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Mesoscale and Nanoscale PhysicsEnglishPublished

Theoretical calculation of electron–phonon cooling noise in monolayer and bilayer graphene

November 4, 2026arXiv: 2611.03316v1

A recent theoretical study computes how electrons in monolayer and bilayer graphene exchange heat with lattice vibrations. The authors build a symmetric heat–current operator and evaluate the non‑equilibrium current–current correlator at finite frequency for unequal electron and phonon temperatures. Analysis yields full analytic expressions in the Bloch–Grüneisen (BG) and equipartition (EP) regimes, and their low‑frequency limits are compared with complete doped intraband on‑shell calculations.

At equilibrium the zero‑frequency noise obeys the thermal fluctuation–dissipation theorem and reproduces established cooling‑power and thermal‑conductance laws. In the BG regime the equilibrium noise scales as |μ| T⁵, while in the EP regime it scales as T⁴ for monolayer graphene and follows a different chemical‑potential dependence for bilayer graphene.

Table 1 shows equilibrium zero‑frequency noise power‑law scalings for monolayer and bilayer graphene in the Bloch–Grüneisen and equipartition regimes, with explicit μ and T dependencies.
System and RegimeCooling lawGep/A
S⁡(0)/A
MLG BGΣMLG​(Te4−Tph4)4​ΣMLG​T38​kB​ΣMLG​T5
MLG EPgMLG​(μ,Te)​(Te−Tph)gMLG​(μ,T)2​kB​T2​gMLG​(μ,T)
BLG BGΣBLG​(Te4−Tph4)4​ΣBLG​T38​kB​ΣBLG​T5
BLG EPgBLG​(μ,Te)​(Te−Tph)gBLG​(μ,T)2​kB​T2​gBLG​(μ,T)
Table 1. Table 1 lists the equilibrium zero‑frequency noise scalings measured in the Bloch–Grüneisen regime (|μ| T⁵) and, in the equipartition limit, the T⁴ scaling for monolayer graphene and the distinct chemical‑potential dependence for bilayer graphene.Haseeb, Muhammad Waqas, Idrisov, Edvin G. · arXiv:2611.03316v1 · Table 1: · CC BY 4.0

Finite‑frequency corrections are at the percent level in the upper‑GHz to sub‑THz range for representative graphene parameters. This indicates that for fast thermometry and calorimetric detection, the noise must be evaluated directly rather than inferred from conductance.

Figure 5 displays a contour map of the finite‑frequency percentage correction to noise as a function of frequency and temperature bias for monolayer and bilayer graphene, highlighting corrections up to 10 % in the sub‑THz range.
Figure 5. Figure 5 maps the finite‑frequency percentage correction 𝒫 (contours at 1 %, 5 %, and 10 %) versus ordinary frequency and symmetric temperature bias for representative graphene parameters, illustrating percent‑level corrections in the upper‑GHz to sub‑THz window.Haseeb, Muhammad Waqas, Idrisov, Edvin G. · arXiv:2611.03316v1 · Figure 5: · CC BY 4.0

The model focuses on clean graphene coupled only to longitudinal acoustic phonons through an unscreened deformation potential. It does not include screening, disorder‑assisted supercollisions, flexural or optical phonons, substrate modes, or interface thermal resistance. The analytical results assume |μ|≫k_B T and that all relevant frequencies remain far below the interlayer hopping energy γ₁, ensuring the validity of the low‑energy bilayer description.

The Bloch–Grüneisen and equipartition expressions are asymptotic limits; a full on‑shell calculation is needed to capture the crossover at intermediate temperatures.

Source paper

Electron--phonon cooling noise in monolayer and bilayer graphene

Mesoscale and Nanoscale Physics
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