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Register a new userStatistics of Spectra for One-dimensional Quasi-Periodic Systems at the Metal-Insulator Transition
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We study spectral statistics of one-dimensional quasi-periodic systems at the metal-insulator transition. Several types of spectral statistics are observed at the critical points, lines, and region. On the critical lines, we find the bandwidth distribution $P_B(w)$ around the origin (in the tail) to have the form of $P_B(w) sim w^{alpha}$ ($P_B(w) sim e^{-beta w^{gamma}}$) ($alpha, beta, gamma > 0 $), while in the critical region $P_B(w) sim w^{-alpha}$ ($alpha > 0$). We also find the level spacing distribution to follow an inverse power law $P_G(s) sim s^{- delta}$ ($delta > 0$)
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The quasi-one-dimensional linear chain compound HfTe3 is experimentally and theoretically explored in the few- to single-chain limit. Confining the material within the hollow core of carbon nanotubes allows isolation of the chains and prevents the rapid oxidation which plagues even bulk HfTe3. High-resolution transmission electron microscopy combined with density functional theory calculations reveals that, once the triple-chain limit is reached, the normally parallel chains spiral about each other, and simultaneously a short-wavelength trigonal anti-prismatic rocking distortion occurs that opens a significant energy gap. This results in a size-driven metal-insulator transition.
Experimental evidence for the possible universality classes of the metal-insulator transition (MIT) in two dimensions (2D) is discussed. Sufficiently strong disorder, in particular, changes the nature of the transition. Comprehensive studies of the charge dynamics are also reviewed, describing evidence that the MIT in a 2D electron system in silicon should be viewed as the melting of the Coulomb glass. Comparisons are made to recent results on novel 2D materials and quasi-2D strongly correlated systems, such as cuprates.
We explore the scaling description for a two-dimensional metal-insulator transition (MIT) of electrons in silicon. Near the MIT, $beta_{T}/p = (-1/p)d(ln g)/d(ln T)$ is universal (with $p$, a sample dependent exponent, determined separately; $g$--conductance, $T$--temperature). We obtain the characteristic temperatures $T_0$ and $T_1$ demarking respectively the quantum critical region and the regime of validity of single parameter scaling in the metallic phase, and show that $T_1$ vanishes as the transition is approached. For $T<T_1$, the scaling of the data requires a second parameter. Moreover, all of the data can be described with two-parameter scaling at all densities -- even far from the transition.
Effects of non-magnetic disorder on the critical temperature T_c and on diamagnetism of quasi-one-dimensional superconductors are reported. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between wires and that T_c vanishes discontinuously at a critical disorder-strength. The parallel and transverse components of the penetration-depth are evaluated. They diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking respectively. The interplay between disorder and quantum phase fluctuations is shown to result in quantum critical behavior at T=0, which manifests itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.
We perform combined resistivity and compressibility studies of two-dimensional hole and electron systems which show the apparent metal-insulator transition - a crossover in the sign of dR/dT with changing density. No thermodynamic anomalies have been detected in the crossover region. Instead, despite a ten-fold difference in r_s, the compressibility of both electrons and holes is well described by the theory of nonlinear screening of the random potential. We show that the resistivity exhibits a scaling behavior near the percolation threshold found from analysis of the compressibility. Notably, the percolation transition occurs at a much lower density than the crossover.
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