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Quantum transport and microwave scattering on fractal lattices

  • Krishnasamy Subramaniam , Matthias Zschornak EMAIL logo and Sibylle Gemming
Published/Copyright: March 24, 2022
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 237 Issue 4-5

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.

Keywords: electromagnetic waves; electron transport; electronic behavior; metamaterial; Sierpinski triangle; tight binding
Corresponding author: Matthias Zschornak, TU Chemnitz, Institute of Physics, Reichenhainer Straße 70, D-09126 Chemnitz, Germany; and TU Bergakademie Freiberg, Leipziger Straße 23, D-09596 Freiberg, Germany, E-mail:

Funding source: DFG

Award Identifier / Grant number: 405595647

Award Identifier / Grant number: 409743569

Award Identifier / Grant number: 442646446

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors acknowledge funding by the DFG within the projects DFG 405595647 (GE 1202/12-1), DFG 409743569 (ZS 120/1-1), and DFG 442646446 (ZS 120/5-1).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix

The electronic structure was created using Pybinding with in-lead connections at the bottom and the out-connection at the top. The in-lead connections have multiple paths to inject electrons and the out-lead connection does not have multiple paths for electrons to leave. The transport calculations are achieved by using Kwant, by exporting the complete structure with in-lead and out-lead connections from Pybinding to Kwant.

Figure A.1: (a) The electronic structure for iteration 3 of the ST with in-lead as lead 0 and out-lead as lead 1 (at the left), (b) The experimental setup with initial scattering angle ( θ = 0 ° $\theta =0^{\circ} $ ) for the sample orientation 0 ° ${0}^{^{\circ} }$ (at the right).
Figure A.1:

(a) The electronic structure for iteration 3 of the ST with in-lead as lead 0 and out-lead as lead 1 (at the left), (b) The experimental setup with initial scattering angle ( θ = 0 ° ) for the sample orientation 0 ° (at the right).

The experimental setup [39] has microwave transmitter (at the top left) and receiver (at the top right) with a horn shaped outlet, where the transmitter and the receiver are free to move from 0 to 90° together in a coupled mode. The microwave transmitter connected to the power supply setup (at the bottom left) for generating microwave frequencies and the received signals are processed using the receiver setup (at the bottom right) and then measured using a multimeter. The sample was placed in the center which is free to rotate from 0 to 360°.

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Received: 2021-11-29
Accepted: 2022-02-16
Published Online: 2022-03-24
Published in Print: 2022-05-25

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. In this issue
  3. Preface
  4. Crystallography in Germany rejuvenated
  5. Original Papers
  6. CalcOPP: a program for the calculation of one-particle potentials (OPPs)
  7. Synthesis and coordination to the coinage metals of a trimethylpyrazolyl substituted 3-arylacetylacetone
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  9. Structural study of anhydrous and hydrated 5-fluorouracil co-crystals with nicotinamide and isonicotinamide
  10. Synthesis, crystal-structure refinement and properties of bastnaesite-type PrF[CO3], SmF[CO3] and EuF[CO3]
  11. Crystallographic complexity partition analysis
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  13. Structure relations in the family of the solid solution Hf x Zr1−x O2
  14. The crystal structure of single crystalline PrCa4O[BO3]3
  15. Crystal structure of a hexacationic Ag(I)-pillarplex-dodecyl-diammonium pseudo-rotaxane as terephthalate salt
  16. Quantum transport and microwave scattering on fractal lattices
  17. Leveraging dewetting models rather than nucleation models: current crystallographic challenges in interfacial and nanomaterials research
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https://doi.org/10.1515/zkri-2021-2070
Keywords for this article
electromagnetic waves; electron transport; electronic behavior; metamaterial; Sierpinski triangle; tight binding

Articles in the same Issue

  1. Frontmatter
  2. In this issue
  3. Preface
  4. Crystallography in Germany rejuvenated
  5. Original Papers
  6. CalcOPP: a program for the calculation of one-particle potentials (OPPs)
  7. Synthesis and coordination to the coinage metals of a trimethylpyrazolyl substituted 3-arylacetylacetone
  8. Occupancy disorder in the magnetic topological insulator candidate Mn1−x Sb2+x Te4
  9. Structural study of anhydrous and hydrated 5-fluorouracil co-crystals with nicotinamide and isonicotinamide
  10. Synthesis, crystal-structure refinement and properties of bastnaesite-type PrF[CO3], SmF[CO3] and EuF[CO3]
  11. Crystallographic complexity partition analysis
  12. The “ferros” of MAPbI3: ferroelectricity, ferroelasticity and its crystallographic foundations in hybrid halide perovskites
  13. Structure relations in the family of the solid solution Hf x Zr1−x O2
  14. The crystal structure of single crystalline PrCa4O[BO3]3
  15. Crystal structure of a hexacationic Ag(I)-pillarplex-dodecyl-diammonium pseudo-rotaxane as terephthalate salt
  16. Quantum transport and microwave scattering on fractal lattices
  17. Leveraging dewetting models rather than nucleation models: current crystallographic challenges in interfacial and nanomaterials research
  18. Electronic structure of the homologous series of Ruddlesden–Popper phases SrO(SrTiO3) n , (n = 0–3, ∞)
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