High-field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math> noise in hBN-encapsulated graphene transistors

$1/f$ electronic noise is a conductance fluctuation, expressed in terms of a mobility ``$\ensuremath{\alpha}$-noise'' by Hooge and Kleinpenning. Understanding this noise in graphene is key for high-performance electronics. Early investigations pointed out a deviation from the standard Hooge formula, with the free-carrier density substituted by a constant density ${n}_{\mathrm{\ensuremath{\Delta}}}\ensuremath{\sim}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Here we investigate hBN-encapsulated graphene transistors where high mobility gives access to the velocity-saturation regime. We show that $\ensuremath{\alpha}$-noise is still accounted for by the Hooge formula on substituting conductance by differential conductance $G$, resulting in a bell-shaped dependence of flicker noise with bias voltage. The same analysis holds in the Zener regime at even larger bias, with two main differences. The first one is a strong enhancement of the Hooge parameter reflecting the hundred-times larger coupling of interband excitations to the hyperbolic phonon-polariton (HPhP) modes of the midinfrared Reststrahlen (RS) bands of hBN, which is supported by microwave noise thermometry measurements. The second is an exponential suppression of this coupling at large fields, which we attribute to decoherence effects. The phenomenology of $1/f$ noise in graphene supports a quantum-coherent bremsstrahlung interpretation of $\ensuremath{\alpha}$-noise.