Quantum interferences in quasicrystals

– Contributions of quantum interference effects occuring in quasicrystals are reported. First conversely to metallic systems, quasiperiodic ones are shown to enclose original alterations of their conductive properties while downgrading long range order. Besides, origin of localization mechanism are outlined within the context of the original metal-insulator transition (MIT) found in these materials. Introduction. – Despite sustained effort and concern, today’s understanding of exotic electronic properties of quasicrystals [1] remains unsatisfactory although quasicrytalline materials have already been implemented to miscellanous concrete applications[2, 3]. In particular, the role of quasiperiodic order on electronic localization and transport is believed to genuinely entail the most unexpected experimental features whereas so far, no coherent theoretical framework has been successfully ascertained[4, 5, 6, 7]. As a matter of fact, one of the unprecedented tendency of quasicrystals is the enhancement of their conductive ability upon increasing contribution of static (structural disorder) or dynamical excitations (phonons). This has been strongly supported by many experimental evidences[4] and is often refered as an original property in the litterature. Notwithstanding theoretically, given heuristical arguments[5, 8] and numerical investigations (e.g. the Landauer conductance for quasiperiodic Penrose lattices [9] or Kubo formula for 3D-quasiperiodic models [10] ) yield to uncomplete understanding of the observed properties which range from anomalously metallic behaviors to insulating ones [11]. It is generally assumed that a specific “geometrical localization process” takes place in quasicrystals (sustained by critical states[12, 13]) and that local disruptions of corresponding mesoscopic order reduce quantum interferences, resulting in an increase of conductivity. To tackle this issue on 1D quasiperiodic potential, tight-binding (TBM) as well as continuous Kronig-Penney models have been considered [14], and phason-type disorder were shown to disclose manifestations of quantum interferences in quasiperiodic order. Here we will show that alteration of critical states may under certain circumstances entail alteration of their propagating ability. Besides, the role of quantum interferences on both sides of the quasicrystalline MIT for higher Typeset using EURO-TEX 2 EUROPHYSICS LETTERS dimensional materials is outlined. Anomalous electronic conductance in 1D-quasicrystals. – For 1D-quasiperiodic systems, we define phasons [14] that keep the essential characteristic of real systems, in the sense that they are a generic form of disorder which has no equivalent in usual metallic and periodic systems. Introducing random disorder into the 1D quasicrystal yield to Anderson localization in the infinite limit. For finite systems, localization lengthes may be much larger than the characteristic size so that conductance fluctuations as a function of energy of tunneling electrons (from the leads to the system) keep its self-similar nature and still follow power law behavior[15]. It is thus difficult to relate localization and transport in such situations. On the other hand, tight-binding models (TBM) of perfect quasiperiodic chains have been intensively worked out both analytically and numerically only for some given energies, but the results are supposed to have provided typical features of localization in quasiperiodic structures, such as power-law decrease of wavefunctions or power-law bounded resistances [12]. Let us investigate the role of phasons in TBM. Hamiltonian is H = ∑ n tn(|n〉〈n + 1| + |n + 1〉〈n|) (γ = tA/tB will stand for intensity of quasiperiodic potential, following a Fibonacci sequence ABAABABAABAAB. . . , whereas site energies are kept constant) and the Schrödinger equation on a localized basis gives