Understanding delocalization in the Continuous Random Dimer model

We propose an explanation of the bands of extended states appearing in random one dimensional models with correlated disorder, focusing on the Continuous Random Dimer model [A.\ S\'{a}nchez, E.\ Maci\'a, and F.\ Dom\'\i nguez-Adame, Phys.\ Rev.\ B {\bf 49}, 147 (1994)]. We show exactly that the transmission coefficient at the resonant energy is independent of the number of host sites between two consecutive dimers. This allows us to understand why are there bands of extended states for every realization of the model as well as the dependence of the bandwidths on the concentration. We carry out a perturbative calculation that sheds more light on the above results. In the conclusion we discuss generalizations of our results to other models and possible applications which arise from our new insight of this problem.Comment: REVTeX 3.0, 4 pages, 4 figures (hard copy on request from [email protected]), Submitted to Phys Rev

Zero-energy peak of the density of states and localization properties of a one-dimensional Frenkel exciton: Off-diagonal disorder

We study a one-dimensional Frenkel Hamiltonian with off-diagonal disorder, focusing our attention on the physical nature of the zero-energy peak of the density of states. The character of excitonic states (localized or delocalized) is also examined in the vicinity of this peak. It is shown that the state being responsible for the peak is localized. A detailed comparison of the nearest-neighbor approach with the long-range dipole-dipole coupling is performed.Comment: 15 pages with 7 figures (REVTeX). To appear in Physical Review

Oxidation-assisted alkaline precipitation : the effect of H2O2 on the size of CuO and FeOOH nanoparticles

H2O2 was demonstrated to narrow the size distribution and decrease the size of CuO and hydrous FeOOH (2-line ferrihydrite) nanoparticles under conditions of high supersaturation. We introduce oxidation-assisted alkaline precipitation (Ox-AP) and compare it to traditional alkaline precipitation (AP). While for AP, a metal salt solution (e.g., CuCl2) is mixed with an alkali (e.g., NaOH), for Ox-AP, the more reduced form of that metal salt solution (e.g., CuCl) is simultaneously mixed with that alkali and an oxidant (e.g., H2O2). The resulting precipitates were characterized with SEM, XRD, DLS and single particle ICP-MS and shown to be nanoparticles (NPs). Ox-AP CuO NPs were up to 3 times smaller than AP NPs. Ox-AP FeOOH NPs were up to 22.5% smaller than AP NPs. We discuss and propose a possible mechanism of Ox-AP through careful consideration of the known reaction chemistry of iron and copper. We propose that an increased monomer formation rate enhances the nucleation rate, which ultimately results in smaller particles with a more narrow distribution. The more distinct effect of Ox-AP on copper, was attributed to the fast formation of the stable CuO monomer, compared to AP, where the Cu(OH)(2) and/or Cu-2(OH)(3)Cl monomers are more likely formed. Although, the exact mechanism of Ox-AP needs experimental confirmation, our results nicely demonstrate the potential of using Ox-AP to produce smaller NPs with a more narrow distribution in comparison to using AP

Fraunhofer pattern in the presence of Majorana zero modes

Majorana bound states (MBSs) emerge as zero energy excitations in topological superconductors. At zero temperature, their presence gives a quantized conductance in NS junctions and a fractional Josephson effect in Josephson junctions when the parity is conserved. However, most of current experiments deviate from the theoretical predictions, yielding for example a non-quantized conductance or the absence of only few odd Shapiro steps. Although these results might be compatible with a topological ground state, it is also possible that a trivial scenario can mimic similar results, by means of accidental zero energy Andreev bound states (ZEABS) or simply by non-adiabatic transitions between trivial Andreev bound states. Here, we propose a new platform to investigate signatures of the presence of MBSs in the Fraunhofer pattern of Josephson junctions featuring quantum spin Hall edge states on the normal part and Majorana bound states at the NS interfaces. We use a tight-binding model to demonstrate a change in periodicity of the Fraunhofer pattern when comparing trivial and non-trivial regimes. We explain these results in terms of local and crossed Andreev bound states, which due to the spin-momentum locking, accumulate different magnetic flux and therefore become distinguishable in the Fraunhofer periodicity. Furthermore, we introduce a scattering model that captures the main results of the microscopic calculations with MBSs and extend our discussion to the main differences found using accidental ZEABS.Comment: 17 pages, 14 figures. Comments are welcom

Chiral corrections to the SU(2)×SU(2)SU(2)\times SU(2) Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $\delta_\pi$, the value $\delta_\pi = (6.2, \pm 1.6)$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $\simeq \equiv |_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (\nu_\chi = M_\rho) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (\nu_\chi = M_\eta) = - (5.7 \pm 2.0)\times 10^{-3}$.Comment: A comment about the value of the strong coupling has been added at the end of Section 4. No change in results or conslusion

Experimental evidence of delocalized states in random dimer superlattices

We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disorder by means of photoluminescence and vertical dc resistance. The results are compared to those obtained in ordered and uncorrelated disordered superlattices. We report the first experimental evidence that spatial correlations inhibit localization of states in disordered low-dimensional systems, as our previous theoretical calculations suggested, in contrast to the earlier belief that all eigenstates are localized.Comment: 4 pages, 5 figures. Physical Review Letters (in press