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We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature T / V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on $Tproptosqrt{V}$ behavior at high bias, which corresponds to a T4 dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant $Sigma$ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of $Sigma$, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.
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Many promising optoelectronic devices, such as broadband photodetectors, nonlinear frequency converters, and building blocks for data communication systems, exploit photoexcited charge carriers in graphene. For these systems, it is essential to understand, and eventually control, the cooling dynamics of the photoinduced hot-carrier distribution. There is, however, still an active debate on the different mechanisms that contribute to hot-carrier cooling. In particular, the intrinsic cooling mechanism that ultimately limits the cooling dynamics remains an open question. Here, we address this question by studying two technologically relevant systems, consisting of high-quality graphene with a mobility >10,000 cm$^2$V$^{-1}$s$^{-1}$ and environments that do not efficiently take up electronic heat from graphene: WSe$_2$-encapsulated graphene and suspended graphene. We study the cooling dynamics of these two high-quality graphene systems using ultrafast pump-probe spectroscopy at room temperature. Cooling via disorder-assisted acoustic phonon scattering and out-of-plane heat transfer to the environment is relatively inefficient in these systems, predicting a cooling time of tens of picoseconds. However, we observe much faster cooling, on a timescale of a few picoseconds. We attribute this to an intrinsic cooling mechanism, where carriers in the hot-carrier distribution with enough kinetic energy emit optical phonons. During phonon emission, the electronic system continuously re-thermalizes, re-creating carriers with enough energy to emit optical phonons. We develop an analytical model that explains the observed dynamics, where cooling is eventually limited by optical-to-acoustic phonon coupling. These fundamental insights into the intrinsic cooling mechanism of hot carriers in graphene will play a key role in guiding the development of graphene-based optoelectronic devices.
We study a setup where a single negatively-charged silicon-vacancy center in diamond is magnetically coupled to a low-frequency mechanical bending mode and via strain to the high-frequency phonon continuum of a semi-clamped diamond beam. We show that under appropriate microwave driving conditions, this setup can be used to induce a laser cooling like effect for the low-frequency mechanical vibrations, where the high-frequency longitudinal compression modes of the beam serve as an intrinsic low-temperature reservoir. We evaluate the experimental conditions under which cooling close to the quantum ground state can be achieved and describe an extended scheme for the preparation of a stationary entangled state between two mechanical modes. By relying on intrinsic properties of the mechanical beam only, this approach offers an interesting alternative for quantum manipulation schemes of mechanical systems, where otherwise efficient optomechanical interactions are not available.
Recent theory has predicted large temperature differences between the in-plane (LA and TA) and out-of-plane (ZA) acoustic phonon baths in locally-heated suspended graphene. To verify these predictions, and their implications for understanding the nonequilibrium thermodynamics of 2D materials, experimental techniques are needed. Here, we present a method to determine the acoustic phonon bath temperatures from the frequency-dependent mechanical response of suspended graphene to a power modulated laser. The mechanical motion reveals two counteracting contributions to the thermal expansion force, that are attributed to fast positive thermal expansion by the in-plane phonons and slower negative thermal expansion by the out-of-plane phonons. The magnitude of the two forces reveals that the in-plane and flexural acoustic phonons are at very different temperatures in the steady-state, with typically observed values of the ratio $Delta T_{mathrm{LA+TA}}/Delta T_{mathrm{ZA}}$ between 0.2 and 3.7. These deviations from the generally used local thermal equilibrium assumption ($Delta T_{mathrm{LA+TA}}=Delta T_{mathrm{ZA}}$) can affect the experimental analysis of thermal properties of 2D materials.
At high phonon temperature, defect-mediated electron-phonon collisions (supercollisions) in graphene allow for larger energy transfer and faster cooling of hot electrons than the normal, momentum-conserving electron-phonon collisions. Disorder also affects the heat flow between electrons and phonons at very low phonon temperature, where the phonon wavelength exceeds the mean free path. In both cases, the cooling rate is predicted to exhibit a characteristic cubic power law dependence on the electron temperature, markedly different from the T^4 dependence predicted for pristine graphene. The impact of defect-induced cooling on the performance of optoelectronic devices is still largely unexplored. Here we study the cooling mechanism of hot-electron bolometers based on epitaxial graphene quantum dots where the defect density can be controlled with the fabrication process. The devices with high defect density exhibit the cubic power law. Defect-induced cooling yields a slower increase of the thermal conductance with increasing temperature, thereby greatly enhancing the device responsivity compared to devices with lower defect density and operating with normal-collision cooling.
Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the experimental data over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4-150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.
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