Anomalous electronic transport in quasicrystals and related complex metallic alloys

Abstract

We analyze the transport properties in approximants of quasicrystals α-AlMnSi, 1/1-AlCuFe and for the complex metallic phase λ-AlMn. These phases presents strong analogies in their local atomic structures and are related to existing quasicrystalline phases. Experimentally they present unusual transport properties with low conductivities and a mix of metallic-like and insulating-like characteristics. We compute the band structure and the quantum diffusion in the perfect structure without disorder and introduce simple approximations that allow to treat the effect of disorder. Our results demonstrate that the standard Bloch-Boltzmann theory is not applicable to these intermetallic phases. Indeed their dispersion relation are flat indicating small band velocities and corrections to quantum diffusion that are not taken into account in the semi-classical Bloch-Boltzmann scheme become dominant. We call this regime the small velocity regime. A simple Relaxation Time Approximation to treat the effect of disorder allows us to reproduce the main experimental facts on conductivity qualitatively and even quantitatively.To cite this article: Guy Trambly de Laissardière, D. Mayou, C. R. Physique XXXX (20XX). RésuméTransportélectronique anormal dans les quasicristaux et les alliages métalliques complexes reliés. Nous analysons les propriétés de transportélectronique dans les approximants de quasicristaux α-AlMnSi, 1/1-AlCuFe et pour la phase complexe reliée λ-AlMn. Ces phases présentent de fortes analogies de leurs structures atomiques locales et sont reliéesà des phases quasicrystallines existantes. Expérimentallement elles présentent des propriétés de transport inhabituelles avec une faible conductivité et un mélange de propriétés de type métallique et de type isolant. Nous calculons la structure de bande et la diffusion quantique de la structure parfaite et introduisons une approximation simple qui permet de traiter l'effet du désordre. Nos résultats démontrent que la théorie standard de Bloch-Boltzmann n'est pas applicableà ces systèmes intermétalliques. En effet leurs relations de dispersion sont plates indiquant une faible vitesse de bande et les correctionsà la diffusion quantique qui ne sont pas prises en compte par la théorie semi-classique deviennent dominantes. Nous appelons ce régime le régime de faible vitesse. Une simple approximation de temps de relaxation pour traiter l'effet du désordre permet de reproduire les principaux résultats expérimentaux sur la conductivité qualitativement et même quantitativement.Pour citer cet article : Guy Trambly de Laissardière, D. Mayou, C. R. Physique XXXX (20XX).

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

“…where V 0 (E) is a velocity at the energy E and short time t. In crystals, V 0 ≥ V B where V B is the Boltzmann velocity (intra-band velocity) [39]. In BLG and MLG, V 0 and V B have the same order of magnitude: V 0 (BLG) = V 0 (MLG) = √ 2V B (MLG) [38].…”

Sub-diffusive electronic states in octagonal tiling

“…non-Boltzmann propagation found in realistic approximants of i-AlMnSi and i-AlCuFe [10,11], in the complex inter-metallic alloys λ-AlMn [12], and in small approximants of octagonal and Penrose tilings [13,14].…”

“…• At very small time, typically when L(t) < a, the mean spreading grows linearly with t, L(t) = V 0 t (ballistic behaviour), where V 0 > V B [10,12]. • For times, corresponding to L(t) a few a, the propagation seems to become diffusive as the diffusion coefficient is almost constant, D(t) D dif .…”

Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments

“…Furthermore, Ref. 7 also reports that no NFL behavior emerges when one considers a crystalline approximant instead of the quasicrystal, suggesting that this NFL regime is associated with the particular electronic states present in the quasicrystal but not in the approximant [9][10][11][12][13][14]. Conventional QCP approaches have been employed to explain the fascinating behavior in this alloy [15,16], but they consider the effects of quasicrystalline environment of the conduction electrons only minimally.…”