Various lattice geometries and boundary conditions are used to investigate valence-bond-solid (VBS) ordering in the ground state of an $S=1/2$ square-lattice quantum spin model—the $J$-$Q$ model, in which four- or six-spin interactions $Q$ are added to the standard Heisenberg exchange $J$. Ground-state results for finite systems (with up to thousands of spins) are obtained using an unbiased projector quantum Monte Carlo method. It is found that great care has to be taken when extrapolating the order parameter to infinite lattice size, in particular, in cylinder geometry. Even though strong VBS order exists in two dimensions, and is established clearly with increasing system size on $L\times L$ lattices (or $L_x\times L_y$ lattices with a fixed aspect ratio $L_x/L_y$ of order 1), only short-range VBS correlations are observed on long cylinders (when $L_x\to \infty$ at fixed $L_y$). The correlation length increases with the cylinder width, until long-range order sets in at a “critical” width. This width is very large even when the 2D order is relatively strong. For example, for a system in which the order parameter is $70\%$ of the largest possible value, $L_y=8$ is required for ordering. Extrapolations of the VBS order parameter based on correlation functions (the square of the order parameter) for small $L\times L$ lattices can also be misleading. For a $20\%$-ordered system, results for $L$ up to $\approx$20 appear to extrapolate clearly to a vanishing order parameter, while for larger lattices the scaling behavior crosses over and extrapolates to a nonzero value (with exponentially small finite-size corrections). The VBS order parameter also exhibits interesting edge effects related the known emergent U(1) symmetry close to a “deconfined” critical point, which, if not considered properly, can lead to wrong conclusions for the thermodynamic limit. The observed finite-size behavior for small $L\times L$ lattices and long cylinders is very similar to that predicted for a $Z_2$ spin liquid. The results therefore raise concerns about recent numerical work claiming $Z_2$ spin-liquid ground states in 2D frustrated quantum spin systems, in particular, the Heisenberg model with nearest and next-nearest-neighbor couplings. Based on the results presented so far, a VBS state in this system cannot be ruled out.

Recent theoretical progress has identified a class of time-reversal invariant topological superconductors, called helical superconductors. While candidate materials exist, to the best of our knowledge, no such system has been observed yet in experiments. Existing proposals for the detection of this phase provide only indirect and partial information, and often are quite difficult to implement experimentally. Here we show that the presence of this phase can be directly probed through the easily measurable nonlocal charge conductance. Focusing on a ring geometry, we suggest two experiments that provide robust qualitative signatures that unambiguously reveal the helical superconductor phase.

We report the effect of Sn doping on the transport properties of the topological insulator Bi${}_2$Te${}_2$Se studied in a series of Bi${}_{2-x}$Sn${}_x$Te${}_2$Se crystals with 0 $\le$ $x$ $\le$ 0.02. The undoped stoichiometric compound ($x$ $=$ 0) shows an $n$-type metallic behavior with its Fermi level pinned to the conduction band. In the doped compound, it is found that Sn acts as an acceptor and leads to a downshift of the Fermi level. For $x$ $\ge$ 0.004, the Fermi level is lowered into the bulk forbidden gap and the crystals present a resistivity considerably larger than 1 $\Omega$ cm at low temperatures. In those crystals, the high-temperature transport properties are essentially governed by thermally activated carriers whose activation energy is 95–125 meV, which probably signifies the formation of a Sn-related impurity band. In addition, the surface conductance directly obtained from the Shubnikov–de Haas oscillations indicates that a surface-dominated transport can be achieved in samples with several $\mu$m thickness.

We report growth of Sr${}_2$CrReO${}_6$ epitaxial films with 99$\%$ Cr/Re ordering and crystalline perfection comparable to those of high-quality semiconductor films. The Sr${}_2$CrReO${}_6$ films show a Curie temperature of 508 K and a saturation magnetization of 1.29 ${\mu }_{\mathrm{B}}$ per formula unit, which confirms the presence of strong spin-orbit coupling. Unexpectedly, electrical transport and optical absorption measurements indicate that Sr${}_2$CrReO${}_6$ is a semiconductor with a band gap of 0.21 eV. The unique combination of high temperature ferrimagnetism and semiconductivity is both scientifically interesting and highly attractive for applications.

It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity coupled to a bulk superconductor. The wires should have strong spin-orbit coupling with appropriate symmetry, and their electrons should be partially polarized by a strong Zeeman field. Then, if the Fermi level is in an appropriate range, the wire can be in a topological superconducting phase, with Majorana states that occur at wire ends and at $Y$ junctions, where three topological superconductor segments may be joined. Here we generalize these ideas to consider a three-dimensional network. The positions of Majorana states can be manipulated, and their non-Abelian properties made visible, by using external gates to selectively deplete portions of the network or by physically connecting and redividing wire segments. Majorana states can also be manipulated by reorientations of the Zeeman field on a wire segment, by physically rotating the wire about almost any axis, or by evolution of the phase of the order parameter in the proximity-coupled superconductor. We show how to keep track of sign changes in the zero-energy Hilbert space during adiabatic manipulations by monitoring the evolution of each Majorana state separately, rather than keeping track of the braiding of all possible pairs. This has conceptual advantages in the case of a three-dimensional network, and may be computationally useful even in two dimensions, if large numbers of Majorana sites are involved.

We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely related particle entanglement spectrum and carry out the Schmidt decomposition of the Laughlin state analytically at large size.

We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard $U$ is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.

We present a comprehensive study of electron spin decoherence in bulk germanium. As a first cornerstone, the effective $g$ tensor of $L$-valley electrons in germanium is deduced from time-domain magneto-optical experiments. The decay of the ensemble spin polarization is then found to be closely related to intervalley scattering. In particular, the angular and temperature dependences of the experiment are well described in a model including Elliott-Yafet-type spin-flip processes as well as dephasing due to scattering between valleys exhibiting different effective $g$ factors.

We present a systematic study of the electronic structure of several prototypical correlated transition-metal oxides: VO${}_2$, V${}_2$O${}_3$, Ti${}_2$O${}_3$, LaTiO${}_3$, and YTiO${}_3$. In all these materials, in the low-temperature insulating phases the local and semilocal density approximations (LDA and GGA, respectively) of density-functional theory yield a metallic Kohn-Sham band structure. Here we show that, without invoking strong-correlation effects, the role of nonlocal exchange is essential to cure the LDA/GGA delocalization error and provide a band-structure description of the electronic properties in qualitative agreement with the experimental photoemission results. To this end, we make use of hybrid functionals that mix a portion of nonlocal Fock exchange with the local LDA exchange-correlation potential. Finally, we discuss the advantages and the shortcomings of using hybrid functionals for correlated transition-metal oxides.

We discuss the effects of the spin-orbit interaction on heavy-atom organic magnets with specific reference to a series of isostructural sulfur- and selenium-based radical ferromagnets of tetragonal space group $P\overline{4}{2}_{1}m$. By using a perturbative approach, we show the spin-orbit effects lead to a pairwise anisotropic exchange interaction between neighboring radicals that provides an easy magnetic axis running parallel to the $c$-axis. Estimates of the magnitude of this magnetic anisotropy explain the significant increase in the coercive fields by virtue of selenium incorporation. Complementing this theoretical discussion are the results of ferromagnetic resonance studies, which provide an experimental verification of both the magnitude and symmetry of the spin-orbit terms. Taken as a whole, the results underscore the importance of heavy atoms and crystal symmetry in the design of molecular ferromagnets with large magnetic anisotropy and high ordering temperatures.

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the $S=5/2$ compound Bi${}_2$Fe${}_4$O${}_9$. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and we investigate the nature of the ground state as a function of their ratio $x$ and the spin $S$. After establishing the classical phase diagram, we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for $S=1/2$ include (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small $x$ (related to an emergent $J_1$-$J_2$ effective model with $J_2\gg J_1$), and (ii) a nonmagnetic and possibly spin-nematic phase with $d$-wave symmetry at intermediate $x$.

A common limitation of experiments using color centers in diamond is the poor photon collection efficiency of microscope objectives due to refraction at the diamond interface. We present a simple and effective technique to detect a large fraction of photons emitted by color centers within a planar diamond sample by detecting light that is guided to the edges of the diamond via total internal reflection. We describe a prototype device using this “side-collection” technique, which provides a photon collection efficiency $\approx 47\%$ and a photon detection efficiency $\approx 39\%$. We apply the enhanced signal-to-noise ratio gained from side collection to ac magnetometry using ensembles of nitrogen-vacancy (NV) color centers, and demonstrate an ac magnetic field sensitivity $\approx 100\mathrm{pT}/\sqrt{\mathrm{Hz}}$, limited by added noise in the prototype side-collection device. Technical optimization should allow significant further improvements in photon collection and detection efficiency as well as subpicotesla NV-diamond magnetic field sensitivity using the side-collection technique.

We examine spontaneous emission in organic electroluminescent devices and investigate the influence of the local photonic mode density on the emissive properties of molecular emitters. Spontaneous emission in organic electroluminescent devices is modeled by means of an approximate closed-form solution for the exciton rate equation, which yields the efficiency of conversion of electrical charges into molecular excited states. The exciton decay rate and the efficiency of conversion of molecular excitation into far-field radiated photons are described using a state-of-the-art classical electromagnetic formalism suitable to model multilayered organic light-emitting diodes (OLEDs). We present an in-depth analysis of the influence of optical microcavities and the corresponding resonant modes on the luminescent properties of organic molecules. Near-field coupling and coupling to metallic reflectors are demonstrated as the main effects responsible for environment-induced modifications of the rate and efficiency of spontaneous emission. The extent to which the excitonic decay rate is modified by the optical microcavity (Purcell effect) is shown to be strictly dependent on the intrinsic luminescence quantum yield of the molecular emitter. The modeling formalism is successfully validated against experimental results obtained on three series of small-molecule $p$-$i$-$n$ OLED samples, featuring phosphorescent or fluorescent molecular emitters, with a widely varying thickness of the optical microcavity. We demonstrate that, within its limits of validity, the theoretical treatment in this work provides a rigorous quantitative description of spontaneous emission in organic luminescent devices and allows for the identification of the factors determining the OLED internal and external quantum efficiencies.

A model that describes exciton diffusion in disordered organic materials is introduced that is capable of quantitatively describing the effects of inhomogeneous broadening and energetic disorder on the energy transfer. The model is tested on a system that consists of a polymer matrix containing the perylene bisimide dye Perylene Red at high concentration as active sites. Excitons can be efficiently exchanged between the dye molecules by Förster energy transfer, resulting in a fairly high mobility of the excitons. Compared to polymers, the investigated system provides better insight into the parameters controlling the mobility of the excitons. Using femtosecond absorption spectroscopy, clear signatures for dispersive energy migration are found, namely, a shift of the exciton energy to lower energies within the first picoseconds and an anisotropy decay that deviates slightly from the predictions of classical Förster theory. Both effects are quantitatively reproduced by the model, which extends previous theories and takes explicitly into account the dependence of the Förster radius on the donor and the acceptor energy in a disordered sample of equal chromophores. The model predicts correctly the order of the exciton diffusion constant and provides a quantitative linkage between the exciton mobility and the inhomogeneous line width.

We report a study of low-energy electronic structure and Fermi surface topology for the recently discovered iron-based superconductor Ca${}_{10}$(Pt${}_3$As${}_8$)(Fe${}_2$As${}_2$)${}_5$ (the 10-3-8 phase, with $T_c\sim 8$ K), via angle-resolved photoemission spectroscopy (ARPES). Despite its triclinic crystal structure, ARPES results reveal a fourfold symmetric band structure with the absence of Dirac-cone-like Fermi dots (related to magnetism) found around the Brillouin zone corners in other iron-based superconductors. Considering that the triclinic lattice and structural supercell arise from the Pt${}_3$As${}_8$ intermediary layers, these results indicate that those layers couple only weakly to the FeAs layers in this new superconductor at least near the surface, which has implications for the determination of its pairing mechanism.

We analyze the ordered state of nuclear spins embedded in an interacting two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI). Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic dependences of the electron spin susceptibility ${\chi }^{ij}$ on the momentum ($\tilde{\mathbf{q}}$) and on the SOI coupling constant ($\alpha$). The uniform ($\tilde{q}=0$) spin susceptibility is anisotropic (with the out-of-plane component ${\chi }^{zz}$ being larger than the in-plane one ${\chi }^{xx}$ by a term proportional to $U^2\left(2k_F\right)\left|\alpha \right|$, where $U\left(q\right)$ is the electron-electron interaction). For $\tilde{q}\le 2m^{*}\left|\alpha \right|$, corrections to the leading $U^2\left(2k_F\right)\left|\alpha \right|$ term scale linearly with $\tilde{q}$ for ${\chi }^{xx}$ and are absent for ${\chi }^{zz}$. This anisotropy has important consequences for the ferromagnetic nuclear-spin phase: (i) the ordered state—if achieved—is of an Ising type and (ii) the spin-wave dispersion is gapped at $\tilde{q}=0$. To second order in $U\left(q\right)$, the dispersion is a decreasing function of $\tilde{q}$, and anisotropy is not sufficient to stabilize long-range order. However, renormalization in the Cooper channel for $\tilde{q}\ll 2m^{*}\left|\alpha \right|$ is capable of reversing the sign of the $\tilde{q}$ dependence of ${\chi }^{xx}$ and thus stabilizing the ordered state. We also show that a combination of the electron-electron and spin-orbit (SO) interactions leads to a new effect: long-wavelength Friedel oscillations in the spin (but not charge) electron density induced by local magnetic moments. The period of these oscillations is given by the SO length $\pi /m^{*}\left|\alpha \right|$.

The field of topological insulators (TIs) is rapidly growing. Concerning possible applications, the search for materials with an easily controllable TI phase is a key issue. The quantum spin Hall effect, characterized by a single pair of helical edge modes protected by time-reversal symmetry, has been demonstrated in HgTe-based quantum wells (QWs) with an inverted band gap. We analyze the topological properties of a generically coupled HgTe-based double QW and show how in such a system a TI phase can be driven by an interlayer bias voltage, even when the individual layers are noninverted. We argue that this system allows for (layer-)pseudospin-based physics similar to that in bilayer graphene but with the crucial absence of a valley degeneracy.

We investigate the entanglement spectra arising from sharp real-space partitions of the system for quantum Hall states. These partitions differ from the previously utilized orbital and particle partitions and reveal complementary aspects of the physics of these topologically ordered systems. We show, by constructing one to one maps to the particle partition entanglement spectra, that the counting of the real-space entanglement spectra levels for different particle number sectors versus their angular momentum along the spatial partition boundary is equal to the counting of states for the system with a number of (unpinned) bulk quasiholes excitations corresponding to the same particle and flux numbers. This proves that, for an ideal model state described by a conformal field theory, the real-space entanglement spectra level counting is bounded by the counting of the conformal field theory edge modes. This bound is known to be saturated in the thermodynamic limit (and at finite sizes for certain states). Numerically analyzing several ideal model states, we find that the real-space entanglement spectra indeed display the edge modes dispersion relations expected from their corresponding conformal field theories. We also numerically find that the real-space entanglement spectra of Coulomb interaction ground states exhibit a series of branches, which we relate to the model state and (above an entanglement gap) to its quasiparticle-quasihole excitations. We also numerically compute the entanglement entropy for the $\nu =1$ integer quantum Hall state with real-space partitions and compare against the analytic prediction. We find that the entanglement entropy indeed scales linearly with the boundary length for large enough systems, but that the attainable system sizes are still too small to provide a reliable extraction of the subleading topological entanglement entropy term.

The application of Wilson's numerical renormalization group (NRG) method to dissipative quantum impurity models, in particular the sub-Ohmic spin-boson model, has led to conclusions regarding the quantum critical behavior which are in disagreement with those from other methods and which are by now recognized as erroneous. The errors of NRG remained initially undetected, because NRG delivered an internally consistent set of critical exponents satisfying hyperscaling. Here we discuss how the conspiracy of two errors—the Hilbert-space truncation error and the mass-flow error—could lead to this consistent set of exponents. Remarkably, both errors, albeit of different origin, force the system to obey naive scaling laws even when the physical model violates naive scaling. In particular, we show that a combination of the Hilbert-space truncation and mass-flow errors induce an artificial nonanalytic term in the Landau expansion of the free energy which dominates the critical behavior for bath exponents $s<1/2$.

Model quantum Hall states including Laughlin, Moore-Read, and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multibody Hamiltonians, and explicitly illustrate the existence of geometric degree of freedom in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.