We study the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of fractional quantum Hall liquids, using numerical diagonalization of finite-size systems. The filling factors studied include 1/3, 5/2, 2/5, and 2/3. In the absence of Zeeman splitting and an edge, the first two have spin fully polarized ground states, while the latter two have singlet ground states. We find that with few exceptions, edge instabilities of these systems are triggered by softening of edge spin waves for Abelian fractional quantum Hall liquids ($1/3$, $2/5$, and $2/3$ liquids), and are triggered by softening of edge magnetoplasmon excitations for non-Abelian $5/2$ liquid at the smoother confinement side. Phase diagrams are obtained in the accessible parameter spaces.

We present a theoretical study of the relationships between intermolecular vibrations and anisotropic transport properties of pentacene and rubrene single-crystal organic semiconductors. Using our wave-packet approach based on the Kubo formula beyond the effective-mass approximation with the assumption of an isotropic momentum-relaxation time, we find that the intermolecular vibrations induce a strong anisotropic momentum-relaxation time but moderate the anisotropy of carrier mobility much more than that of the effective mass. This clarifies the mechanism behind the deviation of the anisotropic ratio of mobility from that of effective mass observed in angle-resolved photoelectron spectroscopy experiments.

Excitonic states and the line shape of optical transitions in coupled quantum dots (quantum dot molecules) are studied theoretically. For a pair of electrically tunable, vertically aligned quantum dots we investigate the coupling between spatially direct and indirect excitons caused by different mechanisms such as tunnel coupling, Coulomb coupling, coupling due to the spin-orbit interaction, and coupling induced by a structural asymmetry. The peculiarities of the different types of couplings are reflected in the appearance of either crossings or avoided crossings between direct and indirect excitons, the latter ones being directly visible in the absorption spectrum. We analyze the influence of the phonon environment on the spectrum by calculating the line shape of the various optical transitions including contributions due to both pure dephasing and phonon-induced transitions between different exciton states. The linewidth enhancement due to phonon-induced transitions is particularly pronounced in the region of an anticrossing and it strongly depends on the energy splitting between the two exciton branches.

We investigate spontaneous emission from excitons beyond the point source dipole approximation and show how the symmetry of the exciton wave function plays a crucial role. We find that for spherically symmetric wave functions, the Purcell effect is independent of the wave function size and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations.

We study the out-of-equilibrium transport in a Tomonaga-Luttinger liquid containing a weak or a tunneling barrier coupled to an arbitrary electromagnetic environment. This applies as well to a coherent one-channel noninteracting conductor with a transmission coefficient close to one or to zero. We derive formal expressions for the current and finite-frequency (FF) noise at arbitrary voltages, temperatures, and frequency-dependent impedance $Z\left(\omega \right)$ in the regimes of weak and strong backscattering. We show that these two regimes are no longer related by duality at finite frequency. We then carry explicit computations of the nonlinear conductance and FF noise when $Z\left(\omega \right)$ describes a harmonic oscillator such as an $\mathit{LC}$ circuit or a cavity.

We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector $\mathbf{q}$ around the $\Gamma$ ($\mathbf{q}=0$) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in $\mathbf{q}$ we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of $\Gamma$. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids $\mathbf{23}$, 447 (1962)] to higher orders in $\mathbf{q}$. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.

We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and lattice contributions. We introduce practical supercell-based methods for calculating the flexoelectric coefficients from first principles, and demonstrate them by computing the coefficients for a variety of cubic insulating materials including C, Si, MgO, NaCl, CsCl, BaZrO${}_3$, BaTiO${}_3$, PbTiO${}_3$, and SrTiO${}_3$.

In this study, we present the phase relations, crystal structure, and physical properties of the MgZn${}_2$-type Laves phases in the Mn-Cu-Si and Mn-Ni-Si systems. Our results evidence that the homogeneous regime of the Laves phase in the Mn-Cu-Si system at $800{}^{\circ }\mathrm{C}$ ranges from 32.5 to 36.7 at.% Mn and from 11.5 to 13.5 at.% Si, indicating the Laves phase in this system having an ideal stoichiometry AB${}_2$, inconsistent with previous reports. For structural and physical property investigations, two alloys with compositions MnCu${}_{1.65}$Si${}_{0.35}$ and MnNi${}_{1.25}$Si${}_{0.75}$ are considered. In both alloys, Mn atoms are preferably situated at the $4f$ site and Cu(Ni) and Si share the $2a$ and $6h$ sites. Both are antiferromagnets with $T_N\approx 800$ K for MnCu${}_{1.65}$Si${}_{0.35}$ and $T_N\approx 630$ K for MnNi${}_{1.25}$Si${}_{0.75}$. Rietveld refinements of the room-temperature neutron diffraction data demonstrate that in both cases only the Mn atoms carry magnetic moments, which are aligned antiferromagnetically along the $c$ axis. The magnetic moments at room temperature are $2.7{\mu }_B$/Mn for MnCu${}_{1.65}$Si${}_{0.35}$ and $2.9{\mu }_B$/Mn for MnNi${}_{1.25}$Si${}_{0.75}$, respectively. The magnetic properties are confirmed by transport, magnetization, NMR measurements, and band-structure calculations.

We discuss mapping the Bloch-Redfield master equation to Lindblad form and then unraveling the resulting evolution into a stochastic Schrödinger equation according to the quantum-jump method. We give two approximations under which this mapping is valid. This approach enables us to study solid-state systems of much larger sizes than is possible with the standard Bloch-Redfield master equation, while still providing a systematic method for obtaining the jump operators and corresponding rates. We also show how the stochastic unraveling of the Bloch-Redfield equations becomes the kinetic Monte Carlo algorithm in the secular approximation when the system-bath-coupling operators are given by tunneling operators between system eigenstates. The stochastic unraveling is compared to the conventional Bloch-Redfield approach with the superconducting single-electron transistor (SSET) as an example.

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with $2/3$, 1, and $4/3$ filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional $XY$ university, with dynamical exponent $z=1$ and correlation exponent $\nu =0.67155$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.

We investigate the angular dependence of the magnetoresistance of thin (<1 nm), metallic SrTiO${}_3$ quantum wells epitaxially embedded in insulating, ferrimagnetic GdTiO${}_3$ and insulating, antiferromagnetic SmTiO${}_3$, respectively. The SrTiO${}_3$ quantum wells contain a high density of mobile electrons (∼$7\times {10}^{14}{\mathrm{cm}}^{-2}$). We show that the longitudinal and transverse magnetoresistance in the structures with GdTiO${}_3$ are consistent with anisotropic magnetoresistance, and thus indicative of induced ferromagnetism in the SrTiO${}_3$, rather than a nonequilibrium proximity effect. Comparison with the structures with antiferromagnetic SmTiO${}_3$ shows that the properties of thin SrTiO${}_3$ quantum wells can be tuned to obtain magnetic states that do not exist in the bulk material.

Recently, a golden colored, dense polymorph of titanium sesquioxide, Ti${}_2$O${}_3$ with a Th${}_2$S${}_3$-type structure, has been synthesized at high-pressure high-temperature conditions. In this paper, we present results of investigations of structural, optical, and electronic transport properties of this unusual golden polymorph of Ti${}_2$O${}_3$ under high pressure. Several experimental techniques were used, including x-ray diffraction studies using synchrotron radiation, Raman spectroscopy, electrical resistivity, and thermoelectric power. The structural studies showed that the Th${}_2$S${}_3$-type lattice is conserved under pressure, while it is subjected to an isostructural phase transition with a ∼0.7$\%$ volume drop at 38.5 GPa. We speculated that this transition could be driven by the $s\to d$ electron transfer in the Ti atoms. For the Th${}_2$S${}_3$-type Ti${}_2$O${}_3$, we have established a bulk modulus value, $B_0$ $=$ 258.3 GPa at $B_0^{\prime }$ $=$ 4.1. A full profile analysis of the diffraction patterns allowed us to discover anomalies in the compression behavior of the Th${}_2$S${}_3$-type structure. The bond valence sums method suggested that at ambient conditions the Ti cations have predominantly Ti${}^{3+}$ oxidation state, but applied pressure stimulates a partial charge disproportionation between the Ti1 and Ti2 sites achieving the maximal effect—reduction of the Ti1 cations to ∼Ti${}^{2.5+}$ and oxidation of the Ti2 ones to ∼Ti${}^{3.5+}$ near 14 GPa. Pressure evolution of Raman spectra across the above crossovers showed distinct changes corroborating the above findings. The high-pressure electronic transport studies confirmed that the Th${}_2$S${}_3$-type Ti${}_2$O${}_3$ remains semiconducting up to 21 GPa at ambient and low temperatures down to 4.2 K. These studies found additional features, e.g., in the activation energy curve near 7 GPa, that is accompanied by inversion of the dominant conductivity type from electron to hole. The intriguing high-pressure behavior of Ti${}_2$O${}_3$ with the Th${}_2$S${}_3$-type structure can contribute to better understanding of high-pressure properties of transition-metal sesquioxides.

Neutron Compton scattering experiments on crystalline lithium hydride and deuteride are presented and compared with existing experimental data and first-principles predictions. With currently available instrumentation, these measurements demonstrate sufficient mass selectivity for studies of nuclear-momentum distributions of protons, deuterons, and lithium using forward and backscattering geometries. In both materials, spectral discrimination of lithium-recoil features is highest in backscattering geometry, although mass isolation is also possible in the forward-scattering direction. These results evince the possibility of performing simultaneous mass-selective neutron spectroscopic studies for nuclei with $m>4$ amu. We also provide an in-depth analysis and assessment of departures from the harmonic and impulse approximations as described by the celebrated Sears expansion of the dynamic structure factor, as well as how these can manifest themselves in the experimental data. We close by outlining the potential of our experimental strategy for mass-selective spectroscopic studies of materials containing protons and other light nuclides.

We investigate the properties of antiferromagnetic spin-$S$ ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes $2S$ times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to $2S$ in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin $2S$ impurity.

Inspired by the models of Rebei and Parker [Phys. Rev. B 67, 104434 (2003)] and [Rebei, Hitchon and Parker Phys. Rev. B 72, 064408 (2005)], we study a physical model which describes the behavior of magnetic moments in a ferromagnet. The magnetic moments are associated to $3d$ electrons which interact with conduction-band electrons and with phonons. We study each interaction separately and then collect the results, assuming that the electron-phonon interaction can be neglected. For the case of the spin-phonon interaction, we study the derivation of the equations of motion for the classical spin vector and find that the correct behavior, as given by the Brown equation for the spin vector and the Bloch equation, using the results obtained by Garanin [Phys. Rev. B 55, 3050 (1997)] for the average over fluctuations of the spin vector, can be obtained in the high-temperature limit. At finite temperatures, we show that the Markovian approximation for the fluctuations is not correct for time scales below some thermal correlation time ${\tau }_{\text{th}}$. For the case of electrons we work a perturbative expansion of the Feynman-Vernon influence functional. We find the expression for the random field correlation function which exhibits the properties of the electron bath; namely, we observe Friedel oscillations at small temperatures. The composite model (as well as the individual models) is shown to satisfy a fluctuation-dissipation theorem for all temperature regimes if the behavior of the coupling constants of the phonon-spin interaction remain unchanged with the temperature. The equations of motion are derived.

On the basis of single-crystal x-ray diffraction we show that TiPO${}_4$ undergoes a spin-Peierls distortion below 74.5(5) K, with a dimerization of the Ti chains along the $\mathbf{c}$ axis. Between 74.5(5) and 111.6(3) K, TiPO${}_4$ develops an incommensurate (IC) phase with temperature-dependent $\mathbf{q}$ vector (${\sigma }_1$,0,0). Density functional calculations strongly suggest that the IC phase results from a frustration of the lock-in spin-Peierls transition due to the competition of three energetically almost degenerate crystal structures and elastic coupling of the Ti chains via the bridging PO${}_4$ units. The phase transition into the IC phase is of second order, but the lock-in transition into the spin-Peierls distortion below 74.5 K is of weak first order in nature.

CeCoIn${}_5$, which has a superconducting transition temperature of 2.3 K, provides an excellent opportunity to study the interplay of superconductivity and magnetism near an antiferromagnetic quantum critical point. Previous studies have explored the effects of electron doping, magnetic field, and positive pressure on this system. To determine the effect of hole doping, we have grown single crystals of Ce(Co${}_{1-x}$Ru${}_x$)In${}_5$ in indium flux. The crystal structure of these Ru-doped samples was identified by powder XRD as the HoCoGa${}_5$-type. We find that the coherence temperature $T^{*}$ and the superconducting transition temperature $T_c$ decrease monotonically with increasing Ru content. Unlike the case of hole doping in CeCo(In${}_{5-x}$Cd${}_x$) alloys in which antiferromagnetism starts to emerge at $x=0.025$, we find no magnetic transition at our maximal nominal doping of $x_{\mathrm{nom}}=0.5$, where $T_c$ is suppressed to 1.5 K. We discuss possible reasons for this difference between these two cases of hole doping.

Using various band-gap materials and tightly focused femtosecond laser pulses with wavelengths in the range 1200–2200 nm, we show that nonlinear absorption is independent of the wavelength except for narrow gap semiconductor materials. This observation corresponds to a transition between multiphoton ionization and tunnel ionization for an adiabaticity parameter of about 3, which compares favorably with Keldysh predictions. Our results indicate that long wavelengths must open up an alternative to pulse shortening for ultraprecision optical breakdown in dielectrics.

We apply a recently introduced hybridization flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard model on the Bethe lattice in infinite dimensions we calculate the local two-particle vertex for the metallic and the insulating phase. Then we go to a two-site cluster DMFT scheme for the two-dimensional Hubbard model that includes short-range antiferromagnetic fluctuations and obtain the local and nonlocal two-particle vertex functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.