Quantum transport and microwave scattering on fractal lattices

Abstract

Studying the wave-particle nature of electrons in different ways has lead to many fundamental discoveries. Particularly, the dimensionality dependent electronic behavior in the Luttinger Liquid (1D), Quantum Hall (2D) and non-interacting Fermi Liquid (3D) regimes have already revolutionized our understanding of the mechanisms behind quantum electronics. In this work, the theoretical and experimental studies focus on the non-integer dimension represented by an sp2-carbon-based Sierpinski triangular structure with a 1.58D space occupancy. In the tight-binding approach, the spectral distribution of electronic states of such a structure exhibits distinct peak patterns, which are well-separated by gaps. Through quantum transport simulation, the conductance of electrons in 1.58D was studied. Both delocalized, conducting and localized, non-conducting states identified, which differ from the established features of both the fully 2D graphene sheet and 1D carbon nanotubes. In microwave scattering measurements on an adequate experimental setting and the respective simulations on the Sierpinski triangle, the obtained diffraction patterns showed interesting peculiarities such as a reduced number of minima and magic angle, next to diffraction regions of high and low intensity, as well as forbidden regions. The fractal geometry of the structure affects the propagation of waves by manipulating the way they interact with each other which results in structural metamaterial-like interference characteristics, decreasing or amplifying the transmitted or reflected signals, or blocking the transport completely.

‘Young crystallographers’ rejuvenate crystallography in Germany

“…Finally, possibly our biggest project so far was our special issue, which appeared in 2022 in the journal Zeitschrift fu ¨r Kristallographie. This issue featured contributions from young crystallographers from all over Germany on a wide variety of topics, including Theory (Subramaniam et al, 2022;Ernst et al, 2022;Nentwich et al, 2022b;Hornfeck, 2022;Wiedemann, 2022), Crystal Growth (van Terwingen et al, 2022;Weigel et al, 2022, Buyer et al, 2022, Structure Solution (Heinen et al, 2022;Folkers et al, 2022;Heidecker et al, 2022), and Properties (Ludt & Zschornak, 2022;Breternitz, 2022).…”

Simultaneous occurrence and compensating effects of multi‐type disorder in two‐dimensional photonic structures

“…Most recently, the topic of transport in disordered structures has also reached the field of acoustics. [23,24] In spite of these manifold applications, fundamental investigations of the functionality limits of real photonic systems have so far looked at individual geometric types disorder, [25][26][27] yet mostly neglected correlations between several types of disorder and the respective influence on device performance. [28] However, these can play a decisive role: deviations from ideal crystallinity occur both in natural and artificial systems.…”