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.

Figure2Ddata.csv 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.

Figure3Bdata.csv 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 K. The next nine rows are the errors on the measurements.

Figure4Cdata.csv 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.

FigureS3data.csv 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.

FigureS4data.csv 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 K - M - K' line of the Brillouin zone.; the first row is for a midpoint at K, and the fifth row is for a midpoint at M. 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.

FigureS6Bdata.csv 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].

FigureS6Cdata.csv 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各图所用的经处理后的数据。下文将逐一说明各文件的内容。

Figure2Ddata.csv 包含正文图2D所用的数据。此处提供的数据为归一化能带占据数（normalized band populations），其中数值1对应样品中的全部原子数。行代表能带索引：第一行数据对应n=1能带，第二行对应n=2能带，依此类推。列代表以弧度为单位的测量转角：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行是n=1能带占据数的误差，第6行是n=2能带占据数的误差，第7行则为索引非1或2的能带总占据数的误差。

Figure3Bdata.csv 包含正文图3B所用的数据。其5列分别对应图3B中展示的5种不同轨迹演化时长（0.5、0.9、1.3、1.7、2.1毫秒）。前9行对应布里渊区（Brillouin zone）内的9个轨迹中点位置，如图3A所示；第一行对应K点处的中点。后续9行为测量值的误差。

Figure4Cdata.csv 包含正文图4C所用的数据。此处提供的数据为归一化能带占据数，其中数值1对应样品中的全部原子数。行代表能带索引：第一行数据对应n=1能带，第二行对应n=2能带，依此类推。列代表以弧度为单位的测量转角：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行是n=3能带占据数的误差，第12行是n=4能带占据数的误差，第13行则为索引非3或4的能带总占据数的误差。

FigureS3data.csv 包含补充材料图3所用的数据。第一行为数据值，第二行为误差棒数据。

FigureS4data.csv 包含补充材料图4所用的数据。前5行分别为布里渊区K-M-K'线上5个不同轨迹中点的归一化基态能带占据数：第一行对应K点处的中点，第五行对应M点处的中点。列代表轨迹穿越时长：第一列对应穿越时长为0.1毫秒，后续每列的时长依次增加0.2毫秒。第6至10行为测量值的误差棒。

FigureS6Bdata.csv 包含补充材料图6B所用的数据。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)。

第1至10行代表能带索引，对应归一化能带占据数：第1行对应能带索引n=1，第10行对应n=10。第21至30行代表能带索引，对应归一化能带占据数：第21行对应能带索引n=1，第30行对应n=10。第41至50行代表能带索引，对应归一化能带占据数：第41行对应能带索引n=1，第50行对应n=10。

第11至20行（第31至40行）[第51至60行]分别对应子图(iii)、(ii)、(i)中测量的能带占据数误差。

FigureS6Cdata.csv 包含补充材料图6C所用的数据。第一（第二）列为纵轴（横轴）数据，第四（第三）列为纵轴（横轴）上各数据点的误差。