Electronic transport in highly doped but still insulating silicon at low temperatures is dominated by hopping between localized states; it serves as a model system of a disordered solid for which the electronic interaction can be investigated. We have studied the frequency-dependent conductivity of phosphorus-doped silicon in the THz frequency range (30 GHz to 3 THz) at low temperatures $T\geq 1.8$ K. The crossover in the optical conductivity from a linear to a quadratic frequency dependence as predicted by Efros and Shklovskii is observed qualitatively; however, the simple model does not lead to a quantitative agreement. Covering a large range of donor concentration, our temperature- and frequency-dependent investigations reveal that electronic correlation effects between the localized states play an important and complex role at low temperatures. In particular we find a super-linear frequency dependence of the conductivity that highlights the influence of the density of states, i.e. the Coulomb gap, on the optical conductivity. When approaching the metal-to-insulator transition by increasing doping concentration, the dielectric constant and the localization length exhibit critical behavior.
Coherent-source THz spectroscopy was employed to measure the charge carrier dynamics and excitations of ultrathin superconducting films at low temperatures. While the properties of weakly disordered superconductors can be well described by the BCS theory, significant deviations are observed as disorder increases towards the superconductor-insulator transition. A comparative study including tunneling and optical spectroscopy reveals the importance of Coulomb interactions on the energy gap of disordered superconductors. We also discuss the possibility of collective low-frequency excitations due to the Higgs mode, which become long-lived and well defined in the vicinity of a quantum critical point.
We have conducted comprehensive electron spin resonance (ESR) investigations on single crystals of the one-dimensional organic compounds $(\mathrm{TMTTF}{)}_{2}{\mathrm{PF}}_{6}, (\mathrm{TMTTF}{)}_{2}{\mathrm{ClO}}_{4},$ $(\mathrm{TMTTF}{)}_{2}\mathrm{Br},$ $(\mathrm{TMTSF}{)}_{2}{\mathrm{PF}}_{6},$ and $(\mathrm{TMTSF}{)}_{2}{\mathrm{AsF}}_{6}$ in the temperature range from 4 to 500 K and additionally, $(\mathrm{TMTSF}{)}_{2}{\mathrm{ReO}}_{4}$ and $(\mathrm{TMTSF}{)}_{2}{\mathrm{ClO}}_{4}$ at room temperature. In contrast to the selenium analogs TMTSF which are one-dimensional metals, the sulfur salts are semiconductors with localized spins on the TMTTF dimers. Taking into account the thermal expansion of the crystals at high temperature $(T>20 \mathrm{K})$ the ESR intensity of all sulfur compounds can be described as a spin-1/2 antiferromagnetic Heisenberg chain with exchange constants $420<~J<~500 \mathrm{K}.$ Although the TMTSF compounds are one-dimensional organic metals down to 10 K, the temperature dependence of the spin susceptibility can also be described within the framework of the Hubbard model in the limit of strong Coulomb repulsion with $J\ensuremath{\approx}1400 \mathrm{K}.$ By modeling $(\mathrm{TMTTF}{)}_{2}{\mathrm{ClO}}_{4}$ as an alternating spin chain, the change of the alternation parameter at the first-order phase transition ${(T}_{\mathrm{AO}}=72.5 \mathrm{K})$ indicates a tetramerization of the chain. $(\mathrm{TMTTF}{)}_{2}{\mathrm{PF}}_{6}$ undergoes a spin-Peierls transition at ${T}_{\mathrm{SP}}=19 \mathrm{K}$ which can be well described by Bulaevskii's model with a singlet-triplet gap ${\ensuremath{\Delta}}_{\ensuremath{\sigma}}(0)=32.3 \mathrm{K}.$ We find evidence of antiferromagnetic fluctuations at temperatures well above the magnetic ordering in $(\mathrm{TMTTF}{)}_{2}\mathrm{Br},$ $(\mathrm{TMTSF}{)}_{2}{\mathrm{PF}}_{6},$ and $(\mathrm{TMTSF}{)}_{2}{\mathrm{AsF}}_{6}$ which follow the critical behavior expected for three-dimensional ordering. $(\mathrm{TMTTF}{)}_{2}{\mathrm{PF}}_{6}$ and $(\mathrm{TMTTF}{)}_{2}\mathrm{Br}$ show one-dimensional lattice fluctuations.
We report on an investigation of optical properties of multiferroic CoCr${}_{2}$O${}_{4}$ at terahertz frequencies in magnetic fields up to 30 T. Below the ferrimagnetic transition (94 K), the terahertz response of CoCr${}_{2}$O${}_{4}$ is dominated by a magnon mode, which shows a steep magnetic-field dependence. We ascribe this mode to an exchange resonance between two magnetic sublattices with different $g$ factors. In the framework of a simple two-sublattice model (the sublattices are formed by Co${}^{2+}$ and Cr${}^{3+}$ ions), we find the inter-sublattice coupling constant, $\ensuremath{\lambda}=\ensuremath{-}(18\ifmmode\pm\else\textpm\fi{}1)$ K, and trace the magnetization for each sublattice as a function of field. We show that the Curie temperature of the Cr${}^{3+}$ sublattice, ${\ensuremath{\Theta}}_{2}$ $=$ $(49\ifmmode\pm\else\textpm\fi{}2)$ K, coincides with the temperature range, where anomalies of the dielectric and magnetic properties of CoCr${}_{2}$O${}_{4}$ have been reported in literature.
Non-Fermi liquid behavior is shown to occur in two-dimensional metals which are close to a charge ordering transition driven by the Coulomb repulsion. A linear temperature dependence of the scattering rate together with an increase of the electron effective mass occur above T*, a temperature scale much smaller than the Fermi temperature. It is shown that the anomalous temperature dependence of the optical conductivity of the quasi-two-dimensional organic metal alpha-(BEDT-TTF)2MHg(SCN)4, with M=NH4 and Rb, above T*=50-100 K, agrees qualitatively with our predictions for the electronic properties of nearly charge ordered two-dimensional metals.
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