Dataset for Direct Geometric Probe of Singularities in Band Structure

Included here is the processed data illustrated in the figures of both the main text, and the supplemental material. Below is a description of each file's contents. <strong>Figure2Ddata.csv</strong> contains the data illustrated in Figure 2D of the main text. The data provided are normalized band populations, such that the value 1 corresponds to the entire atom number in the sample. The rows provide the band index; the first row of data corresponds to the n=1 band, the second row corresponds to the n=2 band, etc. The columns provide the measured turning angle in units of radians; the first column corresponds to a turning angle of zero, and the angle is incremented by pi/12 radians for each column that follows. Row 5 is the error for the n=1 population, row 6 is the error for the n=2 population, and row 7 is the error on the sum of the population in bands with index not equal to 1 or 2. <strong>Figure3Bdata.csv</strong> contains the data illustrated in Figure 3B of the main text. The five columns correspond to the five different trajectory evolution times (0.5, 0.9, 1.3, 1.7, 2.1 milliseconds) shown in the Figure 3B. The first nine rows correspond to the nine trajectory midpoint positions in the Brillouin zone, as showed in Figure 3A; the first row corresponds to a midpoint at <strong>K</strong>. The next nine rows are the errors on the measurements. <strong>Figure4Cdata.csv </strong>contains the data illustrated in Figure 4C of the main text. The data provided are normalized band populations, such that the value 1 corresponds to the entire atom number in the sample. The rows provide the band index; the first row of data corresponds to the n=1 band, the second row corresponds to the n=2 band, etc. The columns provide the measured turning angle in units of radians; the first column corresponds to a turning angle of zero, and the angle is incremented by pi/6 radians for each column that follows. Row 11 is the error for the n=3 population, row 12 is the error for the n=4 population, and row 13 is the error on the sum of the population in bands with index not equal to 3 or 4. <strong>FigureS3data.csv </strong>contains the data illustrated in Figure 3 of the supplementary material. The first row is the data values, and the second row are the error bars. <strong>FigureS4data.csv </strong>contains the data illustrated in Figure 4 of the supplementary material. The first five rows are the normalized ground band population for five different trajectory mid points on the <strong>K</strong> - <strong>M</strong> - <strong>K'</strong> line of the Brillouin zone.; the first row is for a midpoint at <strong>K</strong>, and the fifth row is for a midpoint at <strong>M</strong>. The columns give the trajectory traversal times; the first column corresponds to a traversal time of 0.1 ms and each column corresponds to a new traversal time incremented by 0.2 ms. Rows 6-10 are the error bars for the measurements. <strong>FigureS6Bdata.csv </strong>contains the data illustrated in Figure 6B of the supplementary material. Rows 1-20 correspond to subpanel (iii) in the Figure S6 of the supplementary material. Rows 21-40 correspond to subpanel (ii) in the Figure S6 of the supplementary material. Rows 31-60 correspond to subpanel (i) in the Figure S6 of the supplementary material. Rows 1-10 correspond to the band index and give the normalized band population; row 1 corresponds to band index n=1 and row 10 corresponds to band index n=10. Rows 21-30 correspond to the band index and give the normalized band population; row 21 corresponds to band index n=1 and row 30 corresponds to band index n=10. Rows 41-50 correspond to the band index and give the normalized band population; row 41 corresponds to band index n=1 and row 50 corresponds to band index n=10. Rows 11-20 (31-40) [51-60] give the error in the band populations for measurements in panel iii (ii) [i]. <strong>FigureS6Cdata.csv </strong>contains the data illustrated in Figure 6C of the supplementary material. The first (second) column is the vertical (horizontal) axis. The fourth (third) column is the error in the points on the vertical (horizontal) axis.本数据集包含正文及补充材料附图中的处理后实验数据，下文将逐一说明各文件的具体内容。 **Figure2Ddata.csv** 包含正文图2D对应的实验数据。本次提供的数据为归一化能带占据数，当取值为1时代表样品中全部原子的占据量。各行对应能带的编号：第一行数据对应n=1能带，第二行对应n=2能带，以此类推。各列对应测量得到的转角，单位为弧度；第一列对应转角为0，后续每列的转角依次增加π/12弧度。第5行对应n=1能带占据数的误差，第6行对应n=2能带占据数的误差，第7行对应编号非1或2的能带占据数总和的误差。 **Figure3Bdata.csv** 包含正文图3B对应的实验数据。该文件共5列，分别对应图3B中展示的5种不同的轨迹演化时长（0.5、0.9、1.3、1.7、2.1毫秒）。前9行对应图3A中展示的布里渊区（Brillouin zone）内的9个轨迹中点位置，第一行对应<strong>K</strong>点处的中点；后续9行则为各测量值的误差。 **Figure4Cdata.csv** 包含正文图4C对应的实验数据。本次提供的数据为归一化能带占据数，当取值为1时代表样品中全部原子的占据量。各行对应能带的编号：第一行数据对应n=1能带，第二行对应n=2能带，以此类推。各列对应测量得到的转角，单位为弧度；第一列对应转角为0，后续每列的转角依次增加π/6弧度。第11行对应n=3能带占据数的误差，第12行对应n=4能带占据数的误差，第13行对应编号非3或4的能带占据数总和的误差。 **FigureS3data.csv** 包含补充材料图3对应的实验数据，第一行为数据值，第二行为误差棒数值。 **FigureS4data.csv** 包含补充材料图4对应的实验数据。前5行对应布里渊区（Brillouin zone）内<strong>K</strong>-<strong>M</strong>-<strong>K'</strong>线上5种不同轨迹中点的归一化基态能带占据数：第一行对应<strong>K</strong>点处的中点，第五行对应<strong>M</strong>点处的中点。各列对应轨迹的穿越时长，第一列对应穿越时长为0.1 ms，后续每列的时长依次增加0.2 ms。第6至10行为各测量值的误差棒。 **FigureS6Bdata.csv** 包含补充材料图6B对应的实验数据。第1至20行对应补充材料图S6的子图(iii)，第21至40行对应子图(ii)，第31至60行对应子图(i)。其中，第1至10行、第21至30行、第41至50行分别为子图(iii)、(ii)、(i)的归一化能带占据数，对应能带编号n=1至n=10；第11至20行、第31至40行、第51至60行则分别为上述子图对应能带占据数的测量误差。 **FigureS6Cdata.csv** 包含补充材料图6C对应的实验数据。第1（第2）列为纵轴（横轴）的测量值；第4（第3）列为对应纵轴（横轴）测量点的误差。