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Precise synthesis of graphene nanoribbons (GNRs) is of great interest to chemists and materials scientists because of their unique opto-electronic properties and potential applications in carbon-based nanoelectronics and spintronics. In addition to the tunable edge structure and width, introducing curvature in GNRs is a powerful structural feature for their chemi-physical property modification. Here, we report an efficient solution synthesis of the first pyrene-based GNR (PyGNR) with curved geometry via one-pot K-region oxidation and Scholl cyclization of its corresponding well-soluble tetrahydropyrene-based polyphenylene precursor. The efficient A2B2-type Suzuki polymerization and subsequent Scholl reaction furnishes up to 35 nm long curved GNRs bearing cove- and armchair-edges. The construction of model compound, as a cutout of PyGNR, from a tetrahydropyrene-based oligophenylene precursor proves the concept and efficiency of the one-pot K-region oxidation and Scholl cyclization, which is clearly revealed by single crystal X-ray diffraction analysis. The structure and optical properties of PyGNR are investigated by Raman, FT-IR, solid-state NMR and UV-Vis analysis with the support of DFT calculations. PyGNR shows the absorption maximum at 680 nm, exhibiting a narrow optical bandgap of 1.4 eV, qualifying as a low-bandgap GNR. Moreover, THz spectroscopy on PyGNR estimates its macroscopic charge mobility of 3.6 cm2/Vs, outperforming other curved GNRs reported via conventional Scholl reaction.

Two-dimensional hybrid organic-inorganic metal halide perovskites offer enhanced stability for perovskite-based applications. Their crystal structure's soft and ionic nature gives rise to strong interactions between charge carriers and ionic rearrangements. Here, we investigate the interaction of photo-generated electrons and ionic polarizations in single-crystal 2D perovskite butylammonium lead iodide, varying the inorganic lammelae thickness in the 2D single crystals. We determined the directionality of the transition dipole moments of the relevant phonon modes (in the 0.3-3 THz range) by angle-and-polarization dependent THz transmission measurements. We find a clear anisotropy of the in-plane photoconductivity, with a 10% reduction along the axis parallel with the transition dipole moment of the most strongly coupled phonon. Detailed calculations, based on Feynman polaron theory, indicate that the anisotropy originates from directional electron-phonon interactions., Comment: 50 pages, 5 figures main text, 13 figures in supplementary information

Water plays a crucial role in geological, biological, and technological processes. Nanoscale water confinement occurs in many of these settings, including sedimentary rocks, water channel proteins, and applications like desalination and water purification membranes. The structure and properties of water in nanoconfinement can differ significantly from bulk water, exhibiting, for instance, modified hydrogen bonds, dielectric constant, and phase transitions. Despite the importance of strongly nanoconfined water, experimentally elucidating the nanoconfinement effect on water, such as its orientation and hydrogen bond (H-bond) network, has remained challenging. Here, we study two-dimensionally nanoconfined aqueous electrolyte solutions with tunable confinement from nanoscale to angstrom-scale sandwiched between a graphene sheet and CaF2. We employ heterodyne-detection sum-frequency generation (HD-SFG) spectroscopy, a surface-specific vibrational spectroscopy capable of directly and selective probing water orientation and H-bond environment at interfaces and under confinement. Remarkably, the vibrational spectra of the nanoscale confined water can be described quantitatively by the sum of the individual water surface signals from the CaF2/water and water/graphene interfaces until the confinement reduces to angstrom-scale (< ~8 {\AA}). Ab initio molecular dynamics simulations confirm our experimental observation. These results manifest that interfacial, rather than nanoconfinement effects, dominate the water structure until angstrom-level confinement.

Electron-phonon coupling (EPC) is foundational in condensed matter physics, determining intriguing phenomena and properties in both conventional and quantum materials. In this manuscript, we propose and demonstrate a novel two dimensional (2D) EPC spectroscopy which allows for direct extraction of EPC matrix elements. We find that two pronounced phonon modes of methylammonium lead iodide (MAPI) at room temperature exhibit highly distinctive EPC behaviors, both in strength, geometry, and temperature dependence across the phase transition. This demonstration indicates the potential of our novel 2D spectroscopy for studying the evolution of mode-resolved EPC at various external conditions and phonon-mediated light induced ultrafast control of condensed materials.

Two dimensional van der Waals heterostructures (2D are of significant interest due to their intriguing physical properties that are critically defined by the constituent monolayers and their interlayer coupling . However, typical inorganic 2 D vdWhs fall into the weakly coupled region, limiting efficient interfacial charge flow crucial for developing high performance quantum opto electronics. Here, we demonstrate strong interlayer coupling in Cu3 BHT (BHT = benzenehexathiol) graphene vdWhs an organic inorganic bilayer characterized by prominent interlayer charge transfer Monolayer Cu3 BHT with a Kagome lattice is synthesized on the water surface and then coupled with graphene to produce a cm2 scale 2D vdWh. Spectroscopic and electrical studies, along with theoretical calculation s show significant hole transfer from monolayer Cu3 BHT to graphene upon contact , being characteristic fingerprints for strong interlayer coupling This study unveils the great potential of integrating highly pi-conjugated 2D coordination polymers (2DCPs) into 2D vdWhs to explor e intriguing physical phenomena.

Since the seminal work on MoS2 monolayers, photoexcitation in atomically-thin transition metal dichalcogenides (TMDCs) has been assumed to result in excitons with large binding energies (~ 200-600 meV). Because the exciton binding energies are order-of-magnitude larger than thermal energy at room temperature, it is puzzling that photocurrent and photovoltage generation have been observed in TMDC-based devices, even in monolayers with applied electric fields far below the threshold for exciton dissociation. Here, we show that the photoexcitation of TMDC monolayers results in a substantial population of free charges. Performing ultrafast terahertz (THz) spectroscopy on large-area, single crystal WS2, WSe2, and MoSe2 monolayers, we find that ~10% of excitons spontaneously dissociate into charge carriers with lifetimes exceeding 0.2 ns. Scanning tunnelling microscopy reveals that photo-carrier generation is intimately related to mid-gap defect states, likely via trap-mediated Auger scattering. Only in state-of-the-art quality monolayers14, with mid-gap trap densities as low as 10^9 cm^-2, does intrinsic exciton physics start to dominate the THz response. Our findings reveal that excitons or excitonic complexes are only the predominant quasiparticles in photo-excited TMDC monolayers at the limit of sufficiently low defect densities., Comment: 18 pages, 5 figures, SI

Optical cavities, resonant with vibrational or electronic transitions of material within the cavity, enable control of light-matter interaction. Previous studies have reported cavity-induced modifications of chemical reactivity, fluorescence, phase behavior, and charge transport. Here, we explore the effect of resonant cavity-phonon coupling on the transient photoconductivity in a hybrid organic-inorganic perovskite. To this end, we measure the ultrafast photoconductivity response of perovskite in a tunable Fabry-Perot terahertz cavity, designed to be transparent for optical excitation. The terahertz-cavity field-phonon interaction causes apparent Rabi splitting between the perovskite phonon mode and the cavity mode. We explore whether the cavity-phonon interaction affects the material electron-phonon interaction by determining the charge carrier mobility through the photoconductivity. Despite the apparent hybridization of cavity and phonon modes, we show that the perovskite properties, in both ground (phonon response) and excited (photoconductive response) states, remain unaffected by the tunable light-matter interaction. Yet the response of the integral perovskite-terahertz optical cavity system depends critically on the interaction strength of the cavity with the phonon: the transient terahertz response to optical excitation can be increased up to 3-fold by tuning the cavity-perovskite interaction strength. These results enable tunable switches and frequency-controlled induced transparency devices., Comment: 14 pages, 4 figures

There is compelling evidence that charge carriers in organic semiconductors (OSs) self-localize in nano-scale space because of dynamic disorder. Yet, some OSs, in particular recently emerged high-mobility organic molecular crystals, feature reduced mobility at increasing temperature, a hallmark for delocalized band transport. Here we present the temperature-dependent mobility in two record-mobility OSs: DNTT (dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]-thiophene), and its alkylated derivative, C8-DNTT-C8. By combining terahertz photoconductivity measurements with fully atomistic non-adiabatic molecular dynamics simulations, we show that while both crystals display a power-law decrease of the mobility (\mu) with temperature (T, following: \mu \propto T^(-n)), the exponent n differs substantially. Modelling provides n values in good agreement with experiments and reveals that the differences in the falloff parameter between the two chemically closely related semiconductors can be traced to the delocalization of the different states thermally accessible by charge carriers, which in turn depends on the specific electronic band structure of the two systems. The emerging picture is that of holes surfing on a dynamic manifold of vibrationally-dressed extended states with a temperature-dependent mobility that provides a sensitive fingerprint for the underlying density of states., Comment: 28 pages, 5 Figures

Evidence is accumulating for the crucial role of a solid's free electrons in the dynamics of solid-liquid interfaces. Liquids induce electronic polarization and drive electric currents as they flow; electronic excitations, in turn, participate in hydrodynamic friction. Yet, the underlying solid-liquid interactions have been lacking a direct experimental probe. Here, we study the energy transfer across liquid-graphene interfaces using ultrafast spectroscopy. The graphene electrons are heated up quasi-instantaneously by a visible excitation pulse, and the time evolution of the electronic temperature is then monitored with a terahertz pulse. We observe that water accelerates the cooling of the graphene electrons, whereas other polar liquids leave the cooling dynamics largely unaffected. A quantum theory of solid-liquid heat transfer accounts for the water-specific cooling enhancement through a resonance between the graphene surface plasmon mode and the so-called hydrons -- water charge fluctuations --, particularly the water libration modes, that allows for efficient energy transfer. Our results provide direct experimental evidence of a solid-liquid interaction mediated by collective modes and support the theoretically proposed mechanism for quantum friction. They further reveal a particularly large thermal boundary conductance for the water-graphene interface and suggest strategies for enhancing the thermal conductivity in graphene-based nanostructures.

Terahertz molecular motions are often probed by high-frequency molecular oscillators in different types of non-linear vibrational spectroscopy. Recently developed two-dimensional terahertz-infrared-visible spectroscopy allows direct measuring of this coupling and, thus, obtaining site-specific terahertz vibrational spectrum. However, these data are affected by the intensity and phase of the employed laser pulses. In this work, we develop a method of extracting sample response - representing solely physical properties of a material - from experimental spectra. Using dimethyl sulfoxide (DMSO) as a model molecule to verify this method, we measure the coupling between C-H stretch vibration of its methyl groups and terahertz intramolecular twist and wagging modes.

Molecular-level insight into interfacial water at buried electrode interfaces is essential in elucidating many phenomena of electrochemistry, but spectroscopic probing of the buried interfaces remains challenging. Here, using surface-specific vibrational spectroscopy, we probe and identify the interfacial water orientation and interfacial electric field at the calcium fluoride (CaF2)-supported electrified graphene/water interface under applied potentials. Our data shows that the water orientation changes drastically at negative potentials (<-0.03 V vs. Pd/H2), from O-H group pointing down towards bulk solution to pointing up away from the bulk solution, which arises from charging/discharging not of the graphene but of the CaF2 substrate. The potential-dependent spectra are nearly identical to the pH-dependent spectra, evidencing that the applied potentials change the local pH (more than five pH units) near the graphene electrode even at a current density below 1 microamp per square centimeter. Our work provides molecular-level insights into the dissociation and reorganization of interfacial water on an electrode/electrolyte interface.

The distribution of ions at the air/water interface plays a decisive role in many natural processes. It is generally understood that polarizable ions with low charge density are surface-active, implying they sit on top of the water surface. Here, we revise this established hypothesis by combining surface-specific heterodyne-detected vibrational sum-frequency generation with neural network-assisted ab initio molecular dynamics simulations. Our results directly demonstrate that ions in typical electrolyte solutions are, in fact, located in a subsurface region leading to a stratification of such interfaces into two distinctive water layers. The outermost surface is ion-depleted, and the sub-surface layer is ion-enriched. As a result, an effective liquid/liquid interface buried a few {\AA} inside the solution emerges, creating a second water/electrolyte interface, in addition to the outermost air/water interface.

The controlled introduction of covalent sp$^{3}$ defects into semiconducting single-walled carbon nanotubes (SWCNTs) gives rise to exciton localization and red-shifted near-infrared luminescence. The single-photon emission characteristics of these functionalized SWCNTs make them interesting candidates for electrically driven quantum light sources. However, the impact of sp$^{3}$ defects on the carrier dynamics and charge transport in carbon nanotubes remains an open question. Here, we use ultrafast, time-resolved optical-pump terahertz-probe spectroscopy as a direct and quantitative technique to investigate the microscopic and temperature-dependent charge transport properties of pristine and functionalized (6,5) SWCNTs in dispersions and thin films. We find that sp$^{3}$ functionalization increases charge carrier scattering, thus reducing the intra-nanotube carrier mobility. In combination with electrical measurements of SWCNT network field-effect transistors, these data enable us to distinguish between contributions of intra-nanotube band transport, sp$^{3}$ defect scattering and inter-nanotube carrier hopping to the overall charge transport properties of nanotube networks., Comment: ACS Nano 2022

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.

The charging and dissolution of mineral surfaces in contact with flowing liquids are ubiquitous in nature, as most minerals in water spontaneously acquire charge and dissolve. Mineral dissolution has been studied extensively under equilibrium conditions, even though non-equilibrium phenomena are pervasive and substantially affect the mineral-water interface. Here we demonstrate using interface-specific spectroscopy that liquid flow along a calcium fluoride surface creates a reversible, spatial charge gradient, with decreasing surface charge downstream of the flow. The surface charge gradient can be quantitatively accounted for by a reaction-diffusion-advection model, which reveals that the charge gradient results from a delicate interplay between diffusion, advection, dissolution, and desorption/adsorption. The underlying mechanism is expected to be valid for a wide variety of systems, including groundwater flows in nature and microfluidic systems., Comment: 25 pages, 8 figures, Supplementary Information: 21 pages, 7 figures

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and small material footprint. Ideally, the material system should allow for chip-integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear-optical conversion efficiency. Here we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3$\cdot$10$^{-8}$m$^2$/V$^2$, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to third-harmonic signal with an intensity that is three orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to $\sim$1% using a moderate field strength of $\sim$30 kV/cm. Finally we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the 9$^{\rm th}$ harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS compatible, room temperature, chip-integrated, THz nonlinear conversion applications.

The Drude-Smith model successfully describes the frequency and phase-resolved electrical conductivity data for a surprisingly broad range of systems, especially in the terahertz region. Still, its interpretation is unclear since its original derivation is flawed. We use an intuitive physical framework to derive the Drude-Smith formula for systems where microscopically free charges are accumulated on a mesoscopic scale by localized scatterers. Within this framework, the model allows us to quantify the microscopic momentum relaxation time of the charges and the fraction of mesoscopically localized charges in addition to the direct current limit of the conductivity. We show that the Drude-Smith model is unique among different Drude-Lorentz models because the relaxation time of the free carriers also determines the frequency and damping of the resonance of the bound charges., Comment: The assumptions made in eq. (6) / fig 1 b) are self- contradictory. It is no legitimate to assume that the incoming current stops instantaneously but the back current does not. The state of the art (Ku\v{z}el, P. & N\v{e}mec, H. Adv. Opt. Mater. 8, 1--23 (2020).) is that Drude-Smith is an empirical parameterisation and a general microscopic interpretation of the parameters alone should not be done

Van der Waals heterostructures consisting of graphene and transition metal dichalcogenides (TMDCs) have recently shown great promise for high-performance optoelectronic applications. However, an in-depth understanding of the critical processes for device operation, namely interfacial charge transfer (CT) and recombination, has so far remained elusive. Here, we investigate these processes in graphene-WS$_2$ heterostructures, by complementarily probing the ultrafast terahertz photoconductivity in graphene and the transient absorption dynamics in WS$_2$ following photoexcitation. We find that CT across graphene-WS$_2$ interfaces occurs via photo-thermionic emission for sub-A-exciton excitation, and direct hole transfer from WS$_2$ to the valence band of graphene for above-A-exciton excitation. Remarkably, we observe that separated charges in the heterostructure following CT live extremely long: beyond 1 ns, in contrast to ~1 ps charge separation reported in previous studies. This leads to efficient photogating of graphene. These findings provide relevant insights to optimize further the performance of optoelectronic devices, in particular photodetection.

Terahertz time-domain conductivity measurements in 2 to 100 nm thick iron films resolve the femtosecond time delay between applied electric fields and resulting currents. This response time decreases for thinner metal films. The macroscopic response time depends on the mean and the variance of the distribution of microscopic momentum relaxation times of the conducting electrons. Comparing the recorded response times with DC-conductivities demonstrates increasing variance of the microscopic relaxation times with increasing film thickness. At least two electron species contribute to conduction in bulk with substantially differing relaxation times. The different electron species are affected differently by the confinement because they have different mean free paths., Comment: 11 pages, 3 figures

In graphene nanoribbons (GNRs), the lateral confinement of charge carriers opens a band gap, the key feature to enable novel graphene-based electronics. Successful synthesis of GNRs has triggered efforts to realize field-effect transistors (FETs) based on single ribbons. Despite great progress, reliable and reproducible fabrication of single-ribbon FETs is still a challenge that impedes applications and the understanding of the charge transport. Here, we present reproducible fabrication of armchair GNR-FETs based on a network of nanoribbons and analyze the charge transport mechanism using nine-atom wide and, in particular, five-atom-wide GNRs with unprecedented conductivity. We show formation of reliable Ohmic contacts and a yield of functional FETs close to unity by lamination of GNRs on the electrodes. Modeling the charge carrier transport in the networks reveals that this process is governed by inter-ribbon hopping mediated by nuclear tunneling, with a hopping length comparable to the physical length of the GNRs. Furthermore, we demonstrate that nuclear tunneling is a general charge transport characteristic of the GNR networks by using two different GNRs. Overcoming the challenge of low-yield single-ribbon transistors by the networks and identifying the corresponding charge transport mechanism puts GNR-based electronics in a new perspective.

Vibrational coupling is relevant not only for dissipation of excess energy after chemical reactions but also for elucidating molecular structure and dynamics. It is particularly important for OH stretch vibrational spectra of water, for which it is known that in bulk both intra- and intermolecular coupling alter the intensity and line shape of the spectra. In contrast with bulk, the unified picture of the inter/intra-molecular coupling of OH groups at the water-air interface has been lacking. Here, combining sum-frequency generation experiments and simulation for isotopically diluted water and alcohols, we unveil effects of inter- and intramolecular coupling on the vibrational spectra of interfacial water. Our results show that both inter- and intramolecular coupling contribute to the OH stretch vibrational response of the neat H2O surface, with intramolecular coupling generating a double-peak feature, while the intermolecular coupling induces a significant red shift in the OH stretch response.

Water in contact with mineral interfaces is important for a variety of different processes. Here, we present a combined theoretical-experimental study which provides a quantitative, molecular-level understanding of the ubiquitous and important flourite-water interface. Our results show that, at low pH, the surface is positively charged, causing a substantial degree of water ordering. The surface charge originates primarily from the dissolution of fluoride ions, rather than from adsorption of protons to the surface. At high pH we observe the presence of Ca-OH species pointing into the water. These OH groups interact remarkably weakly with the surrounding water, and are responsible for the free OH signature in the SFG spectrum, which can be explained from local electronic structure effects. The quantification of the surface termination, near-surface ion distribution and water arrangement is enabled by a combination of advanced phase-resolved Vibrational Sum Frequency Generation spectra of flourite-water interfaces and state-of-the-art ab initio molecular dynamics simulations which include electronic structure effects.

A simple refluxing wet-chemical approach is employed for fabricating In2S3/Pt-TiO2 heterogeneous catalysts for hydrogen generation under visible light irradiation. When the mass ratio between Pt-TiO2 and cubic-phased In2S3 (denoted as In2S3/Pt-TiO2) is two, the composite catalyst shows the highest hydrogen production, which exhibits an 82-fold enhancement over in-situ deposited Pt-In2S3. UV-vis diffuse reflectance and valence band X-ray photoelectron spectra elucidate that the conduction band of In2S3 is 0.3 eV more negative compared to that of TiO2, favoring charge separation in the nanocomposites. Photoelectrochemical transient photo-current measurements and optical pump - terahertz probe spectroscopic studies further corroborate the charge separation in In2S3/Pt-TiO2. The migration of photo-induced electrons from the In2S3 conduction band to the TiO2 conduction band and subsequently into the Pt nanoparticles is found to occur within 5 picoseconds. Based on the experimental evidence, a charge separation process is proposed which accounts for the enhanced activity exhibited by the In2S3/Pt-TiO2 composite catalysts.

We report calculations of the surface tension of the water-air interface using ab initio molecular dynamics (AIMD) simulations. We investigate the simulation cell size dependence of the surface tension of water from force field molecular dynamics (MD) simulations, which show that the calculated surface tension increases with increasing simulation cell size, thereby illustrating that a correction for finite size effects is required for the small system used in the AIMD simulation. The AIMD simulations reveal that the double-{\xi} basis set overestimates the experimentally measured surface tension due to the Pulay stress, while the triple and quadruple-{\xi} basis sets give similar results. We further demonstrate that the van der Waals corrections critically affect the surface tension. AIMD simulations without the van der Waals correction substantially underestimate the surface tension, while van der Waals correction with the Grimme's D2 technique results in the value for the surface tension that is too high. The Grimme's D3 van der Waals correction provides a surface tension close to the experimental value. Whereas the specific choices for the van der Waals correction and basis sets critically affect the calculated surface tension, the surface tension is remarkably insensitive to the details of the exchange and correlation functionals, which highlights the impact of long-range interactions on the surface tension. These simulated values provide important benchmarks, both for improving van der Waals corrections, and AIMD simulations of aqueous interfaces., Comment: 21 pages, 2 figures

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 ($\lesssim$ 4 $\mu$J/cm$^2$) in conjunction with sufficiently high Fermi energy ($\gtrsim$ 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., Comment: Nano Letters 2014