Temperature dependence of phonon-induced current noise in micrometer-long metallic carbon nanotubes

Abstract We theoretically investigate the temperature dependence of phonon-induced current noise in micrometer-long metallic single-walled carbon nanotubes using large-scale time-dependent quantum transport simulations. We find that both the average current and its variance exhibit power-law dependencies on temperature in the high-temperature diffusive regime: 〈 J K 〉 ∝ 1/ T and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">〉</mml:mo> <mml:mo>∝</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> , respectively. The observed 1/ T 2 behavior of the current variance stands in stark contrast to the equilibrium Johnson–Nyquist noise, which increases linearly with temperature. Furthermore, we show that the current variance follows a universal scaling law as a function of the normalized channel length L / L 0 , where L 0 denotes the phonon-limited mean free path. This behavior is quantitatively explained by a Gamma-distributed probability density function for the current, combined with a phenomenological model for electronic transport incorporating dephasing effects due to electron–phonon scattering.