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Scaling properties of mono-layer graphene away from the Dirac point
Statistical Mechanics · Submitted 24 Mar 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that, the chemical potential in this system as a random surface, destroys the self-similarity, and the charge field is non-Gaussian.
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The abstract, sentence by sentence
The statistical properties of the carrier density profile of graphene in the ground state in the presence particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi \textit{et al.} (Phys. Rev E95, 032112 (2017)). The non-zero chemical potential ($\mu$) in gated graphene has non-trivial effects on electron-hole puddles, since it generates mass in the Dirac action and destroys the scaling behaviors of the effective Thomas-Fermi-Dirac theory. We provide detailed analysis on the resulting spatially inhomogeneous system in the framework of the Thomas-Fermi-Dirac theory for the Gaussian (white noise) disorder potential. We show that, the chemical potential in this system as a random surface, destroys the self-similarity, and the charge field is non-Gaussian. We find that the two-body correlation functions are factorized to two terms: a pure function of the chemical potential and a pure function of the distance. The spatial dependence of these correlation functions is double-logarithmic, e.g. the two-point density correlation $D_2(r,\mu)\propto \mu^2\exp\left[-\left(-a_D\ln\ln r^{\beta_D}\right)^{\alpha_D} \right]$ ($\alpha_D=1.82$, $\beta_D=0.263$ and $a_D=0.955$). The Fourier power spectrum function behaves like $\ln(S(q))=-\beta_S^{-a_S}\left(\ln q \right)^{a_S}+2\ln \mu$ ($a_S=3.0\pm 0.1$ and $\beta_S=2.08\pm 0.03$) in contrast to the ordinary Gaussian rough surfaces for which $a_S=1$ and $\beta_S=\frac{1}{2}(1+\alpha)^{-1}$, ($\alpha$ being the roughness exponent). The geometrical properties are however similar to the un-gated ($\mu=0$) case, with the exponents that are reported in the text.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The statistical properties of the carrier density profile of graphene in the ground state in the presence particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi \textit{et al.} (Phys. Rev E95, 032112 (2017)). | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s1 | The non-zero chemical potential ($\mu$) in gated graphene has non-trivial effects on electron-hole puddles, since it generates mass in the Dirac action and destroys the scaling behaviors of the effective Thomas-Fermi-Dirac theory. | background 0.88 | 0.19 | 0.23 | asserted 1.00 |
| s2 | We provide detailed analysis on the resulting spatially inhomogeneous system in the framework of the Thomas-Fermi-Dirac theory for the Gaussian (white noise) disorder potential. | method 0.64 | 0.88 | 0.05 | asserted 0.88 |
| s3 | We show that, the chemical potential in this system as a random surface, destroys the self-similarity, and the charge field is non-Gaussian. | result 0.98 | 0.91 | 0.30 | asserted 1.00 |
| s4 | We find that the two-body correlation functions are factorized to two terms: a pure function of the chemical potential and a pure function of the distance. | result 1.00 | 0.95 | 0.21 | asserted 1.00 |
| s5 | The spatial dependence of these correlation functions is double-logarithmic, e.g. the two-point density correlation $D_2(r,\mu)\propto \mu^2\exp\left[-\left(-a_D\ln\ln r^{\beta_D}\right)^{\alpha_D} \right]$ ($\alpha_D=1.82$, $\beta_D=0.263$ and $a_D=0.955$). | result 1.00 | 0.93 | 0.27 | asserted 1.00 |
| s6 | The Fourier power spectrum function behaves like $\ln(S(q))=-\beta_S^{-a_S}\left(\ln q \right)^{a_S}+2\ln \mu$ ($a_S=3.0\pm 0.1$ and $\beta_S=2.08\pm 0.03$) in contrast to the ordinary Gaussian rough surfaces for which $a_S=1$ and $\beta_S=\frac{1}{2}(1+\alpha)^{-1}$, ($\alpha$ being the roughness exponent). | result 1.00 | 0.85 | 0.19 | asserted 1.00 |
| s7 | The geometrical properties are however similar to the un-gated ($\mu=0$) case, with the exponents that are reported in the text. | result 0.62 | 0.65 | 0.11 | asserted 0.99 |
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The paper
Original abstract
The statistical properties of the carrier density profile of graphene in the ground state in the presence particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi \textit{et al.} (Phys. Rev E95, 032112 (2017)). The non-zero chemical potential ($\mu$) in gated graphene has non-trivial effects on electron-hole puddles, since it generates mass in the Dirac action and destroys the scaling behaviors of the effective Thomas-Fermi-Dirac theory. We provide detailed analysis on the resulting spatially inhomogeneous system in the framework of the Thomas-Fermi-Dirac theory for the Gaussian (white noise) disorder potential. We show that, the chemical potential in this system as a random surface, destroys the self-similarity, and the charge field is non-Gaussian. We find that the two-body correlation functions are factorized to two terms: a pure function of the chemical potential and a pure function of the distance. The spatial dependence of these correlation functions is double-logarithmic, e.g. the two-point density correlation $D_2(r,\mu)\propto \mu^2\exp\left[-\left(-a_D\ln\ln r^{\beta_D}\right)^{\alpha_D} \right]$ ($\alpha_D=1.82$, $\beta_D=0.263$ and $a_D=0.955$). The Fourier power spectrum function behaves like $\ln(S(q))=-\beta_S^{-a_S}\left(\ln q \right)^{a_S}+2\ln \mu$ ($a_S=3.0\pm 0.1$ and $\beta_S=2.08\pm 0.03$) in contrast to the ordinary Gaussian rough surfaces for which $a_S=1$ and $\beta_S=\frac{1}{2}(1+\alpha)^{-1}$, ($\alpha$ being the roughness exponent). The geometrical properties are however similar to the un-gated ($\mu=0$) case, with the exponents that are reported in the text.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
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The methods employed in these systems have wide applications, ranging from the classical [ref] to the quantum systems [ref] .
Gaussian Free Field in the iso-height random islands tuned by percolation model · A review on the scale-invariant rough surfaces · 0.98
What it cites · 2 sentences without a confident label
Cites as background 1 paper
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The other sources of scattering are ripples [ref] and point defects (which is responsible for high-density saturation of conductivity [ref] ) which are not considered in this paper.
Graphene as an electronic membrane · Ground state of Graphene · 0.80
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