Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport (3d); precisely at the transition, the system displays sub-diffusive critical states. We calculate the beta function $\beta(g) = dln(g)/dln(L)$ and show that, in 1d and 2d, single-parameter scaling is unable to describe the transition. Further- more, the conductances show strong non-monotonic variations with L and an intricate structure of resonant peaks and subpeaks. In 1d the positions of these peaks can be related precisely to the prop- erties of the number that characterizes the quasiperiodicity of the potential; and the L-dependence of the Thouless conductance is multifractal. We find that, as d increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our results for $\beta(g)$ are reasonably well approximated by single-parameter scaling.Comment: 13 pages, 6 figure

Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations

We provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the non-interacting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all SP excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the non-local FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the decay of the non-local propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.Comment: 17 pages, 15 figures (main text + Appendices

Carbon Nanotube and Its Derived Nanomaterials Based High Performance Biosensing Platform

After the COVID-19 pandemic, the development of an accurate diagnosis and monitoring of diseases became a more important issue. In order to fabricate high-performance and sensitive biosensors, many researchers and scientists have used many kinds of nanomaterials such as metal nanoparticles (NPs), metal oxide NPs, quantum dots (QDs), and carbon nanomaterials including graphene and carbon nanotubes (CNTs). Among them, CNTs have been considered important biosensing channel candidates due to their excellent physical properties such as high electrical conductivity, strong mechanical properties, plasmonic properties, and so on. Thus, in this review, CNT-based biosensing systems are introduced and various sensing approaches such as electrochemical, optical, and electrical methods are reported. Moreover, such biosensing platforms showed excellent sensitivity and high selectivity against not only viruses but also virus DNA structures. So, based on the amazing potential of CNTs-based biosensing systems, healthcare and public health can be significantly improved