Nano-compositional imaging of the lanthanum silicide system at THz wavelengths.

Terahertz scattering-type scanning near-field optical microscopy (THz-sSNOM) provides a noninvasive way to probe the low frequency conductivity of materials and to characterize material compositions at the nanoscale. However, the potential capability of atomic compositional analysis with THz nanoscopy remains largely unexplored. Here, we perform THz near-field imaging and spectroscopy on a model rare-earth alloy of lanthanum silicide (La-Si) which is known to exhibit diverse compositional and structural phases. We identify subwavelength spatial variations in conductivity that is manifested as alloy microstructures down to much less than 1 µm in size and is remarkably distinct from the surface topography of the material. Signal contrasts from the near-field scattering responses enable mapping the local silicon/lanthanum content differences. These observations demonstrate that THz-sSNOM offers a new avenue to investigate the compositional heterogeneity of material phases and their related nanoscale electrical as well as optical properties.

Resonant and antiresonant frequency dependence of the effective parameters of metamaterials.

We present a numerical study of the electromagnetic response of the metamaterial elements that are used to construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an antiresonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus antiresonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the antiresonant behavior.

Levitation of current carrying states in the lattice model for the integer quantum Hall effect.

The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice model. The Hall conductivity and the localization length are calculated numerically near the transition. For uncorrelated and weakly correlated disorder potentials the current carrying states are annihilated by the negative Chern states originating from the band center. In the presence of correlated disorder potentials with correlation length larger than approximately half the lattice constant the floating up of the critical states in energy without merging is observed. This behavior is similar to the levitation scenario proposed for the continuum model.

Effective medium theory of left-handed materials.

We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity epsilon and permeability micro. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut wires, split ring resonators (SRRs), closed SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left or right handed.