Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models

We present a functional renormalization group flow for many-fermion lattice models into phases with broken spin-rotational symmetry. The flow is expressed purely in terms of fermionic vertex functions. The symmetry breaking is seeded by a small initial anomalous self-energy which grows at the transition scale and which prevents a runaway-flow at nonzero scales. Focusing on the case of commensurate antiferromagnetism we discuss how the interaction vertex can be parametrized efficiently. For reduced models with long-range bare interactions we show the results of standard mean-field theory are reproduced by the fRG and how anisotropies in the spin sector change the flows. We then describe a more efficient decomposition of the interaction vertex that should allow for the treatment of more general models.Comment: revised version; 12 pages, 9 figure

Universality in antiferromagnetic strange metals

We propose a theory of metals at the spin-density wave quantum critical point in spatial dimension $d=2$. We provide a first estimate of the full set of critical exponents (dynamical exponent $z=2.13$, correlation length $\nu =1.02$, spin susceptibility $\gamma = 0.96$, electronic non-Fermi liquid $\eta^f_\tau = 0.53$, spin-wave Landau damping $\eta^b_\tau = 1.06$), which determine the universal power-laws in thermodynamics and response functions in the quantum-critical regime relevant for experiments in heavy-fermion systems and iron pnictides. We present approximate numerical and analytical solutions of Polchinski-Wetterich type flow equations with soft frequency regulators for an effective action of electrons coupled to spin-wave bosons. Performing the renormalization group in frequency -instead of momentum- space allows to track changes of the Fermi surface shape and to capture Landau damping during the flow. The technique is easily generalizable from models retaining only patches of the Fermi surface to full, compact Fermi surfaces.Comment: 46 pages, 13 figures, typos fixed; as accepted to Physical Review

Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures

We review the basic physics of surface-plasmon excitations occurring at metal/dielectric interfaces with special emphasis on the possibility of using such excitations for the localization of electromagnetic energy in one, two, and three dimensions, in a context of applications in sensing and waveguiding for functional photonic devices. Localized plasmon resonances occurring in metallic nanoparticles are discussed both for single particles and particle ensembles, focusing on the generation of confined light fields enabling enhancement of Raman-scattering and nonlinear processes. We then survey the basic properties of interface plasmons propagating along flat boundaries of thin metallic films, with applications for waveguiding along patterned films, stripes, and nanowires. Interactions between plasmonic structures and optically active media are also discussed

Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

We present a functional renormalization group (fRG) formalism for interacting fermions on lattices that captures the flow into states with commensurate spin-density wave order. During the flow, the growth of the order parameter is fed back into the flow of the interactions and all modes can be integrated out. This extends previous fRG flows in the symmetric phase that run into a divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering scale. We use the corresponding Ward identity to check the accuracy of the results. We apply our new method to a model with two Fermi pockets that have perfect particle-hole nesting. The results obtained from the fRG are compared with those in random phase approximation.Comment: revised version; 24 pages, 12 figure

Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model

We perform an instability analysis of the Emery three-band model at hole doping and weak coupling within a channel-decomposed functional renormalization group flow proposed in Phys. Rev. B 79, 195125 (2009). In our approach, momentum dependences are taken into account with improved precision compared to previous studies of related models. Around a generic parameter set, we find a strong competition of antiferromagnetic and d-wave Cooper instabilities with a smooth behavior under a variation of doping and additional hopping parameters. For increasingly incommensurate ordering tendencies in the magnetic channel, the d-wave pairing gap is deformed at its maxima. Comparing our results for the Emery model to those obtained for the two-dimensional one-band Hubbard model with effective parameters, we find that, despite considerable qualitative agreement, multi-orbital effects have a significant impact on a quantitative level.Comment: revised version: 22 pages, 11 figure

Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss

Near-field interactions between closely spaced Au nanoparticles were characterized by studying the spectral position of the extinction bands corresponding to longitudinal (L) and transverse (T) plasmon-polariton modes of Au nanoparticle chains. Far-field spectroscopy and finite-difference time-domain simulations on arrays of 50 nm diameter Au spheres with an interparticle spacing of 75 nm both show a splitting DeltaE between the L and T modes that increases with chain length and saturates at a length of seven particles at DeltaE = 65 meV. We show that the measured splitting will result in a propagation loss of 3 dB/15 nm for energy transport. Calculations indicate that this loss can be reduced by at least one order of magnitude by modifying the shape of the constituent particles

Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices

The transport of electromagnetic energy along structures consisting of arrays of closely spaced metal rods (spacing = 0.2 cm) was investigated in the microwave regime at 8.0 GHz (lambda= 3.7 cm). The dispersion relation shows that information transport occurs at a group velocity of 0.6c. The electromagnetic energy is highly confined to the arrays (90% within a distance of 0.05lambda from the array). The propagation loss in a straight array is 3 dB/8 cm. Routing of energy around 90° corners is possible with a power loss of 3–4 dB. Analogies to plasmon wires consisting of arrays of nm-size metal clusters are discussed

Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models

We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis.We first give two analytically accessible examples. Then we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations. As a consequence, the point-group symmetries can be used to reduce the computational effort in perturbative many-particle approaches such as the functional renormalization group.Comment: revised version: 38 pages, 4 figure

Optical pulse propagation in metal nanoparticle chain waveguides

Finite-difference time-domain simulations show direct evidence of optical pulse propagation below the diffraction limit of light along linear arrays of spherical noble metal nanoparticles with group velocities up to 0.06c. The calculated dispersion relation and group velocities correlate remarkably well with predictions from a simple point-dipole model. A change in particle shape to spheroidal particles shows up to a threefold increase in group velocity. Pulses with transverse polarization are shown to propagate with negative phase velocities antiparallel to the energy flow