Dataset DOI: 10.5061/dryad.hx3ffbgsq

Description of the data and file structure

Data Set For: Isostructural electronic transition in MoS2 probed by solid-state high harmonic generation spectroscopy

This data set contains all raw data and scripts for analysis of the data.

Description of the data and file structure:

The data repository contains subfolders corresponding to each figure that contains the raw data for that figure. Subfolder and file names are descriptive and note the critical parameter (most often pressure) that is varied between data files in each figure. An additional folder contains functions written in Matlab that were used for analysis of the raw data. Beyond basic functions used in analysis as described for each figure, the function “loadSHHGanisotropy.m” is a useful tool in applying some of the initial analysis steps automatically to sHHG anisotropy scans and loading large data sets into easy-to-use cell structures in Matlab. Descriptions of each function’s purpose, parameters, and outputs can be found in the code comments.

Files and variables

File: sHHG_DAC_MoS2_dataRepository.zip

Description: 

This ZIP file contains the following sub-folder structure:

├── analysisScripts

├── Fig2_sHHGexampleSpectrumAnisotropy

├── Fig3_pressureDependentMoS2sHHG

├── Fig4_bandStructure

├── Fig5_sHHGtheoryAnisotropy

├── FigS01_Raman

├── FigS03_MIRspectrum

├── FigS04_MIRpolarization

├── FigS05_sHHGdacBackground

├── FigS06_powerDependence

├── FigS07_convergence

├── FigS08_pdos

├── FigS09_populationDynamics

└── FigS10_currentDynamics

Specific content listing the figure number of the associated manuscript and in parenthesis the associated folder in the ZIP file:

Figure 2 (“Fig2_sHHGexampleSpectrumAnisotropy\”):

Subfolder “A_images\” contains the raw images used in Fig 1a. The larger, lower magnification image was made by overlaying the sHHG signal image taken with the lower-magnification lens (“sHHG_lens.png”) on top of the white light microscope image taken through the same optic (“MoS2_lens.png”). The top image was made slightly transparent to see both images at once. The same process was applied to the higher magnification inset taken with the 50x objective and these files contain “objective” in the names.

Subfolder “B_rawSpectra\” contains the raw angle-dependent sHHG spectra at ambient pressure (“00_0_GPa\”) and 30.5 GPa (“30_5_GPa\”). Each anisotropy scan involves 4 “.txt” tab delimited files with the same time stamp in the file names and there are several anisotropy scans at each pressure. The “header” file contains anisotropy scan parameters in this order: anisotropy start angle in the lab frame (degrees), anisotropy end angle in the lab frame (degrees), anisotropy angle step size (degrees), integration time for each spectrum (?s), and number of averages in the scan (set to 1 for all data here). The “wavelength” file contains the x axis of wavelength (nm) for all spectra in the anisotropy scan. The “0_data” file contains the spectral data taken parallel to the MIR driver and the “90_data” file contains the spectral data taken perpendicular to the MIR driver. Each row in these files is the intensity of a spectrum at an angle as defined by the start, end, and step angles defined in the “header” file. To obtain the spectra shown in Fig. 1b, first cosmic rays were removed from each spectrum in each anisotropy scan using the

Subfolder “C_fitAnisotropy\” contains the fit and averaged angular dependence of each harmonic observed in the raw spectrum data. This data was obtained by applying the “multiGaussFit.m” function to each spectrum of the raw data from “B_rawSpectra\” after cosmic ray removal and dividing by the integration time. The function ”harmonicFitBounds.m” was used to generate the input bounds and initial guesses for the fits done with “multiGaussFit.m” using the input parameters of MIR energy (0.38 eV) and the harmonic orders to fit. Like the raw data, each row of the data corresponds to the angle in the anisotropy scan. The harmonic orders that were fit are given in the first row of the data. There are two columns corresponding to each harmonic. The first represents the mean fit Gaussian amplitude for that harmonic at each angle. The second column labeled with the same harmonic order is the standard deviation of the Gaussian amplitude. The anisotropy plot in Fig. 2c compares specifically the 7th harmonic anisotropy at the two pressures plotted in polar coordinates and is the sum of the parallel and perpendicular data with error bars of the standard deviation. In all anisotropy plots including this, the same constant angular offset of -12° was added to the angular axis for ease of comparison with theoretical data.

Figure 3: (“Fig3_pressureDependentMoS2sHHG\”):

Subfolder “rawSpectra\” contains the raw angle-dependent sHHG spectra at all pressures measured. The data is separated into subfolders by pressure (e.g. “03_3_GPa\” corresponds to a pressure value of 3.3 GPa). The data at 0 and 30.5 GPa is the same data used in Fig. 2 and all data was analyzed in the same way as in Fig. 2 to obtain the data in the subfolder “fitAnisotropy\”.

The data in “fitAnisotropy\” is also formatted in the same way as the anisotropy data for Fig. 2. The anisotropy traces in Fig. 3 are plotted with a vertical offset for clarity and using the standard deviation for the shaded error bars. The total intensity of each harmonic at each pressure was obtained by summing over 180° of the angular axis.

Figure 4 (“Fig4_bandStructure\”):

The theoretical band structure of MoS2 at each pressure is provided in two-column format with the file name containing the pressure value. Column 1 is the horizontal k axis, and the second column is the band energies. A separate file “fermiEnergies.txt” is provided giving the Fermi energy at each pressure which was subtracted from all energies when plotting to create Fig. 4b-f. Fig. 4g was created by subtracting the first valence band maximum from the first conduction band minimum at the K and ? points to get two direct band gaps at each pressure. Fig. 4f represents integrated theoretical population dynamics and is reproduced from Fig. S9f. The data for this panel is provided in the folder for Fig. S9 and will be explained with Fig. S9.

Figure 5 (“Fig5_sHHGtheoryAnisotropy\”):

The subfolder “experiment\” contains the experimental data compared to the theoretical results in Fig. 5. This data is a subset of the Gaussian-fit anisotropy data from Fig. 3, chosen for the closest pressures to those used in the theoretical calculations. The pressure values are given in the subfolder names like the Fig. 3 data along with the figure panel letters where the data is used.

The subfolder “theory\” contains the theoretical sHHG anisotropy data in folders named by pressure and the figure panel letters where the data is used. Each file contains two tab-delimited columns where the first is angle (°) and the second is the intensity of the harmonic. Each panel in Fig. 5 represents the anisotropy of a single harmonic at a specific pressure compared between experiment and theory. For clearer comparison of the angular dependence, both the theoretical and experimental data are normalized in Fig. 5.

Figure S1 (“FigS01_Raman\”):

Each file of the pressure-dependent Raman data has the pressure in the file name. Each file has two columns of data, one labeled “wavelength” which is the x axis in wavenumbers (cm-2), and one labeled “intensity” which gives the Raman intensity. In Fig. S01 the Raman spectra were offset vertically for clarity and colored corresponding to pressure.

Figure S3 (“FigS03_MIRspectrum\”):

The file “MIRspectrum.txt” contains an exemplary spectrum of the MIR driver used throughout for sHHG, giving wavelength (nm) in one column and intensity in the other as labeled.

Figure S4 (“FigS04_MIRpolarization\”):

Two subfolders “A_horizontal\” and “B_vertical\” correspond to panels S4a and S4b respectively. Each file contains three tab-delimited columns: angle (°), intensity (µJ), and standard deviation (?J). Angle is the polar axis in Fig. S4, intensity is the radial axis, and standard deviation gives the shaded error bars. All traces are normalized in Fig. S4 for ease of observing changes to polarization.

Figure S5 (“FigS05_sHHGdacBackground\”):

Subfolder “AB_images\” contains the images used in panels S5a and S5b. The images in “onMoS2sample\” are the same ones used Fig. 2a. The images in “offMoS2sample\” are images where the MIR beam passes through the DAC such that it does not hit the MoS2 and only passes through the diamond and He of the DAC. These images can be combined to give Fig. S5b in the same way as the images on the MoS2 sample used in Fig. 2a.

Subfolder “rawSpectra\” contains the raw angle-dependent sHHG spectra corresponding to the MIR passing through the DAC but not MoS2 at a pressure of 30.5 GPa as shown by the image in Fig. S5a. These files are formatted in the same way as previous raw sHHG anisotropy data. The diamond spectrum in Fig. S5c was obtained using the raw spectral data after removing cosmic rays and dividing by the integration time. The angle-dependent spectra were averaged over angle and then averaged between scans in the same wavelength range to create the averaged diamond spectrum. The diamond spectrum in Fig. S5c is compared to the MoS2 spectrum, which is the same as the 30.5 GPa spectrum in Fig. 2b.

Subfolder “fitAnisotropy\” contains the Gaussian amplitude and standard deviation for the harmonics emitted from the diamond of the DAC. This data was analyzed in the same way as previous Gaussian fit harmonics and is formatted in the same way. This data was plotted like previous anisotropy data in Fig. S5d with the standard deviation used for the shaded error bars. The 7th harmonic was multiplied by 100 for clarity.

Figure S6 (“FigS06_powerDependence\”):

Each text file for this figure is an sHHG spectrum of MoS2 at 30.5 GPa. The MIR polarization was set to maximize signal, and the MIR pulse energy is given in nJ in the name of each file. Each file has two tab-delimited columns, the first is wavelength (nm), and the second is intensity (cts). To get the power dependencies in Fig S6, these spectra were first divided by the integration time given in the file name in s and cosmic rays were removed using the function “tinHat.m”. Next, these spectra were analyzed using the “harmonicFitBounds.m” and “multiGaussFit.m” functions to get a Gaussian amplitude for each harmonic at each pulse energy. After converting the pulse energy to peak power (TW/cm2) using the laser parameters of 100 fs pulse duration and 1 kHz repetition rate, this data was plotted on a log-log scale in Fig. S6. With the data in a log scale, the data for each harmonic was fit to a line to obtain the slope, which corresponds to power law order of each harmonic.

Figure S7 (“FigS07_convergence\”):

Subfolder “A_dephasing\” contains a comma delimited “.csv” file providing the theoretical sHHG spectra for different values of the dephasing parameter. The x axis in energy (eV) is given in the first column labeled “wlist”. The other columns give the log of sHHG intensity, and each column is labeled at the top with the value of the dephasing parameter used to produce that spectrum in meV. These logarithmic spectra are plotted together with energy on the x axis in panel S7a.

Subfolder “B_depopulation\” contains a comma delimited “.csv” file providing the theoretical sHHG spectra for different values of the depopulation parameter. The x axis in energy (eV) is given in the first column labeled “wlist”. The other columns give the log of sHHG intensity, and each column is labeled at the top with the value of the depopulation parameter used to produce that spectrum in meV. These logarithmic spectra are plotted together with energy on the x axis in panel S7b.

Figure S8 (“FigS08_pdos\”):

Subfolder “A_GammaPoint\” contains the pressure-dependent projected density of states data at the ?-point shown in panel S8a at each pressure and subfolder “B_Kpoint\” contains the pressure-dependent projected density of state data at the K-point shown in panel S8b at each pressure. Each file at each pressure is named with element (Mo or S), an atom number (corresponding to multiple atoms of each type in the unit cell), wavefunction number separating different orbitals on a certain element, and the orbital type (s, p, or d). In each file, the first column is energy (ev) used for the x axis in Fig. S8, and the other columns give the density of states. One column in each file is labeled “ldos”, which gives the total density of states for a type of orbital on a specific atom. The other column(s) labeled “pdos” project that total density into the different angular momentum states of the orbital. For the d orbitals on Mo, there are 5 columns labeled “pdos” corresponding to dz2, dzx, dzy, dx2-y2 and dxy in that order. For p orbitals on both elements, there are three columns labeled “pdos” corresponding to pz, px, and py in that order. To create the plots in Fig. S8, the same orbital wavefunctions with the same angular momentum (e.g. pz) at the same pressure were added together across the multiple atoms of the same element (e.g. S) to give the total projected density of states for each angular momentum state as shown by the keys in Fig. S8.

Figure S9 (“FigS09_populationDynamics\”):

Each subfolder for Fig. S9 contains the simulated time-dependent population data for the first conduction band at a pressure given by the folder name corresponding to the panels S9a-e. For each pressure, the population is given in the region around the K-point and the region around the ?-point as denoted by the file names. The first column in each file is time in “units” where 1 fs = 20.5 units. The second column in each file is the population. The population was plotted vs time (fs) for panels S9a-e. For panel S9f, the population at each pressure for the K- and ?-point data was integrated over the time range of 200 fs to give the time-integrated population.

Figure S10 (“FigS10_currentDynamics\”):

Like Fig. S9, each subfolder for S10 corresponds to theoretical data for each pressure as noted by the folder names. The current is given in the region around the K- and \Gamma-points at each pressure as noted by the file names. In addition, a third file for each pressure gives the total time dependent current across the full k-space. Files are in the same format as Fig. S9 with the same time units, except that the current is in complex number format. In panels S10a-e, the real part of the current was plotted against the time (fs) for the K-point, \Gamma-point, and total current data at each pressure. The time-integrated current given in panel S10f was obtained by first taking the absolute value of the time-dependent current data at each pressure, then integrating over the time range of 200 fs.

Code/software

Commented data analysis codes are included in the subfolder "analysisScripts". The usage of the script is specified in the Files section where we describe how each figure is created; in cases were the Matlab scripts are used a description of usage is provided.