Impact of doping on the carrier dynamics in graphene

We present a microscopic study on the impact of doping on the carrier dynamics in graphene, in particular focusing on its influence on the technologically relevant carrier multiplication in realistic, doped graphene samples. Treating the time- and momentum-resolved carrier-light, carrier-carrier, and carrier-phonon interactions on the same microscopic footing, the appearance of Auger-induced carrier multiplication up to a Fermi level of 300 meV is revealed. Furthermore, we show that doping favors the so-called hot carrier multiplication occurring within one band. Our results are directly compared to recent time-resolved ARPES measurements and exhibit an excellent agreement on the temporal evolution of the hot carrier multiplication for n- and p-doped graphene. The gained insights shed light on the ultrafast carrier dynamics in realistic, doped graphene sample

Negative Correlation Learning for Customer Churn Prediction: A Comparison Study

Recently, telecommunication companies have been paying more attention toward the problem of identification of customer churn behavior. In business, it is well known for service providers that attracting new customers is much more expensive than retaining existing ones. Therefore, adopting accurate models that are able to predict customer churn can effectively help in customer retention campaigns and maximizing the profit. In this paper we will utilize an ensemble of Multilayer perceptrons (MLP) whose training is obtained using negative correlation learning (NCL) for predicting customer churn in a telecommunication company. Experiments results confirm that NCL based MLP ensemble can achieve better generalization performance (high churn rate) compared with ensemble of MLP without NCL (flat ensemble) and other common data mining techniques used for churn analysis

Relaxationsdynamik in Graphen

In dieser Arbeit wird eine theoretische Studie über die Nichtgleichgewichtsdynamik der Ladungsträger in Graphen präsentiert. Basierend auf der Dichtematrixtheorie wird die Wechselwirkung von Ladungsträger mit Licht, Phononen und Elektronen theoretisch modelliert. Die resultierende zeit-, impuls- und winkelaufgelösten Simulation der Ladungsträger ermöglicht die Interpretation von experimentellen Ergebnissen. Typischerweise wird die Relaxationsdynamik mit Hilfe von hoch aufgelösten Pump-Probe Experimenten untersucht. Alle experimentellen Studien haben einen doppelt exponentiellen Zerfall des pump-induzierte differentiellen Transmissionsspektrums (DTS) gemeinsam. Die schnelle Zerfallskomponente, die einige zehn Femtosekunden andauert, wird durch die ultraschnelle Coulomb-dominierten Dynamik induziert, wobei sich ein neues Quasigleichgewicht einstellt. Die zweite, langsamere Zerfallskonstate beschreibt die phonon-induzierte Energiedissipation an das Kristallgitter und findet auf einer Picosekunden-Zeitskala statt. Nach dem ersten Zerfall des DTS-Signals beobachten viele experimentelle Pump-Probe Studien im zeitlichen Verlauf des Spektrums einen Nulldurchgang, wobei die zweite Zerfallskomponente die Abklingzeit des DTS-Signals darstellt. In sehr guter Übereinstimmung mit Experimenten von Prof. Manfred Helm (Helmholtz-Zentrum Dresden-Rossendorf) konnte eine mikroskopische Erklärung für das negative DTS Signal in Graphen gefunden werden. Dabei wurde die Wechselwirkung von Intra- und Interband-Absorptionsprozessen untersucht, in der phonon-assistierte Prozesse zu einer erhöhten Absorption führen, welche den experimentellen beobachteten Nulldurchgang des DTS-Signals erklären. In Zusammenarbeit mit der Gruppe von Prof. Theodore B. Norris (Michigan University, USA) wird die mikroskopische Theorie mit der ultraschnellen Terahertz-Spektroskopie kombiniert, um systematisch die Terahertz-Dynamik von Ladungsträgern für verschiedene Graphen-Proben zu untersuchen. Dabei beschreibt die Theorie explizit die zeitabhängige Dynamik des Systems, welches durch einen Terahertz-Testpuls induziert wird. Es konnte in exzellenter Übereinstimmung mit den Experimenten gezeigt werden, dass die Dynamik ohne den Einfluss von externen Parameter, phänomenologisch Modellen oder extrinsischen Effekten qualitativ erklärt werden kann. Die Terahertz-Dynamik wird hierbei durch die effiziente Elektron-Elektron sowie Elektron-Phonon Wechselwirkung beschrieben. Weiterhin demonstriert die Theorie, dass das idealisierte Drude-Modell nicht ausreicht, um die volle zeitliche Dynamik zu bestimmen. Neben den Pump-Probe Studien werden die Absorptionsspektrum von Graphen und Bilayer Graphen mit dem Einfluss der optischen und Coulomb-Matrixelementen präsentiert. In guter Übereinstimmung mit Experimenten konnte gezeigt werden, dass die Absorption in Graphen durch einen konstante Wert im nah-infraroten Spektralbereich und einem ausgezeichnet Peak im ultravioletten Bereich charakterisiert ist. Im Unterschied zur linearen Bandstruktur von Graphen, enthält Bilayer Graphen vier parabolische Energiebänder, wodurch interessante optische Eigenschaften resultieren: Das Absorptionsspektrum von Bilayer Graphen enthält einen ausgezeichneten Peak im niedrigen Energiebereich, welcher durch spezielle Interbandübergänge in der Nähe des Dirac-Punktes induziert wird. Im ultravioletten Energiebereich ist das Spektrum durch zwei energetisch nah beieinander liegenden Peaks charakterisiert. Weiterhin ist die Einbeziehung der Coulomb-Wechselwirkung für die Absorptionsspektren von Mono- und Bilayer Graphen von entscheidender Bedeutung, da die Elektron-Elektron Wechselwirkung zur Entstehung von sogenannten Sattelpunkt-Exzitonen führt. Im letzten Abschnitt der Arbeit wird die Relaxationsdynamik im dotierten Graphen untersucht. Hierbei wird vor allem der Einfluss von Doping auf die Carrier Multiplication untersucht. Dieses interessante ultraschnelle Phänomen ist stark mit der linearen Bandstruktur von Graphen verbunden, welche effiziente Coulomb-induzierte Auger Prozesse ermöglicht. Betrachtet man ein dotiertes System, kann man zwischen der Carrier Multiplication (CM) und hot Carrier Multiplication (hCM) unterscheiden: Auger Streuprozesse führen zu einer Überbrückung von Valenz- und Leitungsband und können zu einer Vervielfachung der Ladungsträgerkonzentration in Graphen führen. Im Unterschied dazu führt die hCM, welche durch Coulomb-induzierte Intraband-Streuung hervorgerufen wird, zu einer Überbrückung der Zustände unter und über dem Fermilevel. Dabei kommt es zu einer Erhöhung der heißen Ladungsträgeranzahl. In exzellenter Übereinstimmung mit zeitaufgelösten ARPES Messungen, wurde die zeitabhängige hCM für n- sowie p-dotiertem Graphen theoretisch modelliert.In this thesis, the relaxation dynamics of nonequilibrium carriers in graphene is investigated. Based on the density matrix approach, the interaction of carriers with light, phonons and electrons is theoretically modelled. The resulting time-, momentum-, and angle-resolved simulation of the carrier dynamics enables the interpretation of recent experimental observations. Typically, the carrier relaxation has been accessed via high-resolution pump-probe experiments. Common to all studies is a bi-exponential decay of the pump-induced differential transmission (DT) spectrum. The fast decay component in the range of few tens of femtoseconds is assigned to an ultrafast Coulomb-dominated carrier redistribution towards a hot Fermi-Dirac distribution, whereas the slower decay component in the range of a picosecond reflects the equilibration between the electron and the phonon system. However, many studies report a zero-crossing after the initial decay in the transient DT spectrum, where the second decay component characterizes the recovering of the DT signal. In very good agreement with recent pump-probe experiment performed by the group of Prof. Manfred Helm (Helmholtz-Zentrum Dresden-Rossendorf), a microscopic explanation for the occurrence of transient negative differential transmission in graphene is found, where a detailed interplay of intraand interband absorption processes on the transient DT in graphene is investigated. In particular, phonon-assisted intraband processes are shown to lead to an enhanced absorption giving rise to the experimentally observed zero-crossing from positive to negative DT signals. In collaboration with the group of Prof. Theodore B. Norris (Michigan University, USA), theoretical studies combined with ultrafast time-resolved THz spectroscopy were performed to systematically investigate the hot-carrier dynamics in an array of graphene samples. The theory calculates explicitly the time-dependent response of the system to a THz probe pulse. The calculations reveal that the observed dynamics can be accounted for qualitatively without including any fitting parameters, phenomenological models or extrinsic effects. Specifically, the hot-carrier dynamics are governed by the coupling of extraordinarily efficient carrier-carrier and carrier-phonon interactions. Furthermore, the theory demonstrates that the simple Drude model is insufficient to fully account for the THz interactions. Beside pump-probe studies, the thesis presents the absorption spectra of mono- and bilayer graphene including the impact of the fully momentum-dependent optical and Coulomb matrix elements. In agreement with recent experiments, the absorbance of graphene is characterized by a frequency-independent value in the near-infrared spectral region and a pronounced peak in the ultraviolet region resulting from interband transition. In contrast to the linear band structure of graphene, the energy dispersion of bilayer graphene exhibits four parabolic bands resulting in interesting optical features: The absorbance exhibits in the low energy spectrum a pronounced peak, which can be unambiguously ascribed to interband cross transitions at the Dirac point. In the ultraviolet region, the spectrum is characterized by two pronounced energetically close absorption peaks. For both mono- and bilayer graphene, the calculations reveal the importance of the Coulomb interaction resulting in the formation of saddle-point excitons. Finally, the relaxation dynamics in doped graphene is discussed, where the main focus lies on the carrier multiplication. This is an interesting ultrafast phenomenon that is related to the linear electronic band structure of graphene opening up the possibility of efficient Coulomb-induced Auger processes. Introducing doping, the Coulomb-induced processes of carrier multiplication (CM) and hot carrier multiplication (hCM) are to be distinguished: Auger scattering bridging the valence and the conduction band gives rise to CM corresponding to an increase of the number of charge carriers in graphene. In contrast, hCM is induced by Coulomb-induced intraband scattering bridging the states below and above the Fermi level and resulting in an increase of the number of hot carriers. Comparing the theoretical results with recent time-resolved ARPES measurements, an excellent agreement on the temporal evolution of the hot carrier multiplication for n- and p-doped graphene is found

Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene

International audienceThe ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamentalcarrier–carrier interactions and carrier–phonon relaxation processes in two-dimensionalmaterials, and understanding of the physics underlying novel high-speed electronic andoptoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopyand related techniques have interpreted the variety of observed signals withinphenomenological frameworks, and sometimes invoke extrinsic effects such as disorder.Here, we present an integrated experimental and theoretical programme, using ultrafast timeresolvedterahertz spectroscopy combined with microscopic modelling, to systematicallyinvestigate the hot-carrier dynamics in a wide array of graphene samples having varyingamounts of disorder and with either high or low doping levels. The theory reproduces theobserved dynamics quantitatively without the need to invoke any fitting parameters,phenomenological models or extrinsic effects such as disorder. We demonstrate that thedynamics are dominated by the combined effect of efficient carrier–carrier scattering, whichmaintains a thermalized carrier distribution, and carrier–optical–phonon scattering, whichremoves energy from the carrier liquid

ARTICLE Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene

The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier-carrier interactions and carrier-phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of observed signals within phenomenological frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated experimental and theoretical programme, using ultrafast timeresolved terahertz spectroscopy combined with microscopic modelling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amounts of disorder and with either high or low doping levels. The theory reproduces the observed dynamics quantitatively without the need to invoke any fitting parameters, phenomenological models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier-carrier scattering, which maintains a thermalized carrier distribution, and carrier-optical-phonon scattering, which removes energy from the carrier liquid