We construct an effective Hamiltonian for electrons in the fractional quantum Hall regime for GaAs and graphene that takes into account Landau level mixing (for both GaAs and graphene) and subband mixing (for GaAs, due to the nonzero width of the quantum well). This mixing has the important qualitative effect of breaking particle-hole symmetry as well as renormalizing the strength of the interparticle interactions. Both effects could have important consequences for the prospect that the fractional quantum Hall effect at $\nu =\frac{5}{2}$ is described by states that support non-Abelian excitations such as the Moore-Read Pfaffian or anti-Pfaffian states. For GaAs, Landau level and subband mixing break particle-hole symmetry in all Landau levels and subband mixing, due to finite thickness, causes additional short-distance softening of the Coulomb interaction, further renormalizing the Hamiltonian; additionally, the Landau level and subband energy spacings are comparable so it is crucial to consider both effects simultaneously. We find that in graphene, Landau level mixing only breaks particle-hole symmetry outside of the lowest Landau level ($N\ne 0$). Landau level mixing is likely to be especially important in graphene since the Landau level mixing parameter is independent of the external magnetic field and is of order one. Our realistic Hamiltonians will serve as starting points for future numerical studies.

We present a combined experimental and theoretical study of two-photon emission from the biexciton cascade in single GaN quantum dots. By changing the biexciton binding energy, pump power, and temperature, the balance between the one- and two-photon decay processes is controlled in this four-level system, which drastically affects the photon statistics of the resulting emission. As the most pronounced feature of this interplay we observe a bunching phenomenon and a transition from sub- to super-Poissonian photon statistics, originating from the complex nature of the biexciton cascade. This work highlights how photon statistics can be steered between one- and two-photon processes towards an increased, bunched two-photon emission probability up to 50 K with the perspective for efficient photon pair generation in the UV spectral range.

A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [C. Bihler et al., Phys. Rev. B 79, 045205 (2009)], this formalism accounts for elliptical magnetization precession and magnetic properties arbitrarily varying across the layer thickness, including the magnetic anisotropy parameters, the exchange stiffness, the Gilbert damping, and the saturation magnetization. To demonstrate the usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As samples grown by low-temperature molecular-beam epitaxy by means of angle-dependent standing spin-wave resonance spectroscopy and electrochemical capacitance-voltage measurements. By applying our modeling approach, the angle dependence of the spin-wave resonance data can be reproduced in a simulation with one set of simulation parameters for all external field orientations. We find that the approximately linear gradient in the out-of-plane magnetic anisotropy is related to a linear gradient in the hole concentrations of the samples.

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated Fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.

We present an efficient method for calculating the prefactors of harmonic transition state theory rates. We reformulate the prefactors in terms of the density of states (DOS) of the Hessian matrices at the basin minimum and the saddle point. The DOS is then approximated using the kernel polynomial method as an expansion in terms of Chebyshev polynomials. The cost of the calculation scales linearly with the number of atoms, in contrast with the cubic scaling of the direct method. This approach hence greatly facilitates the investigations of kinetic processes in very large systems. We demonstrate the method by calculating the prefactors of the transition rates for two processes in bulk silver: vacancy hopping and Frenkel pair formation.

We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here, we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic orders at half-filling.

When gold is deposited on Si(553), the surface self-assembles to form a periodic array of steps with nearly perfect structural order. In scanning tunneling microscopy these steps resemble quasi-one-dimensional atomic chains. At temperatures below $\sim$50 K the chains develop a tripled periodicity. We recently predicted, on the basis of density-functional theory calculations at $T=0$, that this tripled periodicity arises from the complete polarization of the electron spin on every third silicon atom along the step; in the ground state these linear chains of silicon spins are antiferromagnetically ordered. Here we explore, using ab initio molecular dynamics and kinetic Monte Carlo simulations, the behavior of silicon spin chains on Si(553)-Au at finite temperature. Thermodynamic phase transitions at $T>0$ in one-dimensional systems are prohibited by the Mermin-Wagner theorem. Nevertheless we find that a surprisingly sharp onset occurs upon cooling—at about 30 K for perfect surfaces and at higher temperature for surfaces with defects—to a well-ordered phase with tripled periodicity, in good agreement with experiment.

The recently synthesized MgFeGe compound is isostructural and isoelectronic with superconducting LiFeAs. Both materials are paramagnetic metals at room temperature. Inspection of their electronic structures without spin polarization reveals hardly any difference between the two. This fact was interpreted as evidence against popular theories relating superconductivity in Fe-based materials with spin fluctuations. We show that in the magnetic domain the two compounds are dramatically different, and the fact that MgFeGe does not superconduct, is, on the contrary, a strong argument in favor of theories based on spin fluctuations.

We investigate the bilayer Ruddlesden-Popper iridate Sr${}_3$Ir${}_2$O${}_7$ by temperature-dependent angle-resolved photoemission. At low temperatures, we find a fully gapped correlated insulator, characterized by a small charge gap and narrow bandwidths. The low-energy spectral features show a pronounced temperature-dependent broadening and non-quasiparticle-like Gaussian line shapes. Together, these spectral features provide experimental evidence for a polaronic ground state. We observe similar behavior for the single-layer cousin Sr${}_2$IrO${}_4$, indicating that strong electron-boson coupling dominates the low-energy excitations of this exotic family of $5d$ compounds.

We study origin of Rashba spin-orbit interaction at SrTiO${}_3$ surfaces and LaAlO${}_3$/SrTiO${}_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that in a simple tight-binding model involving $3d$ $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO${}_3$/SrTiO${}_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO${}_3$ surfaces and LaAlO${}_3$/SrTiO${}_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO${}_3$/SrTiO${}_3$ by calculating weak antilocalization corrections to the conductance and to universal conductance fluctuations.

We derive effective Hamiltonians for the fractional quantum Hall effect in $n=0$ and $n=1$ Landau levels that account perturbatively for Landau-level mixing by electron-electron interactions. To second order in the ratio of electron-electron interaction to cyclotron energy, Landau-level mixing is accounted for by constructing effective interaction Hamiltonians that include two-body and three-body contributions characterized by Haldane pseudopotentials. Our study builds upon previous treatments, using as a stepping stone the observation that the effective Hamiltonian is fully determined by the few-body problem with $N=2$ and $N=3$ electrons in the partially filled Landau level. For the $n=0$ case we use a first quantization approach to provide a compact and transparent derivation of the effective Hamiltonian which captures a class of virtual processes omitted in earlier derivations of Landau-level-mixing corrected Haldane pseudopotentials.

We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero mode, so that it can be observed in the gate-voltage-averaged differential conductance $\langle dI/dV\rangle$ as a $4e^2/h$ zero-bias peak above a $(\frac{2}{3}{\pi }^2-4)e^2/h$ background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.

We present an efficient optimization method to determine the structure of disordered systems in agreement with available experimental data. Our approach permits the application of accurate electronic structure calculations within the structure optimization. This technique is demonstrated within density functional theory by the calculation of a model of amorphous carbon.

Magnetic order and low-energy spin dynamics in the zero field ground state of Ni${}_3$V${}_2$O${}_8$ are revealed in elastic and inelastic neutron scattering experiments. Neutron diffraction shows that below $T=2.3$ K the Ni${}^{2+}$ moments (spin $S=1$) order in a cycloid pattern with incommensurate wave vector ${\mathit{k}}_{\text{ICM}}=(0,1,\tau )$, where $\tau =0.4030\pm 0.0004$, which is superimposed on a commensurate antiferromagnetic spin arrangement with ${\mathit{k}}_{\text{CM}}=(0,0,0)$. Three spin wave modes are discerned below $E\sim 3$ meV in inelastic measurements and qualitatively described by a model Hamiltonian that involves near neighbor exchange, local anisotropy, and a small biquadratic coupling between the spine and cross-tie sites. Results from both elastic and inelastic scattering experiments suggest that the two sublattices on spine and cross-tie sites are largely decoupled.

There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism occurring in ordinary SU(2) quantum magnets. Here we consider theories of so-called su(2)${}_k$ anyons, well-known deformations of SU(2), in which only the first $k+1$ angular momenta of SU(2) occur. In this paper, we discuss in particular anyonic generalizations of ordinary SU(2) spin chains with an emphasis on anyonic spin $S=1$ chains. We find that the overall phase diagrams for these anyonic spin-1 chains closely mirror the phase diagram of the ordinary bilinear-biquadratic spin-1 chain including anyonic generalizations of the Haldane phase, the AKLT construction, and supersymmetric quantum critical points. A novel feature of the anyonic spin-1 chains is an additional topological symmetry that protects the gapless phases. Distinctions further arise in the form of an even/odd effect in the deformation parameter $k$ when considering su(2)${}_k$ anyonic theories with $k\ge 5$, as well as for the special case of the su(2)${}_4$ theory for which the spin-1 representation plays a special role. We also address anyonic generalizations of spin-$\frac{1}{2}$ chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into the context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.

The optical conductivity of quasicrystals is characterized by two features not seen in ordinary metallic systems. There is an absence of the Drude peak and the interband conductivity rises linearly from a very low value up to normal metallic levels over a wide range of frequencies. The absence of a Drude peak has been attributed to a pseudogap at the Fermi surface but a detailed explanation of the linear behavior has not been found. Here we show that the linear conductivity, which seems to be universal in all Al based icosahedral quasicrystal families, as well as their periodic approximants, follows from a simple model that assumes that the entire Fermi surface is gapped except at a finite set of Dirac points. There is no evidence of a semiconducting gap in any of the materials suggesting that the Dirac spectrum is massless, protected by topology leading to a Weyl semimetal. This model gives rise to a linear conductivity with only one parameter, the Fermi velocity. This picture suggests that decagonal quasicrystals should, like graphene, have a frequency independent conductivity, without a Drude peak. This is in accord with the experimental data as well.

We consider theoretically, using the random phase approximation (RPA), low-energy intrinsic plasmons for two-dimensional (2D) systems obeying Dirac-like linear chiral dispersion with the chemical potential set precisely at the charge neutral Dirac point. The “intrinsic Dirac plasmon” energy has the characteristic $\sqrt{q}$ dispersion in the 2D wave vector $q$, but vanishes as $\sqrt{T}$ in temperature for both monolayer and bilayer graphene. The intrinsic plasmon becomes overdamped for a fixed $q$ as $T\to 0$ since the level broadening (i.e., the decay of the plasmon into electron-hole pairs due to Landau damping) increases as $1/\sqrt{T}$ as temperature decreases, however, the plasmon mode remains well defined at any fixed $T$ (no matter how small) as $q\to 0$. We find the intrinsic plasmon to be well defined as long as $q<\frac{k_{B}T}{e^2}$. We give analytical results for low and high temperatures, and numerical RPA results for arbitrary temperatures, and consider both single- and double-layer intrinsic Dirac plasmons. We provide extensive comparison and contrast between intrinsic and extrinsic graphene plasmons, and critically discuss the prospects for experimentally observing intrinsic Dirac point graphene plasmons.

We report a combined experimental and theoretical study of the spin $S=\frac{1}{2}$ nanomagnet Cu${}_5$(OH)${}_2$(NIPA)${}_4·$10H${}_2$O (Cu${}_5$-NIPA). Using thermodynamic, electron spin resonance, and ${}^1$H nuclear magnetic resonance measurements on one hand, and ab initio density-functional band-structure calculations, exact diagonalizations, and a strong-coupling theory on the other, we derive a microscopic magnetic model of Cu${}_5$-NIPA and characterize the spin dynamics of this system. The elementary fivefold Cu${}^{2+}$ unit features an hourglass structure of two corner-sharing scalene triangles related by inversion symmetry. Our microscopic Heisenberg model comprises one ferromagnetic and two antiferromagnetic exchange couplings in each triangle, stabilizing a single spin $S=\frac{1}{2}$ doublet ground state (GS), with an exactly vanishing zero-field splitting (by Kramers' theorem), and a very large excitation gap of $\Delta \simeq 68$ K. Thus, Cu${}_5$-NIPA is a good candidate for achieving long electronic spin relaxation ($T_1$) and coherence ($T_2$) times at low temperatures, in analogy to other nanomagnets with low-spin GS's. Of particular interest is the strongly inhomogeneous distribution of the GS magnetic moment over the five Cu${}^{2+}$ spins. This is a purely quantum-mechanical effect since, despite the nonfrustrated nature of the magnetic couplings, the GS is far from the classical collinear ferrimagnetic configuration. Finally, Cu${}_5$-NIPA is a rare example of a $S=\frac{1}{2}$ nanomagnet showing an enhancement in the nuclear spin-lattice relaxation rate $1/T_1$ at intermediate temperatures.

We report the observation of superconductivity in the CuIr${}_2$Se${}_4$ spinel induced by partial substitution of Pt for Ir. The optimal doping level for superconductivity in Cu(Ir${}_{1-x}$Pt${}_x$)${}_2$Se${}_4$ is $x$ $=$ 0.2, where $T_c$ is 1.76 K. A superconducting $T_c$ vs composition dome is established between the metallic, normal conductor CuIr${}_2$Se${}_4$ and semiconducting CuIrPtSe${}_4$. Electronic structure calculations show that the optimal $T_c$ occurs near the electron count of a large peak in the calculated electronic density of states and that CuIrPtSe${}_4$ is a band-filled insulator. Characterization of the superconducting state in this heavy metal spinel through determination of $\Delta C/\gamma T_c$ indicates that it is BCS-like. The relatively high upper critical field at the optimal superconducting composition [$H_c$${}_2$(0) $=$ 3.2 T] is much larger than that reported for analogous rhodium spinels and is comparable to or exceeds the Pauli field (${\mu }_0{H}_P$), suggesting that strong spin-orbit coupling may influence the superconducting state. Further, comparison to doped CuIr${}_2$S${}_4$ suggests that superconductivity in iridium spinels is not necessarily associated with the destabilization of a charge-ordered spin-paired state through doping.

In the effective Ising spin-1/2 antiferromagnetic chain system BaCo${}_{\text{2}}$V${}_{\text{2}}$O${}_{\text{8}}$ the magnetic-field influence is highly anisotropic. For magnetic fields along the easy axis $c$, the Néel order is strongly suppressed already at low fields and an incommensurate order is entered above 4 T. We present a detailed study of the magnetic phase diagrams for different magnetic field directions, which are derived from magnetization data, high-resolution thermal expansion, and magnetostriction measurements as well as from the thermal conductivity. Zero-field thermal-expansion data reveal that the magnetic transition is accompanied by an orthorhombic distortion within the $ab$ plane. Under ambient conditions the crystals are heavily twinned, but the domain orientation can be influenced either by applying uniaxial pressure or a magnetic field along the [100] direction. In addition, our data reveal a pronounced in-plane magnetic anisotropy for fields applied within the $ab$ plane. For $H\parallel \left[110\right]$, the magnetic field influence on $T_{\text{N}}$ is weak, whereas for magnetic fields applied along [100], $T_{\text{N}}$ vanishes at about 10 T and the zero-field Néel order is completely suppressed as is confirmed by neutron diffraction data. The second-order phase transition strongly suggests a quantum critical point being present at $H\simeq 10$ T parallel [100].