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<p>We study the interplay of electron–phonon and electron–impurity scattering in graphene and its manifestations in thermopower <i>S</i>. Electron scattering by acoustic phonons dominating in clean samples results in energy-independent carrier diffusivity, which translates into zero value of <i>S</i>. Inclusion of charged impurities plays a twofold role. At low impurity densities, the diffusivity becomes energy-dependent, which elevates <i>S</i>. In largely disordered samples, the carrier density becomes inhomogeneous, which results in self-averaging of thermopower. The latter effect is tackled here with effective medium theory, and predicts a slow drop in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S\)</EquationSource> <!--JETPLet2560961Nikulin-m1--> </InlineEquation> with increasing the impurity density. The competition of these effects results in thermopower maximization at an optimal density of impurities <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{n}_{{{\text{imp}}}}}\)</EquationSource> <!--JETPLet2560961Nikulin-m2--> </InlineEquation>. The latter is estimated as <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(2 \times {{10}^{{11}}}\)</EquationSource> <!--JETPLet2560961Nikulin-m3--> </InlineEquation> cm<sup>–2</sup> at room temperature, which corresponds to the highest-quality chemical vapor deposited graphene.</p>

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Maximization of Thermopower in Optimally-Disordered Graphene

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • E. I. Nikulin,
  • A. I. Chernov,
  • D. A. Svintsov

摘要

We study the interplay of electron–phonon and electron–impurity scattering in graphene and its manifestations in thermopower S. Electron scattering by acoustic phonons dominating in clean samples results in energy-independent carrier diffusivity, which translates into zero value of S. Inclusion of charged impurities plays a twofold role. At low impurity densities, the diffusivity becomes energy-dependent, which elevates S. In largely disordered samples, the carrier density becomes inhomogeneous, which results in self-averaging of thermopower. The latter effect is tackled here with effective medium theory, and predicts a slow drop in \(S\) with increasing the impurity density. The competition of these effects results in thermopower maximization at an optimal density of impurities \({{n}_{{{\text{imp}}}}}\) . The latter is estimated as \(2 \times {{10}^{{11}}}\) cm–2 at room temperature, which corresponds to the highest-quality chemical vapor deposited graphene.