Multiple optical harmonic generation-the multiplication of photon energy as a result of nonlinear interaction between light and matter-is a key technology in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency, and the generation of frequency combs. Owing to the unique electronic band structure of graphene, which features massless Dirac fermions, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technologically important terahertz frequencies. However, these predictions have yet to be confirmed experimentally under technologically relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temperature and under ambient conditions, driven by terahertz fields of only tens of kilovolts per centimetre, and with field conversion efficiencies in excess of 10, 10 and 10 for the third, fifth and seventh terahertz harmonics, respectively. These conversion efficiencies are remarkably high, given that the electromagnetic interaction occurs in a single atomic layer. The key to such extremely efficient generation of terahertz high harmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were observed directly in the time domain as electromagnetic field oscillations at these newly synthesized higher frequencies. The effective nonlinear optical coefficients of graphene for the third, fifth and seventh harmonics exceed the respective nonlinear coefficients of typical solids by 7-18 orders of magnitude. Our results provide a direct pathway to highly efficient terahertz frequency synthesis using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.

The outstanding charge transport properties of graphene enable numerous electronic applications of this remarkable material, many of which are expected to operate at ultrahigh speeds. In the regime of ultrafast, sub-picosecond electric fields, however, the very high conduction properties of graphene are not necessarily preserved, with the physical picture explaining this behaviour remaining unclear. Here we show that in graphene, the charge transport on an ultrafast timescale is determined by a simple thermodynamic balance maintained within the graphene electronic system acting as a thermalized electron gas. The energy of ultrafast electric fields applied to graphene is converted into the thermal energy of its entire charge carrier population, near-instantaneously raising the electronic temperature. The dynamic interplay between heating and cooling of the electron gas ultimately defines the ultrafast conductivity of graphene, which in a highly nonlinear manner depends on the dynamics and the strength of the applied electric fields.

For most optoelectronic applications of graphene, a thorough understanding of the processes that govern energy relaxation of photoexcited carriers is essential. The ultrafast energy relaxation in graphene occurs through two competing pathways: carrier−carrier scattering, creating an elevated carrier temperature, and optical phonon emission. At present, it is not clear what determines the dominating relaxation pathway. Here we reach a unifying picture of the ultrafast energy relaxation by investigating the terahertz photoconductivity, while varying the Fermi energy, photon energy and fluence over a wide range. We find that sufficiently low fluence (≲4 μJ/cm 2 ) in conjunction with sufficiently high Fermi energy (≳0.1 eV) gives rise to energy relaxation that is dominated by carrier−carrier scattering, which leads to efficient carrier heating. Upon increasing the fluence or decreasing the Fermi energy, the carrier heating efficiency decreases, presumably due to energy relaxation that becomes increasingly dominated by phonon emission. Carrier heating through carrier−carrier scattering accounts for the negative photoconductivity for doped graphene observed at terahertz frequencies. We present a simple model that reproduces the data for a wide range of Fermi levels and excitation energies and allows us to qualitatively assess how the branching ratio between the two distinct relaxation pathways depends on excitation fluence and Fermi energy. KEYWORDS: Graphene, ultrafast, hot carrier, terahertz, pump−probe G raphene is a promising material for, among others, photosensing and photovoltaic applications, 1 owing to its broadband absorption, 2,3 its high carrier mobility 4,5 and the ability to create a photovoltage from heated electrons or holes. It furthermore uniquely allows for electrical control of the carrier density and polarity. 4 To establish the potential and limitations of graphene-based optoelectronic devices, a thorough understanding of the ultrafast (subpicosecond) primary energy relaxation dynamics of photoexcited carriers is essential. For undoped graphene (with Fermi energy E F ≈ 0), ultrafast energy relaxation through interband carrier−carrier scattering was predicted 7 and observed 8,9 to lead to multiple electron−hole pair excitation. For doped graphene (with Fermi energy |E F | > 0), ultrafast energy relaxation through carrier− carrier interaction also plays an important role, with intraband scattering leading to carrier heating. 10−13 In addition, the ultrafast energy relaxation was ascribed to optical phonon emission, 14,15 which reduces the carrier heating efficiency. Closely related, for undoped graphene the sign of the terahertz (THz) photoconductivity is positive (see, e.g., refs 16−19), whereas for intrinsically doped graphene the sign is negative, meaning that photoexcitation gives rise to an apparent decrease of conductivity. 11,16,17,20−22 This negative photoconductivity was attributed to stimulated THz emission 20 and to a reduction of the intrinsic conductivity by enhanced scatte...

Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities, and superior electrical and optoelectronic properties [1][2][3][4][5][6][7]. Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting [8][9][10][11][12][13][14][15][16] require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons [17][18][19] in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times, for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism through distinct control knobs to vary carrier density and lattice temperature, and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.Owing to its large in-plane thermal conductivity, graphene has been suggested as material for the thermal management of nanoscale devices [8]. At the same time, graphene is well-known for its ability to convert incident light into electrical heat, i.e. hot electrons that can be used to generate photocurrent, with applications in photodetection, data communication and light harvesting [10,20,21]. Understanding, and ultimately controlling, heat flow in graphene-van der Waals heterostructures is therefore of paramount importance. For example, a short cooling time of graphene hot carriers is advantageous for thermal management and for high switching rates of photodetectors (PDs) for data communication, whereas a long cooling time is favorable for photodetection sensitivity [10,20,21]. Of particular relevance are heterostructure devices that contain high-quality graphene encapsulated by layered materials, such as hexagonal BN (hBN) and MoS 2 , which have the potential to crucially improve the performance of electronic and optoelectronic devices [1,2]. * Electronic address: Correspondence: klaas-jan.tielrooij@icfo.eu, frank.koppens@icfo.eu ‡ Equal contribution.A number of cooling pathways for graphene carriers have been proposed, involving among others strongly coupled optical phonons [22][23][24], acoustic phonons [25][26][27][28], substrate phonons [29] and plasmons [30] (see also Appendix 1). Here, using several experimental approaches, we show that cooling in graphene encapsulated by hBN is governed by out-of-plane coupling of graphene electrons to special polar phonon modes that occur in layered materials (LMs): hyperbolic phonon polaritons, where xx zz < 0, with xx and zz the permittivity parallel and perpendicular to the LM plane. Owing to this property, these materials carry deep sub-wavelength, raylike optical phonon polaritons. For hBN, within the two Rest...

On-chip micro-supercapacitors (MSCs) are important Si-compatible power-source backups for miniaturized electronics. Despite their tremendous advantages, current on-chip MSCs require harsh processing conditions and typically perform like resistors when filtering ripples from alternating current (AC). Herein, we demonstrated a facile layer-by-layer method towards on-chip MSCs based on an azulene-bridged coordination polymer framework (PiCBA). Owing to the good carrier mobility (5×10 cm V s ) of PiCBA, the permanent dipole moment of azulene skeleton, and ultralow band gap of PiCBA, the fabricated MSCs delivered high specific capacitances of up to 34.1 F cm at 50 mV s and a high volumetric power density of 1323 W cm . Most importantly, such MCSs exhibited AC line-filtering performance (-73° at 120 Hz) with a short resistance-capacitance constant of circa 0.83 ms.