Light-induced thermal noise textit{anomaly} governed by quantum metric

Traditionally, thermal noise in electric currents, arising from thermal agitation, is expected to increase with temperature $T$ and disappear as $T$ approaches zero. Contrary to this expectation, we discover that the resonant DC thermal noise (DTN) in photocurrents not only persists at $T=0$ but also exhibits a divergence proportional to $1/T$. This thermal noise \textit{anomaly} arises from the unique electron-photon interactions near the Fermi surface, manifesting as the interplay between the inherent Fermi-surface property and the resonant optical selection rules of DTN, and thereby represents an unexplored noise regime. Notably, we reveal that this \textit{anomalous} DTN, especially in time-reversal-invariant systems, is intrinsically linked to the quantum metric. We illustrate this \textit{anomalous} DTN in massless Dirac materials, including two-dimensional graphene, the surfaces of three-dimensional topological insulators, and three-dimensional Weyl semimetals, where the quantum metric plays a pivotal role. Finally, we find that the total noise spectrum at low temperatures, which includes both the DC shot noise and the \textit{anomalous} DTN, will universally peak at $\omega_p=2|\mu|$ with $\omega_p$ the frequency of light and $\mu$ the chemical potential of the bulk crystals.