Microscopic gauge-invariant theory of the c-axis infrared response of bilayer cuprate superconductors and the origin of the superconductivity induced absorption bands

We report on results of our theoretical study of the c-axis infrared conductivity of bilayer high-Tc cuprate superconductors using a microscopic model involving the bilayer-split (bonding and antibonding) bands. An emphasis is on the gauge-invariance of the theory, which turns out to be essential for the physical understanding of the electrodynamics of these compounds. The description of the optical response involves local (intra-bilayer and inter-bilayer) current densities and local conductivities. The local conductivities are obtained using a microscopic theory, where the quasiparticles of the two bands are coupled to spin fluctuations. The coupling leads to superconductivity and is described at the level of generalized Eliashberg theory. Also addressed is the simpler case of quasiparticles coupled by a separable and nonretarded interaction. The gauge invariance of the theory is achieved by including a suitable class of vertex corrections. The resulting response of the model is studied in detail and an interpretation of two superconductivity-induced peaks in the experimental data of the real part of the c-axis conductivity is proposed. The peak around 400/cm is attributed to a collective mode of the intra-bilayer regions, that is an analogue of the Bogolyubov-Anderson mode playing a crucial role in the theory of the longitudinal response of superconductors. For small values of the bilayer splitting, its nature is similar to that of the transverse plasmon of the phenomenological Josephson superlattice model. The peak around 1000/cm is interpreted as a pair breaking-feature that is related to the electronic coupling through the spacing layers separating the bilayers.Comment: 18 pages, 15 figures, submitted to Phys. Rev.

Selfconsistent gauge-invariant theory of in-plane infrared response of high-Tc cuprate superconductors involving spin fluctuations

We report on results of our theoretical study of the in-plane infrared conductivity of the high-Tc cuprate superconductors using the model where charged planar quasiparticles are coupled to spin fluctuations. The computations include both the renormalization of the quasiparticles and the corresponding modification of the current-current vertex function (vertex correction), which ensures gauge invariance of the theory and local charge conservation in the system. The incorporation of the vertex corrections leads to an increase of the total intraband optical spectral weight (SW) at finite frequencies, a SW transfer from far infrared to mid infrared, a significant reduction of the SW of the superconducting condensate, and an amplification of characteristic features in the superconducting state spectra of the inverse scattering rate 1/tau. We also discuss the role of selfconsistency and propose a new interpretation of a kink occurring in the experimental low temperature spectra of 1/tau around 1000cm^{-1}.Comment: 9 pages with 6 figures, submitted to Physical Review

Using Strategy Improvement to Stay Alive

We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides solving an MPG in the usual sense, our algorithm computes more information about the game, information that is important with respect to applications. The weights of the edges of an MPG can be thought of as a gained/consumed energy -- depending on the sign. For each vertex, our algorithm computes the minimum amount of initial energy that is sufficient for player Max to ensure that in a play starting from the vertex, the energy level never goes below zero. Our algorithm is not the first algorithm that computes the minimum sufficient initial energies, but according to our experimental study it is the fastest algorithm that computes them. The reason is that it utilizes the strategy improvement technique which is very efficient in practice

Hidden covalent insulator and spin excitations in SrRu2_2O6_6

The density functional plus dynamical mean-field theory is used to study the spin excitation spectra of SrRu$_2$O$_6$. A good quantitative agreement with experimental spin excitation spectra is found. Depending on the size of the Hund's coupling $J_H$ the systems chooses either Mott insulator or covalent insulator state when magnetic ordering is not allowed. We find that the nature of the paramagnetic state has negligible influence on the charge and spin excitation spectra. We find that antiferromagnetic correlations hide the covalent insulator state for realistic choices of the interaction parameters.Comment: 8 pages, 7 figure

Higgs mode and its decay in a two dimensional antiferromagnet

Condensed-matter analogs of the Higgs boson in particle physics allow insights into its behavior in different symmetries and dimensionalities. Evidence for the Higgs mode has been reported in a number of different settings, including ultracold atomic gases, disordered superconductors, and dimerized quantum magnets. However, decay processes of the Higgs mode (which are eminently important in particle physics) have not yet been studied in condensed matter due to the lack of a suitable material system coupled to a direct experimental probe. A quantitative understanding of these processes is particularly important for low-dimensional systems where the Higgs mode decays rapidly and has remained elusive to most experimental probes. Here, we discover and study the Higgs mode in a two-dimensional antiferromagnet using spin-polarized inelastic neutron scattering. Our spin-wave spectra of Ca$_2$RuO$_4$ directly reveal a well-defined, dispersive Higgs mode, which quickly decays into transverse Goldstone modes at the antiferromagnetic ordering wavevector. Through a complete mapping of the transverse modes in the reciprocal space, we uniquely specify the minimal model Hamiltonian and describe the decay process. We thus establish a novel condensed matter platform for research on the dynamics of the Higgs mode.Comment: original submitted version, Nature Physics (2017). arXiv admin note: substantial text overlap with arXiv:1510.0701

Fermionic response from fractionalization in an insulating two-dimensional magnet

Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs) -- new topological phases which can occur when quantum fluctuations preclude an ordered state -- are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data across a broad energy and temperature range in the two-dimensional material $\alpha$-RuCl$_3$. This shows the importance of magnetic materials as hosts of Majorana fermions. In turn, this first systematic evaluation of the dynamics of a QSL at finite temperature emphasizes the role of excited states for detecting such exotic properties associated with otherwise hard-to-identify topological QSLs.Comment: 5 pages, 3 figure

Direct Evidence for Dominant Bond-directional Interactions in a Honeycomb Lattice Iridate Na2IrO3

Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bond-directional interactions offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model, which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A2IrO3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic x-ray scattering reveals broken spin-rotational symmetry even above Neel temperature, with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spin-space and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.Comment: Nature Physics, accepted (2015

Principles behind evaluations of national food and beverage taxes and other regulatory efforts

Non-PRIFPRI3; ISIPHN