SpectroLab: An Open Source Matlab Based Toolbox for High Throughput Spectroscopy Analysis

The common edge detection algorithms are the Sobel, Canny, Prewitt, Roberts, and fuzzy logic methods[24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. In this paper, we use a modified version of the Sobel filter in order to conduct second derivative calculations. While it is possible to use a convolution neural network (CNN) for feature extraction[34, 35], these networks require a large amount of computational resources and are only applicable to the data set they are trained on. Generative adversarial neural networks (GANs)[36] are a much better alternative to create a neural network feature extraction since it can work on an infinite amount of data sets once it is properly trained. The downside is that a large amount of data sets ($>$1000) are required in order to properly train the neural network. Therefore, we forgo the inclusion of a neural network in our program. The Sobel filter is a 3$\times$3 matrix that calculates the second derivative locally in an image file (where A is the image). There are two versions, the horizontal and the vertical which can be used, in the distributed program. The horizontal $F_{x}$ is convoluted with the image to form the second derivative of the image.

In order to detect edges after the Sobel filter is applied, one would find the square of the absolute value of the resultant $|F_{x}|^{2}$. By not conducting this last step we can resolve weak signals of ARPES. In the case of sharp data, the edge detection feature can be turned on with an additional line of code which we have included. All edge detection algorithms can be accesses via Matlab’s image toolbox.

An energy contour is a slice of a 3D band mapping in ARPES ($k_{x}$,energy,$k_{x}$) where at a constant energy, the 2D $k_{x}$,$k_{y}$ surface is revealed. For constant energy contours we create a function that automatically interprets the energy levels and recreates them in an energy contour. For labeling we included a rounding function that rounds to the nearest significant figure. However, the program can interpret the exact value for publication.

The volumetric plot function takes advantage of how data is formatted for ARPES. Typically data is encoded in an (X,Y,Z,C) format. Where X,Y,and Z are $k_{x}$, $k_{y}$, and energy, while C is the interpretation of the intensity at that location. By using an alpha map, we can make weak signals transparent and reveal the 3D band structure for visualization. This has the ability to be a very powerful tool for investigating anisotropy in bands.

We have included several methods to aid the taking $k_{x}$ and $k_{y}$ momentum cuts from a 3D band mapping. We take these cuts by selecting a value of $k_{x}$ and $k_{y}$ and resolving the cut in a 2D image.

Energy & momentum distribution curves (EDC & MDC) are used for the data analysis of spectroscopic data. In a set amount of intervals a line of data is taken out of the image and then plotted in order to enable researchers to resolve difficult to resolve images from ARPES or other spectroscopic data. We use the waterfall() function in order to reconstruct the EDC and MDC plots seen in literature [22]. The plot also have the benefit of being three dimensional with the ability to add a color map to further define intensity differences.

In order to import theory, we create a 2D surface in a 3D box using Matlab’s meshgrid() function to import an image of the theoretical plot. To insure that the images that we import are of the same size we use the largest image dimensions as the map for all of the subsequent images. We do this because the 3D plot will not work unless we use the same size map. We then offset the images by one for each image. Now, one can scale the distance between image layers using the daspect() function of Matlab to scale the Z (Energy) in order to resolve the layers.

We include a graphical user interface (GUI) [Fig. 1] that can be used as a general tool, more advance data selection and analysis will need to be done in code.

We include a function to extract constant energy contours (ECs) from a 3D band mapping. StackedECP() [Fig. 2(c,d) is a feature that calculates ECs and stacks them on top of each other in order to visualize the bands dispersing in 3D space. The energy contour functions do the same, however the ECs are presented in a 2D format.

In the volumetric plot function, a 3D band mapping is interpreted with an alpha map (transparency map). This allows for all bands to be mapped in a 3D space. In addition, users can rotate and zoom in to further examine the electronic structure.

We have included several methods to aid the taking $k_{x}$ and $k_{y}$ momentum cuts from a 3D band mapping. Plot_KX_KY, Ky cuts (Fig. 3(a)), and Kx cuts (Fig. 3(b)) are all features that allow for one to construct these plots. Plot_KX_KY is a debug tool but can still be used to accomplish this feature.

Energy distribution curves (EDCs) and momentum distribution curves (MDCs) are important tools for the analysis of ARPES data. Here, we construct programs that can create 3D EDC [Fig. 4(a)] and MDC [Fig. 4(b)] plots similar to those found in previous literature. The advantage of these types of plots is that they are able to give a 3D interpretation of the EDC and MDC which will allow for better understanding of the intensity at certain points (such as discerning if there is a band gap or weak feature in the band gap).

Dispersion allows for one to interpret photon energy dependent cuts (not a mapping of photon energy) to include for interpretation or publication. The Dispersion map function can interpret an arbitrary amount of cuts specified by the user. [Fig. 5]

Stacked theory is a function that allows one to import theoretical DFT energy contours and plot them in a way to compare to the stackedECP() function [Fig. 2(b)]. There is also a feature that allows for plotting theory in one of the energy contour functions.

SpectroLab is an open source software package distributed under the MIT License. The code can be downloaded directly from the public code repository: github.com/christophersims/SpectroLab.

The code requires no installation, however, the folders that contain the code must be added to the path in order for them to run correctly (or the user could place all of the .m files in one directory). The user must have a Matlab version year of at least 2018 with the image toolbox add-on installed.

The code can be run by simply specifying the file path of the data one wishes to analyze. If there are no formatting errors the code should run without errors.

For ARPES there are three major file formats used (from the Igor suite), .txt, .ibw, and .pxt. Important data is lost in the .txt format and the .pxt format is compressed and cannot be decompressed outside of the Igor program. Therefore, this program only uses the Igor Binary Wave format (.ibw). In addition, the program only accepts files in the format ($k_{x}$,Energy,$k_{y}$), however, the file can be reformatted within the program.

If the input of the code in not formatted correctly (in the ($k_{x}$,Energy,$k_{y}$) format) it is possible to still run the code by utilizing Matlab’s permute() function. This function allows for one to swap the matrices in order for the program to run correctly. In addition to using the permute the variables in variables() must also be changed in order to match the code. In figure , we present data that was formatted incorrectly but was able to run in the program and produce good results. Here we present the data of Hf₂Te₂P (Fig. 6) and ZrSiS (Fig. 7) which were imported using the permute function.

Our implementation of plotting theory is currently an image importer, however, we have the code that allows for the input if the surface states and Fermi surface generated with the iterative surface green functions[37] imported from Wanniertools[38]. The calculations are not included in this package and must be calculated with tools such as Quantum Espresso[39], VASP[40], Abinit[41], Wannier90[42], etc. In figure 2(b), we show the capability so show stacked theory plots in order to coincide with the stackedECP() function. In addition, we have included a ECP function that also allows for the inclusion of theoretical calculation figures (see supplementary).

Here we present a volumetric plot of both a 3D band mapping correctly formatted Fig. 8(a) and an incorrectly formatted (corrected in code) in Fig. 8(b). This method is a powerful tool that will enable researchers to visualize bands in a 3D space.