An analysis system and method based on first principles and quantum oscillatory testing

Abstract

The application discloses an analysis system and method based on first principle and quantum oscillation test, and the analysis system comprises a data input module, a preprocessing module, an operation module and an output module, wherein the operation module comprises an extreme value orbit visualization unit used for visualizing the position of an extreme value orbit in a Fermi surface, an extreme value curve visualization unit used for outputting a frequency change diagram of the corresponding extreme value orbit in a calculation process, and a Fermi surface selected area calculation unit used for effectively improving the calculation efficiency for a complex Fermi surface. The application can quickly and accurately screen and determine the quantum oscillation frequency and effective mass information of relevant materials based on the marching cubes, slice-to-slice orbit matching in SKEAF and hdbscan algorithm, and further determine the Fermi surface characteristics of the materials, which has important significance for the research on the electronic structure and physical properties of quantum materials.

Description

TECHNICAL FIELD

[0001] The present application relates to a data analysis system and method, in particular to an analysis system and method based on first principle and quantum oscillation test. BACKGROUND

[0002] In the process of studying metal materials, Fermi surface is a collection of equipotential surfaces that separates the occupied states and empty states of the partially filled energy band, and the behavior of electrons near the Fermi surface determines various physical processes of the material. Based on the close relationship between electronic properties and the shape of the Fermi surface, determining the topological structure of the Fermi surface is one of the important steps to understand the physical properties of metal materials. At the same time, the measurement of the Fermi surface also provides experimental verification for the energy band structure based on single-electron approximation.

[0003] The main methods for measuring the Fermi surface of metals are angle-resolved photoelectron spectroscopy (ARPES) and quantum oscillation. ARPES is based on the photoelectric effect, which directly detects the momentum and emission angle distribution of emitted photoelectrons to map the electronic band structure and Fermi surface. ARPES has been widely used by physicists to study the electronic properties of high-temperature superconductors, graphene, topological materials, quantum wells, and materials exhibiting charge density waves.

[0004] Quantum oscillation test is suitable for measuring the Fermi surface in strong magnetic fields. In quantum oscillation experiments, based on the Landau quantization principle of fermions moving in a magnetic field, the magnetic field will periodically affect the electron density of states at the Fermi level, causing quantum oscillations in physical quantities determined by electron density of states, including resistance, Hall resistance, magnetic susceptibility, and thermoelectric potential. By measuring the oscillation phenomena of the corresponding physical quantities in different magnetic field directions, the shape of the Fermi surface of the entire material system can be mapped. Numerical calculation based on quantum oscillation effect refers to extracting quantum oscillation frequency and effective mass from the calculated energy band of the material, and comparing with the experimental measurement results, so as to predict the unmeasured frequency of the material in the experimental process and verify the theoretical model of the material.

[0005] In 2012, P.M.C.Rourke proposed the SKEAF (Supercell K-space Extremal Area Finder) algorithm, which finds the extremal orbit of the Fermi surface by constructing a K-space supercell, and calculates the quantum oscillation frequency and effective mass accordingly. This method effectively finds all quantum oscillation frequencies and compares them with experimental results. However, due to limitations in calculation accuracy and single numerical results, the calculation results may be repetitive, inaccurate, unknown to the Fermi surface, and inefficient for complex Fermi surfaces. The De Hass-Van Alphen (dHvA) oscillation effect is a type of quantum oscillation phenomenon. Under strong magnetic field conditions, the material's magnetization changes with the magnetic field, showing an oscillation phenomenon with a period of the inverse of the magnetic field. This effect is related to the behavior of electrons near the Fermi surface of a metal in a strong magnetic field, and can be used to probe the Fermi surface structure of a material. SUMMARY

[0006] The present application aims to provide an analysis system based on first principles and quantum oscillation testing that can effectively improve calculation efficiency and accuracy. Another purpose of the present application is to provide an analysis method based on first principles and quantum oscillation testing based on the analysis system.

[0007] Technical solution: The present application uses the marching cubes algorithm to present the Fermi surface in three dimensions, accurately locates the position and shape of the extremal orbit, and uses the slice-to-slice orbit matching algorithm in SKEAF to output the extremal curve of the Fermi surface to which the orbit belongs, thereby verifying and excluding the repeated extremal orbits caused by calculation accuracy in three-dimensional perspective.

[0008] In addition, for overly complex Fermi surfaces, the present application uses the hdbscan algorithm to cluster the Fermi surface, which can individually filter a region slice of the Fermi surface and calculate the extremal orbit, effectively eliminating the calculation redundancy problem under structural symmetry, greatly improving the calculation efficiency.

[0009] The three-dimensional Fermi surface visualization data analysis system based on first principles and quantum oscillation testing of the present application comprises:

[0010] A data input module for inputting the energy band file of the material to be studied and the operation parameters.

[0011] A preprocessing module for preprocessing the energy band file data.

[0012] An operation module for calculating the quantum oscillation frequency and related information of the material.

[0013] an output module for visualizing the output result.

[0014] Preferably, the data capable file data format is BXSF format, the band information bands, the base vector matrix bcell and the grid sampling mesh containing three dimensions.

[0015] Preferably, the operation parameters are the unit vector mag_h of the magnetic field direction and the Fermi energy efermi.

[0016] Preferably, the preprocessing module comprises an interpolation unit and a magnetic field direction conversion unit. The interpolation unit comprises a three-dimensional matrixing unit and a three-dimensional interpolation unit; the magnetic field direction conversion unit is used for converting the magnetic field direction into the azimuth angle and the azimuth angle parameters.

[0017] Preferably, the operation module is operated by the built-in SKEAF algorithm, which additionally outputs max(x ki ), max(y ki ), min(x ki ) and min(y ki ) based on the SC (Supercell) coordinate system for each closed orbit i in each slice k on the basis of the original SKEAF algorithm.

[0018] Preferably, the output module comprises a calculation result unit, an extreme value orbit visualization unit, an extreme value curve visualization unit, an extreme value orbit cross section unit and a Fermi surface selected area unit. The calculation result unit is used for outputting a calculation result file; the extreme value orbit visualization unit is used for visualizing the Fermi surface position where the extreme value orbit is located in a three-dimensional interactive interface; the extreme value curve visualization unit is used for visualizing the area change curve of the same orbit in different slices to determine the extreme point position; the extreme value orbit cross section unit is used for visualizing the extreme value orbit shape, extracting the orbit coordinates into two-dimensional plane coordinates for drawing; and the Fermi surface selected area unit is used for selecting an independent area in the Fermi surface and performing re-operation analysis.

[0019] Preferably, the three-dimensional matrixing unit is used for converting the bands into a three-dimensional matrix ebands mesh[0]×mesh[1]×mesh[2] , and the conversion relationship is:

[0020] The value of the index m in the bands corresponds to the index of the ebands

[0021]

[0022] to obtain ebands[i][j][k] = bands[m].

[0023] Preferably, the three-dimensional interpolation unit is used to perform linear interpolation on the bands, and an interpolation cubic point C is set, 8 vertex points being known value points around the point C, and first calculating the offsets x d , y d and z d of three dimensions:

[0024]

[0025] x0 represents a grid point below x, x1 represents a grid point above x, and y0, y1, z0 and z1 are the same. Then, interpolation is performed along the x-axis direction:

[0026] c 00 = V [x0, y0, z0] (1-x d ) + V [x1, y0, z0] x d

[0027] c 01 = V [x0, y0, z1] (1-x d ) + V [x1, y0, z1] x d

[0028] c 10 = V [x0, y1, z0] (1-x d ) + V [x1, y1, z0] x d

[0029] c 11 = V [x0, y1, z1] (1-x d ) + V [x1, y1, z1] x d

[0030] wherein V [x0, y0, z0] represents the energy value c 000 of the vertex (0, 0, 0). Then, interpolation is performed along the y-axis direction:

[0031] c0 = c 00 (1-y d ) + c 10 y d

[0032] c1 = c 01 (1-y d ) + c 11 y d

[0033] Finally, interpolation is performed along the z-axis direction to obtain the predicted energy value c of the point C:

[0034] c = c0 (1-z d ) + c1 z d

[0035] Thus, the new band matrix ebands interp can be obtained by repeating the above steps.

[0036] Preferably, the direction angle The azimuth angle is θ = arctan(mag_h[1] / mag_h[0]).

[0037] Preferably, the SC coordinate system is:

[0038]

[0039] wherein v = sin(θ) and w = cos(θ).

[0040] Preferably, the calculation result unit comprises an extreme orbit coordinate calculation result based on a K-space coordinate system, a closed orbit information calculation result based on an SC coordinate system, and an extreme orbit information calculation result.

[0041] Preferably, the extreme orbit visualization unit comprises a marching cubes algorithm to obtain an intersection coordinate matrix verts and a triangular facet vertex coordinate index table faces of an iso-energy surface based on linear interpolation under efermi.

[0042] A K-space point lattice constructed by basis vectors is established, and the point coordinates in the point lattice satisfy:

[0043]

[0044] A point lattice tree tree is constructed based on a cKDTree algorithm, and the nearest neighbor tree of a point in verts in the tree is indexed according to the position of the point, and the intersection points verts located in the first Brillouin zone are screened out. bz and faces bz The triangular_mesh method of the mayavi library is called as an input parameter to draw a three-dimensional iso-energy surface.

[0045] The extreme orbit coordinates are translated to display the extreme orbit in the first Brillouin zone. The origin coordinate [0, 0, 0] corresponds to the nearest neighbor tree gamma in the tree, and all point coordinates orbit on the extreme orbit satisfy: q×3 The nearest neighbor tree set in the tree is zone = {zone0, zone1…, zone n} and a three-dimensional matrix loc is constructed with the cubic root m of the total number of trees in the tree. m×m×m The vector matrix dif between two trees is obtained by subtracting the coordinates corresponding to all values in gamma and zone in loc. n×3 ,

[0046] gamma pos = loc[gamma], (zone pos ) i = loc[zone i ]

[0047]

[0048] Take the maximum value of each column of the dif matrix as the translation direction vector L,

[0049] L = [max(dif x ), max(dif y ), max(dif z )]

[0050] Convert all coordinates in the orbit from the K-space coordinate system to the basis vector coordinate system, add L, and convert back to the K-space coordinate system to obtain the translated extreme value orbit coordinates,

[0051]

[0052] After the conversion of the extreme value orbit coordinates, all nearest neighbor trees where all the extreme value orbit coordinates are located are used as the drawing Brillouin zone region, so that the complete shape and position of all orbits are displayed on the Fermi surface with the least number of Fermi surfaces.

[0053] Preferably, the extreme value curve visualization unit matches the orbit area of adjacent slices based on the slice-to-slice orbit matching algorithm in the SKEAF, draws an extreme value curve graph, and calculates the coordinate information avg(x i ) k , avg(y i ) k , max(x i ) k , max(y i ) k , min(x i ) k , min(y i ) k , std(x i ) k , and std(y i ) k of the i-th orbit of the k-th slice according to the closed orbit information calculation result based on the SC coordinate system, finds the orbit of the adjacent slice that best matches the current orbit by the following formula, and stops until no matching orbit is found or the first slice or the last slice is reached.

[0054] |avg(x i )k -avg(x j ) knear |≤std(x) cp

[0055] |avg(y i ) k -avg(y j ) knear |≤std(y) cp

[0056] |max(x i ) k -max(x j ) knear |≤2×std(x) cp

[0057] |max(y i ) k -max(y j ) knear |≤2×std(y) cp

[0058] |min(x i ) k -min(x j ) knear |≤2×std(x) cp

[0059] |min(y i ) k -min(y j ) knear |≤2×std(y) cp

[0060] When searching upwards from the current slice, knear=k-1, j is the track index in the knear slice, std(x) cp =std(x i ) k , std(y) cp =std(y i ) k ; when searching downwards, knear=k+1, std(x) cp =std(x j ) k+1 , std(y) cp =std(y j ) k+1 . If multiple matching tracks are found, the B j ,

[0061] Bj = [avg(x i ) k - avg(x j ) knear ] 2 + [avg(y i ) k - avg(y j ) knear ] 2 + [max(x i ) k - max(x j ) knear ] 2 + [max(y i ) k - max(y j ) knear ] 2 + [min(x i ) k - min(x j ) knear ] 2

[0062] B j The minimum value is the matching orbit, and the extreme value curve diagram can be obtained by plotting from small to large according to the slice index of the matched orbit.

[0063] Preferably, the extreme orbit cross-section unit extracts the orbit coordinates into two-dimensional plane coordinates for plotting. First, determine the normal vector of the extreme orbit plane, select any three points p1, p2, p3 in the orbit that are not on a straight line, and use the formula to determine the normal vector n,

[0064] n = p1p2 x p1p3

[0065] After normalization, the z-axis unit vector n of the conversion coordinate system t is obtained z , and n x is defined as p1-p2 and normalized, and n y is [x, y, z], according to the equation,

[0066]

[0067] That is, n y , convert the extreme orbit coordinates to the conversion coordinate system to obtain new coordinates orbit t .

[0068]

[0069] Take orbit t [ :, 0] as the x value, and orbitt [:,1] is the y value to draw the extreme orbit cross-section diagram.

[0070] Preferably, the Fermi surface selection unit includes a midpoint calculation unit, a midpoint conversion unit, a cluster prediction unit and a reconstructed band file unit. The midpoint calculation unit is used to calculate the midpoint mid of the selected orbit and convert mid to the basis vector coordinate system to obtain mid bcell ,

[0071] mid bcell =mid·bcell -1

[0072] The midpoint conversion unit is used to translate the midpoint to the correct position of the ebands matrix, where mid bcell [i]>0, then mid bcell [i]={mid bcell [i]}×mesh[i]; otherwise mid bcell [i]=({mid bcell [i]}+1)×mesh[i].

[0073] The cluster prediction unit uses the HDBSCAN algorithm to cluster and partition the Fermi surface and predict the partition where mid is located. First, set the f≥efermi part in ebands to 1 and the rest to 0 to obtain ebands onehot Matrix; ebands onehot As training data input to the hdbscan algorithm model, ebands onehot Perform three-dimensional clustering and partitioning, and then use the training model to predict mid bcell The area where the coordinates of the area are obtained. mid , which corresponds to the index in ebands.

[0074] The reconstructed band file unit is used to construct a band file in the BXSF file format that only contains the selected band information, and input it into the data input module as an input file for calculation. mid , whose value satisfies,

[0075] ebands mid [zone mid [i]]=ebands[zone mid [i]]

[0076] ebands mid [~zone mid ]=enew

[0077] Among them ~ zonemid represent the rest of the coordinates not in the zone mid The value enew is different according to the type of the selected zone, if the selected zone is of hole type, enew is the value in ebands closest to efermi, if the selected zone is of electron type, enew is the value in ebands farthest to efermi. The ebands mia are unfolded to obtain bands mid , a new BXSF file is reconstructed as new band information and input into the data input module for calculation and analysis.

[0078] The application further provides an analysis method based on the above system, comprising the following steps:

[0079] (1) obtaining band information file and operation parameters;

[0080] (2) preprocessing band data and magnetic field direction;

[0081] (3) obtaining calculation result output file by operation;

[0082] (4) screening for repeated frequency, comparing the coincidence of the selected frequency extreme orbit cross section, the coincidence of the extreme curve and the coincidence of the extreme orbit position to screen out;

[0083] (5) selecting the orbit corresponding to the selected zone, constructing a new band information file, determining the magnetic field direction, and returning to step (1);

[0084] According to the application, the data band file data format in step (1) is BXSF format, the band information bands, the base vector matrix bcell and the grid sampling mesh containing three dimensions are read, the operation parameters are the unit vector mag_h of the studied magnetic field direction and the Fermi energy efermi.

[0085] Preferably, the material to be studied is quantum material including Ni3In2Se2, ReO2, etc.

[0086] Preferably, the magnetic field direction unit vector mag_h corresponding to the calculation of Ni3In2Se2 is [0.95, 0.00, 0.31], [-0.07, -0.98, 0.20], [-0.03, 0.99, 0.10]; the magnetic field direction unit vector corresponding to the calculation of ReO2 is [1.00, 0.00, 0.00].

[0087] Preferably, efermi corresponding to Ni3In2Se2 is 0.568158 / 0.567423 / 0.568893 Ryd, and efermi corresponding to ReO2 is 0.168074 Ryd.

[0088] Preferably, the pre-processing of the energy band data in step (2) is interpolated by a three-dimensional linear interpolation method.

[0089] Preferably, the calculation of the orbital extreme coordinate file in the output result in step (3) includes a numerical value in the relative size unit and a numerical value in the unit of emme.

[0090] Preferably, the orbital extreme cross-section graph in step (4) includes a smoothing process, preferably a B-spline interpolation process.

[0091] Preferably, the hdbscan model used in step (5) sets the parameter min_cluster_size to 5 and alpha to 1.0.

[0092] Beneficial effects: Compared with the prior art, the present application has the following significant advantages: through the introduction of the marching cubes algorithm, the slice-to-slice orbit matching algorithm in SKEAF, and the hdbscan algorithm, the calculation efficiency and accuracy of the traditional SKEAF algorithm are effectively improved. For example, after removing the repeatability and calculation accuracy of the calculation frequency of Ni3In2Se2 in the [0.95, 0.00, 0.31] magnetic field direction, the number of screening is reduced from 8 to 6, and the marching cubes algorithm also improves the visualization calculation time compared with the traditional contour 3D method, from 2 min to 5 s. The analysis method of the present application can quickly and accurately determine the quantum oscillation frequency of the related material, which has significance for the fields of materials science, physics and electronics. BRIEF DESCRIPTION OF DRAWINGS

[0093] Figure 1 A structural framework diagram of the three-dimensional Fermi surface visualization data analysis method based on first-principle calculation and quantum oscillation test in the present application;

[0094] Figure 2 A graph of the extreme curve of the quantum oscillation frequency in the Fermi surface calculated from Ni3In2Se2 in Example 1;

[0095] Figure 3 A graph of the orbital cross-section of the quantum oscillation frequency in the Fermi surface calculated from Ni3In2Se2 in Example 1. DETAILED DESCRIPTION

[0096] The technical solutions of the present application will be further described below in conjunction with the drawings.

[0097] The materials used below are Ni3In2Se2 materials, the magnetic field direction is [0.95, 0.00, 0.31], and the Fermi energy is 0.568158 Ryd.

[0098] This embodiment provides a method for obtaining the dHvA oscillation frequency under a specific magnetic field direction from energy band information data, including the following steps (the structural framework diagram is as follows Figure 1 shown):

[0099] Step 1: Obtain the BXSF file data of Ni3In2Se2 energy band information, and set the magnetic field direction vector mag_h and Fermi energy efermi.

[0100] Step 2: Import the energy band information in step 1 into the preprocessing module, use three-dimensional matrix to convert the energy band information into a three-dimensional matrix, and then interpolate the energy band matrix through three-dimensional interpolation to obtain ebands; convert the magnetic field direction mag_h in step 1 into direction angle and azimuth angle.

[0101] Step 3: Import the data in step 2 into the calculation module to calculate the basic information of the extreme orbit, the extreme orbit coordinate orbit, and the avg(x i ) k 、avg(y i ) k 、max(x i ) k 、max(y i ) k 、min(x i ) k 、min(y i ) k 、std(x i ) k and std(y i ) k information.

[0102] Step 4: Import the calculation results described in step 3 and ebands, mag_h and efermi in step 2, and use the marching cubes algorithm to obtain the intersection coordinate matrix verts and the triangle vertex coordinate index table faces of the isoenergy surface obtained based on linear interpolation under efermi.

[0103] Construct a point matrix tree based on the cKDTree algorithm, and index the nearest tree in the tree according to the position of the verts midpoint, and filter out the intersection verts in the first Brillouin zone. bz and faces bz , as the input parameter, call the triangular_mesh method of the mayavi library to draw the three-dimensional equienergy surface and obtain the first Brillouin zone Fermi surface.

[0104] Translate the coordinates of the extremal orbit to make the extremal orbit show in the first Brillouin zone. The origin coordinate [0, 0, 0] corresponds to the nearest neighbor tree in the tree as gamma, and all point coordinates on the extremal orbit orbit q×3 In the tree, all the nearest neighbor trees are collected as zone = {zone0, zone1…, zone n}, and a three-dimensional matrix loc is constructed with the cube root m of the total number of trees in the tree m×m×m , and the vector matrix dif between two trees is obtained by subtracting the coordinates corresponding to all values in gamma and zone in loc n×3 ,

[0105] gamma pos = loc[gamma], (zone pos ) i = loc[zone i ]

[0106]

[0107] Take the maximum value of each column of the dif matrix as the translation direction vector L,

[0108] L = [max(dif x ), max(dif y ), max(dif z )]

[0109] Convert all coordinates in orbit from K-space coordinates to base vector coordinates, add L, and convert back to K-space coordinates to get the translated extremal orbit coordinates,

[0110]

[0111] After the conversion of the extremal orbit coordinates, all the nearest neighbor trees where all the extremal orbit coordinates are located are used as the Brillouin zone area for drawing, so that the complete shape and position of all orbits can be displayed on the Fermi surface with the least cost.

[0112] According to the slice and orbit index of the extremal orbit of the selected frequency, the matching orbit is found by the following algorithm: the coordinate information avg(x i ) k , avg(y i ) k , max(x i ) k , max(y i ) k , min(x i ) k , min(y i) k , std(x i ) k and std(y i ) k , find the track in the neighboring slice that best matches the current track by the following equations until no match is found or the first slice is reached or the last slice is reached,

[0113] |avg(x i ) k -avg(x j ) knear |≤std(x) cp

[0114] |avg(y i ) k -avg(y j ) knear |≤std(y) cp

[0115] |max(x i ) k -max(x j ) knear |≤2×std(x) cp

[0116] |max(y i ) k -max(y j ) knear |≤2×std(y) cp

[0117] |min(x i ) k -min(x j ) knear |≤2×std(x) cp

[0118] |min(y i ) k -min(y j ) knear |≤2×std(y) cp

[0119] When looking up from the current slice, knear = k - 1, j is the track index in the knear slice, std(x) cp = std(x i ) k , std(y) cp = std(y i ) k; When searching downward, knear=k+1, std(x) cp =std(x j ) k+1 , std(y) cp =std(y j ) k+1 If multiple matching tracks are found, calculate B for each track. j ,

[0120] E j =[avg(x i ) k -avg(x j ) knear ] 2 +[avg(y i ) k -avg(y j ) knear ] 2 +[max(x i ) k -max(x j ) knear ] 2 +[max(y i ) k -max(y j ) knear ] 2 +[min(x i ) k -min(x j ) knear ] 2

[0121] B j The one with the smallest value is the matching orbit. By plotting the matched orbit from small to large slice index, we can get the extreme value curve. The extreme value orbit graph of all calculated frequencies is as follows: Figure 2 shown.

[0122] Extract the orbital coordinates of the selected extreme orbit into two-dimensional plane coordinates for plotting. First determine the normal vector of the extreme orbit plane, select any three points p1, p2, p3 in the orbit that are not on a straight line, and use the formula to determine the direction n.

[0123] n=p1p2×p1p3

[0124] After normalization, we get the z-axis unit vector n of the transformed coordinate system t z , and then define n x Let n be p1-p2 and normalized. y For [x, y, z], according to the equation,

[0125]

[0126] You can solve for n y , transform the extreme orbit coordinates into the transformation coordinate system to obtain the new coordinate orbit t Orbit t [:,0] is the x value, orbit t [:,1] is the y value to draw the extreme orbit cross-section diagram, all extreme orbit cross-section diagrams are as follows Figure 3 shown.

[0127] For the screening of repetitive frequencies, the coincidence of the extreme value orbital sections, the coincidence of the extreme value curves, and the coincidence of the extreme value orbital positions of the selected frequencies are compared for screening. Finally, the frequencies before and after screening are obtained, as well as the comparison of the experimentally measured frequencies are shown in Table 1.

[0128] Step 5: Select the extreme orbit with a frequency of 143.5T for separate analysis, calculate the midpoint mid of the orbit, and convert mid to the basis vector coordinate system to obtain mid bcell . Translate the midpoint to the correct position of the ebands matrix, where mid bcell [i]>0, then mid bcell [i]={mid bcell [i]}×mesh[i]; otherwise mid bcell [i]=({mid bcell [i]}+1)×mesh[i].

[0129] Use the hdbscan algorithm to cluster and partition the Fermi surface and predict the partition where mid is located. First, set the f≥efermi part in ebands to 1 and the rest to 0 to obtain ebands onehot Matrix; ebands onehot As training data input to the hdbscan algorithm model, ebands onehot Perform three-dimensional clustering and partitioning, and then use the training model to predict mid bcell The area where the coordinates of the area are obtained. mid , which corresponds to the index in ebands.

[0130] Construct a band file in BXSF format that only contains the selected band information and input it into the data input module as an input file for calculation. mid , whose value satisfies,

[0131] ebands mid [zone mid [i]]=ebands[zonemid [i]]

[0132] ebands mid [~zone mid ]=enew

[0133] where ~zone mid represents the coordinates not in the zone mid list, enew is set according to the type of the selected zone, if the selected zone is of hole type, enew is the value in ebands closest to efermi, if the selected zone is of electron type, enew is the value in ebands farthest to efermi. Unfold ebands mid to get bands mid , reconstruct a new BXSF file with the new band information, and set the parameters back to step 1 to calculate the orbital positions.

[0134] Table 1

[0135]

[0136] *Vertical ab plane direction.

Claims

1. An analysis system based on first principles and quantum oscillatory testing, characterized in that, The system comprises a data input module, a preprocessing module, a calculation module and an output module; The preprocessing module comprises an interpolation unit and a magnetic field direction conversion unit; The output module comprises a calculation result unit, an extreme orbit visualization unit, an extreme curve visualization unit, an extreme orbit cross-section unit and a Fermi surface selection unit; The extreme orbit visualization unit uses the marching cubes algorithm to perform three-dimensional presentation on the Fermi surface, accurately locates the position and shape of the extreme orbit, and the extreme curve visualization unit uses the slice-to-slice orbit matching algorithm based on SKEAF to output the extreme curve of the Fermi surface to which the orbit belongs, so as to double-verify and exclude the repeated problem of the extreme orbit caused by the calculation accuracy under the three-dimensional perspective; The slice-to-slice orbit matching algorithm calculates the coordinate information of the i-th orbit of the k-th slice according to the SC coordinate system-based closed orbit information calculation result, that is, avg(x i ) k , avg(y i ) k , max(x i ) k , max(y i ) k , min(x i ) k , min(y i ) k , std(x i ) k , and std(y i ) k , and finds the orbit of the adjacent slice that best matches the current orbit by the following formula until no matching is found or the first slice or the last slice is reached, | avg(x i ) k - avg(x j ) knear | ≤ std(x) cp | avg(y i ) k - avg(y j ) knear | ≤ std(y) cp | max(x i ) k | - max(x j ) knear | ≤ 2 x std(x cp | max(y i ) k | ≤ 2 x std(y j ) knear | ≤ 2 x std(y cp | min(x i ) - k * min(x j ) knear | ≤ 2 * std(x) cp | min(y i ) - k * min(y j ) knear | ≤ 2 * std(y cp When searching upwards from the current slice, knear = k-1, j is the track index in the knear slice, std(x) cp =std(x i ) k , std(y) cp =std(y i ) k ; When searching downward, knear=k+1, std(x) cp =std(x j ) k+1 , std(y) cp =std(y j ) k+1 ; If multiple matching tracks are found, calculate B for each track j , B j = [avg(x i ) k - avg(x j ) knear ] 2 + [avg(y i ) k - avg(y j ) knear ] 2 + [max(x i ) k - max(x j ) knear ] 2 + [max(y i ) k - max(y j ) knear ] 2 + [min(x i ) k - min(x j ) knear ] 2 B j The minimum value is the matching orbit, and the extreme value curve diagram can be obtained according to the matched orbit plotted from small to large by slice index.

2. The first-principles and quantum-oscillation-test-based analysis system of claim 1, wherein, The interpolation unit comprises a three-dimensional matrix unit and a three-dimensional interpolation unit; The three-dimensional matrixing unit is configured to convert the bands into a three-dimensional matrix ebands mesh[0]×mesh[1]×mesh[2] with the conversion relationship being The value of index m in bands corresponds to ebands index, Get ebands[i][j][k] = bands[m]; The three-dimensional interpolation unit is used for linear interpolation processing of the bands, an interpolation cubic intermediate C point is set, eight vertices are known value points around the C point, and offsets x d , y d , and z d of three dimensions are calculated first x0 represents a grid point below x, x1 represents a grid point above x, and similarly for y0, y1, z0 and z1; then interpolate along the x-axis direction: c 00 = V [x0, y0, z0] (1 - x d )+ V [x1, y0, z0] x d c 01 = V [x0, y0, zl] (1 - x d )+ V [xl, y0, zl] x d c 10 = V[x0,y1,z0](1 - x d )+ V[x1,y1,z0]x d c 11 = V [x0, y0, z0] (1 - x d )+ V [x1, y1, z1] x d where V [x0, y0, z0] represents the energy value c of the vertex (0, 0, 0) 000 ; and then interpolating along the y-axis direction: c0= c 00 (1-y d )+c 10 y d c1 = c 01 (1 - y d )+ c 11 y d Finally, interpolate along the z-axis direction to get the predicted energy value c of point C: c = c0(1 - z d )+c1z d So repeat to get the new band matrix ebands_interp.

3. The first-principles and quantum-oscillation-test-based analysis system of claim 1, wherein, The extreme orbit visualization unit is used for visualizing the Fermi surface position of the extreme orbit in a three-dimensional interactive interface; the extreme orbit visualization unit comprises a marching cubes algorithm to obtain the intersection coordinate matrix verts of the equal-energy surface based on linear interpolation under efermi and a triangular facet vertex coordinate index table faces; A K-space point array constructed by basis vectors is established, and the point coordinates in the point array satisfy: Based on the cKDTree algorithm, the point array tree is constructed, and the nearest tree of the point in the tree is indexed according to the position of the point in the verts, and the intersection points in the first Brillouin zone are screened out bz And faces bz As an input parameter, the triangular_mesh method of the mayavi library is called to draw a three-dimensional iso-energy surface; Translate the extreme orbit coordinates to make the extreme orbit show in the first Brillouin zone; the origin coordinate [0, 0, 0] corresponds to the nearest tree in the tree as gamma, and all point coordinates on the extreme orbit orbit q×3 In the tree, all the nearest tree set is zone = {zone0, zone1…, zone n}, and a three-dimensional matrix loc m×m×m is constructed with the cubic root m of the total number of trees in the tree, and the vector matrix dif n×3 is obtained by subtracting the coordinates corresponding to all values in gamma and zone in loc. gamma pos = loc[gamma], (zone pos ) i = loc[zone i ] Take the maximum value of each column of the dif matrix as the translation direction vector L, L = [max(dif x ), max(dif y ), max(dif z )] Convert all coordinates in orbit from the K-space coordinate system to the basis vector coordinate system, add L, and convert back to the K-space coordinate system to obtain the translated extreme orbit coordinates, After the conversion of the extreme orbit coordinates is completed, all the nearest neighbor trees where all the extreme orbit coordinates are located are used as the drawing Brillouin zone region, so that the complete shape and position of all orbits are displayed on the Fermi surface.

4. The first-principles and quantum-oscillation testing based analysis system of claim 1, wherein, The extreme orbit cross-section unit is used for visualizing the shape of the extreme orbit, and the orbit coordinates are extracted into two-dimensional plane coordinates for drawing; First, determine the normal vector of the extreme orbit plane, select any three points p1, p2 and p3 in orbit that are not on a straight line, and use the formula to determine the normal vector n, n = p1p2 × p1p3 After normalization, we get the z-axis unit vector n of the transformed coordinate system t z , and then define n x Let n be p1-p2 and normalized. y For [x,y,z], according to the equation, n can be solved y The extreme orbit coordinates are converted to the conversion coordinate system to obtain new coordinates orbit t orbit t [:,0] as x values, orbit t [:,1] as y values.

5. The first-principles and quantum-oscillation testing based analysis system of claim 1, wherein, The Fermi surface selection unit is used for selecting independent regions in the Fermi surface and performing reoperation analysis, including a midpoint calculation unit, a midpoint conversion unit, a clustering prediction unit and a reconstructed band file unit; The midpoint calculating unit is configured to calculate a midpoint mid of the selected orbit, and convert the mid into a base vector coordinate system to obtain mid bcell , mid bcell = mid · bcell -1 The mid-point conversion unit is used to translate the mid-point to the correct position of the ebands matrix, where mid bcell [i] > 0, then mid bcell [i] = {mid bcell [i]} x mesh[i]; otherwise, mid bcell [i] = ({mid bcell [i]} + 1) x mesh[i]; The clustering prediction unit clusters and partitions the Fermi surface by using the hdbscan algorithm, and predicts the partition where the mid is located; first, set the part of ebands where f≥efermi as 1, and set the rest as 0, to obtain ebands onehot The matrix; set ebands onehot As training data input into the hdbscan algorithm model, ebands onehot are clustered and partitioned in three dimensions, and then the training model is used to predict the region where the mid bcell is located, to obtain the coordinates zone mid of the region, that is, the index in ebands. The reconstructed band file unit is used to construct a band file in the BXSF file format containing only selected band information as an input file to the data input module for operation; the band information is ebands mid with the value satisfying, ebands mid [zone mid [i]] = ebands[zone mid [i]] ebands mid [~zone mid ]=enew where ~zone mid represents the rest of the coordinates in the zone mid list, enew is set according to the type of the selected zone. If the selected zone is of hole type, enew is the value in ebands closest to efermi but smaller than efermi. If the selected zone is of electron type, enew is the value in ebands closest to efermi but larger than efermi. ebands mid is unfolded to get bands mid , and a new BXSF file is reconstructed as new band information and input into the data input module for calculation, analysis and operation.

6. An analysis method based on the first-principle and quantum oscillation test based on the system of any one of claims 1-5, characterized in that: The method comprises the following steps: (1) obtaining a band information file and operation parameters; (2) preprocessing band data and magnetic field direction; (3) calculating to obtain a calculation result output file; (4) Screening for the repetition frequency, comparing the coincidence of the selected frequency extreme orbit cross section, the coincidence of the extreme curve, the coincidence of the extreme orbit position to screen out; (5) Selecting the corresponding selected area of the orbit, constructing a new energy band information file, determining the magnetic field direction, and returning to step (1).

7. The first-principles and quantum-oscillation-test-based analysis method according to claim 6, characterized by: The pre-processing energy band data in the step (2) is interpolated by a three-dimensional linear interpolation method; the orbit extreme cross section in the step (4) includes a smoothing process, and the smoothing process is a B-spline interpolation process; the hdbscan model used in the selected area in the step (5) sets the parameter min_cluster_size to 5 and alpha to 1.

0.

8. The first-principles and quantum-oscillation testing based analysis method of claim 6, wherein: The data band file data format in the step (1) is BXSF format, reads the energy band information bands, the base vector matrix bcell and the grid sampling mesh containing three dimensions, and the operation parameters are the unit vector mag_h of the studied magnetic field direction and the Fermi energy efermi.

9. The first-principles and quantum-oscillation testing based analysis method of claim 6, wherein: The material to be studied in the analysis method is a quantum material system including Ni3In2Se2 and ReO2; the calculated magnetic field direction unit vector mag_h corresponding to Ni3In2Se2 is [0.95, 0.00, 0.31], [-0.07, -0.98, 0.20], and [-0.03, 0.99, 0.10]; the calculated magnetic field direction unit vector corresponding to ReO2 is [1.00, 0.00, 0.00]; efermi corresponding to Ni3In2Se2 is 0.568158 / 0.567423 / 0.568893 Ryd, and efermi corresponding to ReO2 is 0.168074 Ryd.

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