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diff --git a/MX2/chapter.tex b/MX2/chapter.tex index 6c59f86..60aa0eb 100644 --- a/MX2/chapter.tex +++ b/MX2/chapter.tex @@ -28,7 +28,7 @@ important when the excitation pulses are temporally overlapped. % In this region, the coherent dynamics create diagonal features involving both the excitonic states and continuum states, while the partially coherent pathways contribute to cross-peak features. % -\section{Introduction} % ------------------------------------------------------------------------- +\section{Introduction} % ========================================================================= Transition metal dichalcogenides (TMDCs), such as MoS\textsubscript{2}, are layered semiconductors with strong spin-orbit coupling, high charge mobility, and an indirect band gap that becomes direct @@ -82,9 +82,7 @@ vector for each beam and the subscripts label the excitation frequencies. % Multidimensional spectra result from measuring the output intensity dependence on frequency and delay times. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.5\textwidth]{MX2/01} \caption[CMDS tutorial]{ (a) Example delays of the $\omega_1$, $\omega_2$, and $\omega_{2^\prime}$ excitation pulses. @@ -98,7 +96,6 @@ delay times. % labeling two diagonal and cross-peak features for the A and B excitons.} \label{fig:Czech01} \end{figure} -\clearpage} \autoref{fig:Czech01} introduces our conventions for representing multidimensional spectra. % \autoref{fig:Czech01}b,d are simulated data. % @@ -144,16 +141,13 @@ The intensity of the cross-peaks depends on the importance of state filling and relaxation of hot A excitons as well as the presence of interband population trnasfer of the A and B exciton states. % -\section{Methods} % ------------------------------------------------------------------------------ +\section{Methods} % ============================================================================== -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/S1} \caption{Schemiatic of the synthetic setup used for Mo thin film sulfidation reactions.} \label{fig:CzechS1} \end{figure} -\clearpage} MoS\textsubscript{2} thin films were prepared \textit{via} a Mo film sulfidation reaction, similar to methods reported by \textcite{LaskarMasihhurR2013a}. % @@ -185,9 +179,7 @@ with DI water, and transferred to a Cu-mesh TEM grid. % TEM experiments were performed on a FEI Titan aberration corrected (S)TEM under 200 kV accelerating voltage. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/10} \caption[Mask and epi vs transmissive.]{ (a) Mask. @@ -198,7 +190,6 @@ voltage. % representative of the pure MoS\textsubscript{2} response.} \label{fig:Czech10} \end{figure} -\clearpage} The coherent multidimensional spectroscopy system used a 35 fs seed pulse, centered at 800 nm and generated by a 1 kHz Tsunami Ti-sapphire oscillator. % @@ -211,14 +202,11 @@ Signal and idler were not filtered out, but played no role due to their low phot Pulse $\omega_2$ was split into pulses labeled $\omega_2$ and $\omega_{2^\prime}$ to create a total of three excitation pulses. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/S4} \caption{OPA outputs at each color explored.} \label{fig:CzechS4} \end{figure} -\clearpage} In this experiment we use motorized OPAs which allow us to set the output color in software. % OPA1 and OPA2 were used to create the $\omega_1$ and $\omega_2$ frequencies, respectively. % @@ -235,14 +223,11 @@ focused onto the sample surface by a 1 meter focal length spherical mirror in a geometry to form a 630, 580, and 580 $\mu$m FWHM spot sizes for $\omega_1$, $\omega_2$, and $\omega_{2^\prime}$, respectively. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/S5} \caption{Spectral delay correction.} \label{fig:CzechS5} \end{figure} -\clearpage} \autoref{fig:CzechS5} represents delay corrections applied for each OPA. % The corrections were experimentally determined using driven FWM output from fused silica. % @@ -277,9 +262,7 @@ signal id is the geometry chosen for this experiment. % This discrimination between a film and the substrate was also seen in reflective and transmissive CARS microscopy experiments. \cite{VolkmerAndreas2001a} % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/11} \caption[MoS\textsubscript{2} post processing.]{ Visualization of data collection and processing. @@ -305,7 +288,6 @@ CARS microscopy experiments. \cite{VolkmerAndreas2001a} % Note that the color bar's range is different than in \autoref{fig:Czech03}.} \label{fig:Czech11} \end{figure} -\clearpage} Once measured, the FWM signal was sent through a four-stage workup process to create the data set shown here. % @@ -326,11 +308,9 @@ signal. % IPython \cite{PerezFernando2007a} and matplotlib \cite{HunterJohnD2007a} were important for data processing and plotting in this work. -\section{Results and discussion} % --------------------------------------------------------------- +\section{Results and discussion} % =============================================================== -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.75\textwidth]{MX2/02} \caption[Few-layer MoS\textsubscript{2} thin film characterization.]{ Characterization of the few-layer MoS\textsubscript{2} film studied in this work. @@ -344,7 +324,6 @@ processing and plotting in this work. and representative excitation pulse shape (red).} \label{fig:Czech02} \end{figure} -\clearpage} The few-layer MoS\textsubscript{2} thin film sample studied in this work was prepared on a transparent fused silica substrate by a simple sufidation reaction of a Mo thin film using a @@ -363,9 +342,7 @@ corresponds to approximately four monolayers. % and B excitonic line shapes that were extracted from the absorption spectrum. A representative excitation pulse profile is also shown in red for comparison. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/S3} \caption[MoS\textsubscript{2} absorbance.]{Extraction of excitonic features from absorbance spectrum. (a) Second derivative spectra of absorbance (black) and fit second derivative @@ -373,7 +350,6 @@ excitation pulse profile is also shown in red for comparison. % (black), Gaussian fits (blue and red), and remainder (black dotted).} \label{fig:CzechS3} \end{figure} -\clearpage} Extracting the exciton absorbance spectrum is complicated by the large ``rising background'' signal from other MoS\textsubscript{2} bands. % @@ -397,9 +373,7 @@ In order to compare the FWM spectra with the absorption spectrum, the signal has the square root of the measured FWM signal since FWM depends quadratically on the sample concentration and path length. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/03} \caption[MoS\textsubscript{2} frequency-frequency slices.]{2D frequency-frequency spectra of the MoS\textsubscript{2} sample in the epi configuration. In all spectra $\tau_{22^\prime}=0$ fs, @@ -412,7 +386,6 @@ concentration and path length. % of the A and B excitons, as designated from the absorption spectrum.} \label{fig:Czech03} \end{figure} -\clearpage} The main set of data presented in this work is an $\omega_1\omega_2\tau_{21}$ ``movie'' with $\tau_{22\prime}=0$. @@ -426,9 +399,7 @@ In contrast, we see no well-defined excitonic peaks along the $\omega_2$ ``pump' Instead, the signal amplitude increases toward bluer $\omega_2$ values. % The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA power. -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.75\textwidth]{MX2/04} \caption[MoS\textsubscript{2} $\omega_1$ Wigner progression.]{Mixed $\omega_1$---$\tau_{21}$ time---frequency representations of the 3D data set at five ascending $\omega_2$ excitation @@ -437,11 +408,8 @@ The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA powe marked as dashed lines within each spectrum.} \label{fig:Czech04} \end{figure} -\clearpage} -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.75\textwidth]{MX2/05} \caption[MoS\textsubscript{2} $\omega_2$ Wigner progression.]{Mixed $\omega_2$---$\tau_{21}$ time---frequency representations of the 3D data set at five ascending $\omega_1$ probe @@ -450,7 +418,6 @@ The decrease in FWM above 2.05 eV is caused by a drop in the $\omega_2$ OPA powe marked as dashed lines within each spectrum.} \label{fig:Czech05} \end{figure} -\clearpage} Figures \ref{fig:Czech04} and \ref{fig:Czech05} show representative 2D frequency-delay slices from this movie, where the absicissa is the $\omega_1$ or $\omega_2$ frequency, respectively, the @@ -477,9 +444,7 @@ Both the line shapes and the dynamics of the spectral features are very similar. \autoref{fig:Czech05} is an excitation spectrum that shows that the dynamics of the spectral features do not depend strongly on the $\omega_1$ frequency. -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.5\textwidth]{MX2/06} \caption[Pathway V, VI liouville pathways.]{Liouville pathways for \autoref{fig:Czech04}. gg and ee designate ground- and excited-state populations, the eg, 2e,e, and e$^\prime$+e,e represent @@ -488,7 +453,6 @@ features do not depend strongly on the $\omega_1$ frequency. either A or B excitonic states.} \label{fig:Czech06} \end{figure} -\clearpage} The spectral features in Figures \ref{fig:Czech03}, \ref{fig:Czech04} and \ref{fig:Czech05} depend on the quantum mechanical interference effects caused by the different pathways. % @@ -580,9 +544,7 @@ $\omega_2$ is lower than the A exciton frequency (the top subplot). % If population transfer of holes from the B to A valence bands occurred during temporal overlap, the B/A ratio would be independent of pump frequency at $\tau_21<0$. -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/07} \caption[MoS\textsubscript{2} transients.]{ Transients taken at the different $\omega_1$ and $\omega_2$ frequencies indicated by the @@ -591,7 +553,6 @@ B/A ratio would be independent of pump frequency at $\tau_21<0$. constant represented as an unchanging offset over this timescale (black dashed line).} \label{fig:Czech07} \end{figure} -\clearpage} \autoref{fig:Czech07} shows the delay transients at the different frequencies shown in the 2D spectrum. % @@ -607,16 +568,13 @@ offset that represents the long time decay. % The 680 fs decay is similar to previously published pump-probe and transient absorption experiments. \cite{NieZhaogang2014a, SunDezheng2014a, DochertyCallumJ2014a} % -\afterpage{ \begin{figure} - \centering \includegraphics[width=\textwidth]{MX2/08} \caption[MoS\textsubscript{2} frequency-frequency slices near pulse overlap.]{2D frequency-frquency spectra near zero $\tau_{21}$ delay times. The signal amplitude is normalized to the brightest features in each spectrum.} \label{fig:Czech08} \end{figure} -\clearpage} The spectral features change quantitatively for delay times near temporal overlap. % \autoref{fig:Czech08} shows a series of 2D spectra for both positive and negative $\tau_{21}$ delay @@ -628,16 +586,13 @@ The spectra also develop more diagonal character as the delay time moves from ne values. % The AB cross-peak is also a strong feature in the spectrum at early times. % -\afterpage{ \begin{figure} - \centering \includegraphics[width=0.5\textwidth]{MX2/09} \caption[Pathways I, III Liouville pathways.]{Liouville pathways for the $\omega_1$, $\omega_2$, and $\omega_{2^\prime}$ time ordering of pulse interactions. e and e$^\prime$ represent either A or B excitonic states.} \label{fig:Czech09} \end{figure} -\clearpage} The pulse overlap region is complicated by the multiple Liouville pathways that must be considered. % @@ -665,7 +620,7 @@ More positie values of $\tau_{21}$ emphasize the \autoref{fig:Czech09} pathways \autoref{fig:Czech06} pathways, accounting for the increasing percentage of diagonal character at increasingly positive delays. % -\section{Conclusions} % -------------------------------------------------------------------------- +\section{Conclusions} % ========================================================================== This paper presents the first coherent multidimensional spectroscopy of MoS\textsubscript{2} thin films. % |