Self-similar conductance patterns in graphene Cantor-like structures

The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of 2 × 2 matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost the same in shape. Whereas, for the smaller wavelength case, the conductivity is strongly modified. In spite of this, for energies close to the Dirac point energy, the conductivity and the Fano factor are quite similar to their unstrained counterpart for the two strain wavelengths here studied.

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“…In this appendix we derive Eqs. (13), (14), (15), and (16). We start by studying each case out of the four possible for Eq.…”

Section: Appendix Amentioning

confidence: 99%

Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

Espinosa-Champo

Roman‐Taboada

Naumis

2018

Physica E: Low-dimensional Systems and Nanostructures

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“…Moreover, we will characterize mathematically the self-similar patterns by deriving scaling expressions numerically in the case of the conductance and spin polarization and analytically for the Seebeck coefficient. We will also show, as in the case of graphene complex structures 8 , that structural parameters such as the generation of the Cantor-like structure N, the height of the barriers and the length of the system w are directly involved in the scaling expressions (self-similar patterns). It is important to remark that all our numerical results are computed for the K valley ( η = +1 ), since the results for the K ′ valley ( η = −1 ) can be obtained straightforwardly by simply reversing the spin orientation, see Fig.…”

Section: Resultsmentioning

confidence: 89%

“…Determining the scale factors of the self-similar conductance patterns can be tricky. However, we can obtain them by following the protocol reported for graphene complex structures 8 . In particular, we can use an auxiliary conductance-related quantity to unravel the precise scale factors.…”

Section: Resultsmentioning

confidence: 99%

Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

Rodríguez-González

Gaggero‐Sager

Rodrı́guez-Vargas

2020

Sci Rep

Self Cite

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2D materials open the possibility to study Dirac electrons in complex self-similar geometries. The two-dimensional nature of materials like graphene, silicene, phosphorene and transition-metal dichalcogenides allow the nanostructuration of complex geometries through metallic electrodes, interacting substrates, strain, etc. So far, the only 2D material that presents physical properties that directly reflect the characteristics of the complex geometries is monolayer graphene. In the present work, we show that silicene nanostructured in complex fashion also displays self-similar characteristics in physical properties. In particular, we find self-similar patterns in the conductance, spin polarization and thermoelectricity of Cantor-like silicene structures. These complex structures are generated by modulating electrostatically the silicene local bandgap in Cantor-like fashion along the structure. The charge carriers are described quantum relativistically by means of a Dirac-like Hamiltonian. The transfer matrix method, the Landauer–Büttiker formalism and the Cutler–Mott formula are used to obtain the transmission, transport and thermoelectric properties. We numerically derive scaling rules that connect appropriately the self-similar conductance, spin polarization and Seebeck coefficient patterns. The scaling rules are related to the structural parameters that define the Cantor-like structure such as the generation and length of the system as well as the height of the potential barriers. As far as we know this is the first time that a 2D material beyond monolayer graphene shows self-similar quantum transport as well as that transport related properties like spin polarization and thermoelectricity manifest self-similarity.

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“…Since fractal dimension is indifferent towards grain size and aggregates, it may be a better indicator as a figure of merit for improving product characteristics in surface response methodology studies (Risović & Pavlović, 2013; Mitic et al ., 2019). Recent studies have investigated the effect of fractal dimension of optoelectrical materials (van Veen et al ., 2017; Rajabi Kalvani et al ., 2019; Ţălu et al ., 2019), and may even lead to self‐similar properties based on self‐similar grain morphology (Tavakoli & Jalili, 2014; García‐Cervantes et al ., 2017).…”

Section: Resultsmentioning

confidence: 99%

Quantitative SEM characterisation of ceramic target prior and after magnetron sputtering: a case study of aluminium zinc oxide

Jahangiri

Kalvani

Shapouri

et al. 2020

Journal of Microscopy

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Summary Till now electron microscopy techniques have not been used to evaluate the plasma–target interactions undergone during the magnetron sputtering process. The destructive nature of this interaction severely alters the target microstructure. Utilising quantitative microscopy techniques can shed light on the complex plasma and solid‐state processes involved which can ultimately lead to improved functional thin film deposition. As a representative functional material, aluminium‐doped‐zinc oxide (AZO) is an upcoming alternative to conventional transparent electrode wherein the process optimisation is of great importance. In this paper, we evaluate the pre‐ and post‐sputter field emission scanning electron microscopy (FESEM) data for ceramic AZO target fabricated at three final sintering temperatures (1100°C, 1200°C and 1300°C). In all cases, grain boundaries are merged in addition to a visible reduction in the secondary phases which makes segmentation‐based image analysis challenging. Through surface statistics (i.e. fractal dimension, autocorrelation length, texture aspect ratio and entropy) as a function of magnification we can quantify the electron microscopy image of the microstructure. We show that the plasma–microstructure interaction leads to an increase in autocorrelation length, texture aspect ratio and entropy for the optimum AZO ceramic sputtering target sintered at 1200°C. Furthermore, a maximum reduction in fractal dimension span (as determined by exponential regression) is also observed for 1200°C. In addition to the evaluation of plasma effects on sintering, our approach can provide a window towards understanding the underlying thin film growth mechanisms. We believe that this technique can be applied to the defect characterisation of a wide range of polycrystalline ceramic sputtering targets (e.g. ITO, CZTS, GAZO and so on) with the ultimate goal of improving the magnetron sputtering process and the resulting functional thin film. Lay Description Magnetron sputtering allows scientists to make functional thin films on the order of the nanoscale. In this technique, atoms are plucked from a ‘target’ then placed onto a substrate forming a thin nanometric film: all thanks to magnets, a special power supply and the fourth state of matter (plasma). Understanding what is going on and how to make a ‘good’ thin film is important for making better light emitting diodes, solar cells and light sensors. Scientists use electron microscopy to see what is going on in the microstructure of the sputtered thin films to fine tune the sputtering recipe. Here, for the first time, we have applied electron microscopy to see the surface of the microstructure before and after magnetron sputtering. This will help us understanding the plasma–microstructure interaction allowing us to make more informed decisions when fine‐tuning the sputtering process to get improved thin films. This is a case study of aluminium‐doped zinc oxide (AZO) target that could potentially replace indium tin oxide (ITO), which is widely used as a tra...

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Self-similar conductance patterns in graphene Cantor-like structures

Cited by 27 publications

References 31 publications

Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

Quantitative SEM characterisation of ceramic target prior and after magnetron sputtering: a case study of aluminium zinc oxide

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