl fermions with different group velocities set by the induced superconducting pairing. We show that this structure of the spectrum results in interference fringes that can be observed in both the two-terminal conductance and shot noise. We develop a complete analytical theory of such fringes for an arbitrary smooth profile of the induced pairing.