Universal conductance fluctuations in Sierpinski carpets

Han, Yulei; Qiao, Zhenhua

doi:10.1007/s11467-019-0919-y

Cited by 10 publications

(4 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sharp peaks in the optical spectrum emerge as a result of electronic transitions between a set of unique state pairings contained in the SC at specified length scales [34]. More theoretical calculations on electronic transport [35,36], quantum Hall effect [37,38], plasmon [39], flatbands [40][41][42], energy spectrum statistics [43], and topological features [44][45][46] point to future applications in electronics and optoelectronics.…”

Section: Introductionmentioning

confidence: 94%

Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

Majhi

Maiti

2023

J. Phys. D: Appl. Phys.

View full text Add to dashboard Cite

In this work, we theoretically investigate the phenomenon of spin polarization in generalized Sierpinski Gasket (SPG) triangles($\Delta NNN$, $\Delta FNN$, $\Delta FFN$, $\Delta FFF$) in the presence of Rashba spin-orbit interaction (RSOI) within a tight-binding(TB) framework. The geometrical construction is addressed for all four types of generalized SPG triangles using an iterative functionsystem that begins with a fixed triangle of any arbitrary side length. The geometry of various types of fractal networks has a majorimpact on the degeneracy of the energy spectrum. It is shown that only the two-terminal setup in the presence of Rashba spin-orbitinteraction is incapable of breaking the spin degeneracy, which necessitates the use of a three-terminal setup to break thetime-reversal symmetry. The effect of flip map induced anisotropic hopping integrals on three-terminal spin-resolved transmissionprobabilities is studied. In several cases, we find almost $100\%$ spin polarization in our considered lattices. We also analyze howspin polarization varies with Rashba spin-orbit interaction strength and fractal generations. Our results indicate that fractal latticesmight be suitable functional elements in designing future spin-based electronic devices.

show abstract

Section: Introductionmentioning

confidence: 94%

Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

Majhi

Maiti

2023

J. Phys. D: Appl. Phys.

View full text Add to dashboard Cite

show abstract

“…A fractal has a hierarchically self-similar block structure quantified by the noninteger Hausdorff dimension d H [1][2][3][4]. The unique self-similarity endows fractal nanostructures with a wealth of exotic and interesting physical features on electronic energy spectrum statistics [5][6][7][8], quantum transport properties [9][10][11][12][13][14][15][16], plasmons [17], flat bands [18][19][20][21], and topological phases [22][23][24][25][26]. Recently, nanoscale fractal structures, such as Sierpinski carpets (SC) and gaskets with atoms or molecules as building units, have been achieved by the bottom-up nanofabrication methods, including molecular selfassembly [27][28][29][30][31][32][33], chemical reactions [34], template packings [35], and atomic manipulations in a scanning tunneling microscope [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Electronic properties and quantum transport in functionalized graphene Sierpinski-carpet fractals

et al. 2022

View full text Add to dashboard Cite

Recent progress in the controllable functionalization of graphene surfaces enables the experimental realization of complex functionalized graphene nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model the SC fractals formed by hydrogen and fluorine functionalized patterns on graphene surfaces, namely, H-SC and F-SC, respectively. We then reveal their electronic properties and quantum transport features. From the calculated results of the total and local densities of state, we find that states in H-SC and F-SC have two characteristics: (i) low-energy states inside about |E /t| 1 (with t as the nearest-neighbor hopping) are localized inside free graphene regions due to the insulating properties of functionalized graphene regions and (ii) high-energy states in F-SC have two special energy ranges including −2.3 < E /t < −1.9 with localized holes only inside free graphene areas and 3 < E /t < 3.7 with localized electrons only inside fluorinated graphene areas. The two characteristics are further verified by the real-space distributions of normalized probability density. We analyze the fractal dimension of their quantum conductance spectra and find that conductance fluctuations in these structures follow the Hausdorff dimension. We calculate their optical conductivity and find that several additional conductivity peaks appear in high-energy ranges due to the adsorbed H or F atoms.

show abstract

“…A fractal, with non-integer Hausdorff dimension d H [1][2][3][4], has a hierarchically self-similar structure. The intrinsic features from this, including electronic energy spectrum statistics and transport [5][6][7][8][9][10][11][12][13][14], quantum Hall effect [15,16], plasmon [17], flat bands [18][19][20][21], and topological properties [22][23][24][25][26] have attracted dense interest. For example, d H determines the box-counting dimension of quantum conductance fluctuations in Sierpinski carpet geometry with infinite ramification number [2,10], and there are sharp peaks in the optical spectrum due to the specific electronic state pairs [11].…”

Section: Introductionmentioning

confidence: 99%

Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals

Yang,

Zhou,

Yao

et al. 2021

Preprint

View full text Add to dashboard Cite

We propose a way to create effective plane fractals for confined electrons by chemical surface doping in two-dimensional materials. In particular, for Sierpinski carpet (SC), we consider the adsorption of hydrogen or fluorine atoms on monolayer graphene, forming an effective fractional geometry (H-SC and F-SC). By calculating the spatial distribution of states and the fractal analysis of quantum conductance fluctuations of H-SC, F-SC, and real SC, we find there is a consistency of the electronic states in these different systems. Further optical calculations verified the fractional confinement of electrons in H-SC and F-SC. Our results indicate that the chemical surface doping on graphene is an efficient and accessible approach to confine the electrons roaming in a fractional dimension, and will stimulate further theoretical and experimental studies of fractals based on twodimensional materials.

show abstract

Universal conductance fluctuations in Sierpinski carpets

Cited by 10 publications

References 34 publications

Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

Electronic properties and quantum transport in functionalized graphene Sierpinski-carpet fractals

Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals

Contact Info

Product

Resources

About