875 research outputs found
Finite-Size Scaling of the Level Compressibility at the Anderson Transition
We compute the number level variance and the level
compressibility from high precision data for the Anderson model of
localization and show that they can be used in order to estimate the critical
properties at the metal-insulator transition by means of finite-size scaling.
With , , and denoting, respectively, system size, disorder strength,
and the average number of levels in units of the mean level spacing, we find
that both and the integrated obey finite-size scaling.
The high precision data was obtained for an anisotropic three-dimensional
Anderson model with disorder given by a box distribution of width . We
compute the critical exponent as and the critical
disorder as in agreement with previous
transfer-matrix studies in the anisotropic model. Furthermore, we find
at the metal-insulator transition in very close
agreement with previous results.Comment: Revised version of paper, to be published: Eur. Phys. J. B (2002
High-pressure phases and transitions of the layered alkaline earth nitridosilicates SrSiN2 and BaSiN2
We investigate the high-pressure phase diagram of SrSiN2 and BaSiN2 with density-functional calculation. Searching a manifold of possible candidate structures, we propose new structural modifications of SrSiN2 and BaSiN2 attainable in high-pressure experiments. The monoclinic ground state of SrSiN2 transforms at 3 GPa into an orthorhombic BaSiN2 type. At 14 GPa a CaSiN2-type structure becomes the most stable configuration of SrSiN2. A hitherto unknown Pbcm modification is adopted at 85 GPa and, finally, at 131 GPa a LiFeO2-type structure. The higher homologue BaSiN2 transforms to a CaSiN2 type at 41 GPa and further to a Pbcm modification at 105 GPa. Both systems follow the pressure-coordination rule: the coordination environment of Si increases from tetrahedral through trigonal bipyramidal to octahedral. Some high-pressure phases are related in structure through simple group–subgroup mechanisms, indicating displacive phase transformations with low activation barriers
Ultra‐short pulsed laser processing of sapphire
Synthetic crystalline sapphire is hard, transparent and inert to most chemical etchants. It is a popular substrate for numerous applications in e.g. semiconductor industry, microfluidics, smartphones and watches. However, sapphire is challenging to machine with traditional techniques such as mechanical dicing. Tightly focusing a femto‐ or picosecond pulsed laser beam inside the bulk of sapphire amorphized a volume in and near the laser focus (diameter ~ 1 micrometer). This amorphized region can be selectively removed by chemical etching in a subsequent step, resulting in hollow volumes and structures [1]. For the technique to be fully exploited, several scientific challenges still need to be overcome. To address these challenges, we combined an experimental and a theoretical approach study and optimize this two‐step method. Our numerical model allows simulation of the laser‐material interaction during short ulsed laser processing of sapphire [2]. Physical phenomena included in the 2D and timedependent model are the laser intensity distribution, free electron density, electron temperature and lattice temperature during and directly after the pulse. Simulation results show that avalanche ionization needs to be triggered for sapphire to absorb laser energy. Our experimental results show that the pulse energy and focus depth are the most dominant laser parameters. Further, the type of etchant used has a strong effect on the resulting structures, not only, in the bulk, but also on the surface of sapphire. Acknowledgement: The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska‐ Curie grant agreement No. 675063
Interacting particles at a metal-insulator transition
We study the influence of many-particle interaction in a system which, in the
single particle case, exhibits a metal-insulator transition induced by a finite
amount of onsite pontential fluctuations. Thereby, we consider the problem of
interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain.
We employ the density-matrix renormalization scheme to investigate the finite
particle density situation. In the case of incommensurate densities, the
expected transition from the single-particle analysis is reproduced. Generally
speaking, interaction does not alter the incommensurate transition. For
commensurate densities, we map out the entire phase diagram and find that the
transition into a metallic state occurs for attractive interactions and
infinite small fluctuations -- in contrast to the case of incommensurate
densities. Our results for commensurate densities also show agreement with a
recent analytic renormalization group approach.Comment: 8 pages, 8 figures The original paper was splitted and rewritten.
This is the published version of the DMRG part of the original pape
General Localization Lengths for Two Interacting Particles in a Disordered Chain
The propagation of an interacting particle pair in a disordered chain is
characterized by a set of localization lengths which we define. The
localization lengths are computed by a new decimation algorithm and provide a
more comprehensive picture of the two-particle propagation. We find that the
interaction delocalizes predominantly the center-of-mass motion of the pair and
use our approach to propose a consistent interpretation of the discrepancies
between previous numerical results.Comment: 4 pages, 2 epsi figure
Weak disorder expansion for localization lengths of quasi-1D systems
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength
Enhanced Charge and Spin Currents in the One-Dimensional Disordered Mesoscopic Hubbard Ring
We consider a one-dimensional mesoscopic Hubbard ring with and without
disorder and compute charge and spin stiffness as a measure of the permanent
currents. For finite disorder we identify critical disorder strength beyond
which the charge currents in a system with repulsive interactions are {\em
larger} than those for a free system. The spin currents in the disordered
repulsive Hubbard model are enhanced only for small , where the magnetic
state of the system corresponds to a charge density wave pinned to the
impurities. For large , the state of the system corresponds to localized
isolated spins and the spin currents are found to be suppressed. For the
attractive Hubbard model we find that the charge currents are always suppressed
compared to the free system at all length scales.Comment: 20 RevTeX 3.0 pages, 8 figures NOT include
The random phase property and the Lyapunov Spectrum for disordered multi-channel systems
A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum
The Aharonov-Bohm effect for an exciton
We study theoretically the exciton absorption on a ring shreded by a magnetic
flux. For the case when the attraction between electron and hole is
short-ranged we get an exact solution of the problem. We demonstrate that,
despite the electrical neutrality of the exciton, both the spectral position of
the exciton peak in the absorption, and the corresponding oscillator strength
oscillate with magnetic flux with a period ---the universal flux
quantum. The origin of the effect is the finite probability for electron and
hole, created by a photon at the same point, to tunnel in the opposite
directions and meet each other on the opposite side of the ring.Comment: 13 RevTeX 3.0 pages plus 4 EPS-figures, changes include updated
references and an improved chapter on possible experimental realization
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