A method, device and medium for measuring the Fermi velocity of two-dimensional Dirac material

Abstract

The present invention provides a method, device and medium for measuring the Fermi velocity of a two-dimensional Dirac material, which relates to the technical field of scanning tunneling microscopy. The device includes a scanning tunneling microscope, a digital lock-in amplifier and a computer. The unit cell parameters of a target sample are obtained based on the scanning tunneling microscope instrument, and the differential conductivity spectrum and current-height spectrum of the target sample are analyzed and processed. The reverse decay length related to the tunneling electron and the bias voltage is combined to calculate the relationship between the parallel component of the Fermi wave vector and the energy in the momentum space, thereby obtaining the Fermi velocity of the two-dimensional Dirac material. The present invention measures the Fermi velocity based on a scanning tunneling microscope, has a spatial resolution as low as the atomic scale, avoids quasi-particle interferometric measurement, omits the operation of artificially introducing scattering centers, greatly reduces the sample processing steps, and improves the measurement efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of scanning tunneling microscopes, and in particular to a method, a device and a medium for measuring the Fermi velocity of a two-dimensional Dirac material. Background Art

[0002] Two-dimensional materials, since the successful isolation of single-layer graphene, have led to a real revolution in contemporary condensed matter physics. One of the most striking properties of Dirac materials, especially those similar to graphene, is their linear dispersion relation. Due to this linear dispersion relation, electrons behave as massless relativistic particles. Since most of the properties of a material are determined by electrons near the Fermi level, the Fermi velocity is a very relevant parameter. The Fermi velocity of free-state graphene is about 10 6 m / s, which is only a small fraction of the speed of light. The Fermi speed of Dirac materials increases with the enhancement of electron-electron interactions, so the Fermi speed can be adjusted by coupling with the substrate, twisting and bending. In short, the measurement of the Fermi speed helps to reveal the behavior of fermions at the quantum scale.

[0003] Previously, there were several methods to measure the Fermi velocity of two-dimensional Dirac materials. Of particular interest are techniques that directly detect the dispersion relations of low-energy electrons in momentum space, such as angle-resolved photoelectron spectroscopy and quasiparticle interferometry. These techniques cannot simultaneously measure the surface morphology and Fermi velocity of the target sample, while scanning tunneling microscopy can simultaneously perform atomic-level imaging and electrical property measurements, making this concept possible. Summary of the invention

[0004] The purpose of the present invention is to provide a method, device and medium for measuring the Fermi velocity of a two-dimensional Dirac material to improve the above-mentioned problem. In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is as follows:

[0005] In a first aspect, the present application provides a method for measuring the Fermi velocity of a two-dimensional Dirac material, comprising:

[0006] Step S1, using a scanning tunneling microscope to perform atomic-level imaging of the area to be measured of the target sample to obtain the crystal structure and unit cell parameters, and verifying whether the area to be measured is the desired target sample by analyzing and comparing the crystal structure and unit cell parameters;

[0007] Step S2, setting scanning parameters of current and voltage according to the target sample, measuring the tunnel current spectrum of the scanning area where the target sample is located, and obtaining current-voltage spectrum data of the scanning area;

[0008] Step S3, measuring the scanning area of ​​the target sample to obtain a first current-height spectrum, and simultaneously obtaining a second current-height spectrum of a calibration material with a known work function, and obtaining the distance between the probe and the target sample by comprehensively analyzing the first current-height spectrum and the scanning parameters of the target sample set current and voltage;

[0009] Step S4, using the current-voltage spectrum data of the scanning area, measuring the differential conductance spectrum of the target sample through the measurement system, and obtaining the linear dispersion characteristics of the two-dimensional Dirac material by analyzing the linear relationship between the state density of the target sample and the bias voltage;

[0010] Step S5, according to the distance between the probe and the target sample, combined with the comparison results of the first current-height spectrum and the second current-height spectrum, calculate the work function difference between the target sample and the calibration material, and obtain the work function of the target sample, and then calculate the average work function of the probe and the target sample;

[0011] Step S6, based on the unit cell parameters and the linear dispersion characteristics, using the energy-momentum relationship in the momentum space, deriving a functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the change of the bias voltage and the first parameter related to the Fermi function;

[0012] Step S7, according to the functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the bias voltage, the differential conductivity spectrum of the target sample is analyzed, and the first parameter related to the Fermi function is extracted, and the Fermi velocity of the target sample is finally obtained by calculation based on the distance between the probe and the target sample, the average work function of the probe and the target sample, and the first parameter.

[0013] Preferably, in step S2, when measuring the tunnel current spectrum of the scanning area where the target sample is located, the constant height mode of the scanning tunneling microscope needs to be turned on for measurement.

[0014] Preferably, in step S3, when measuring the scanning area of ​​the target sample to obtain a first current-height spectrum and simultaneously obtaining a second current-height spectrum of a calibration material with a known work function, the constant voltage mode of the scanning tunneling microscope needs to be turned on for measurement.

[0015] Preferably, in step S4, the measurement system for measuring the differential conductance spectrum of the target sample by the measurement system includes a scanning tunneling microscope and a digital lock-in amplifier, wherein the digital lock-in amplifier needs to add a sinusoidal signal when measuring the current-voltage spectrum to obtain the differential conductance spectrum.

[0016] Preferably, in step S5, the calculation of the work function difference of the target sample and obtaining the work function of the target sample, and then calculating the average work function of the probe and the target sample, includes:

[0017] Analyze the current-height differential spectrum (dln(I) / dz) of the calibration material with known work function, and use the current-height differential spectrum as the calibration value;

[0018] Processing the current-height differential spectrum of the target sample, calculating the difference from the calibrated value, and obtaining the work function of the target sample;

[0019] The work functions of the target sample and the probe are combined to calculate the average value of the probe and the target sample.

[0020] In a second aspect, the present application also provides a device for measuring the Fermi velocity of a two-dimensional Dirac material, comprising:

[0021] Memory for storing computer programs;

[0022] A processor is used to implement the steps of the method for measuring the Fermi velocity of a two-dimensional Dirac material when executing the computer program.

[0023] In a third aspect, the present application further provides a readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the above-mentioned method based on measuring the Fermi velocity of a two-dimensional Dirac material are implemented.

[0024] The beneficial effects of the present invention are:

[0025] A method for measuring the Fermi velocity of a two-dimensional Dirac material disclosed in the present invention obtains a differential conductance spectrum of a target sample through a scanning tunneling microscope instrument, analyzes and processes the differential conductance spectrum of the target sample, and combines the inverse decay length related to tunneling electrons and bias voltage; calculates the relationship between the parallel component of the Fermi wave vector and the energy in the momentum space, and then obtains the Fermi velocity of the two-dimensional Dirac material; the present invention measures the Fermi velocity based on a scanning tunneling microscope, has a spatial resolution as low as the atomic scale, omits operations such as quasi-particle interferometry measurement, avoids the operation of artificially introducing scattering centers, greatly reduces the sample processing steps, and improves measurement efficiency.

[0026] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or be understood by practicing the embodiments of the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0028] Figure 1 This is a schematic flow chart of a method for measuring the Fermi velocity of a two-dimensional Dirac material according to an embodiment of the present invention;

[0029] Figure 2 This is a schematic diagram of the structure of a device for measuring the Fermi velocity of a two-dimensional Dirac material according to an embodiment of the present invention;

[0030] Figure 3 Schematic diagram of the STM image and fast Fourier transform of the graphene / MoS2 heterojunction material in the embodiment of the present invention, wherein (a) is the atomic resolution of graphene, (b) is the moiré superstructure formed by the graphene / MoS2 heterojunction, and (c) is a schematic diagram of the fast Fourier transform of the graphene / MoS2 heterojunction scanning tunneling microscope image corresponding to a 5° rotation angle;

[0031] Figure 4 Schematic diagram of differential conductivity spectrum measured in an embodiment of the present invention;

[0032] Figure 5 Schematic diagram of current-height differential spectrum related to work function in an embodiment of the present invention;

[0033] Figure 6 Schematic diagram of the energy band junction of graphene and molybdenum disulfide materials in the embodiment of the present invention, M, K, Γ are all high symmetry points in the Brillouin zone, E F is the Fermi level, E D For Dirac, The Fermi wave vector in momentum space is relative Parallel components of a point;

[0034] Figure 7 Schematic diagram of comparison between STM measurement and fitting data of graphene state density in the Fermi velocity fitting process in an embodiment of the present invention.

[0035] In the figure: 800, a device for measuring the Fermi velocity of a two-dimensional Dirac material; 801, a processor; 802, a memory; 803, a multimedia component; 804, an I / O interface; 805, a communication component. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0038] Embodiment 1:

[0039] The present invention is different from traditional optical and electron microscopes. The scanning tunneling microscope (STM) relies on the principle of quantum mechanical tunneling. As a high-resolution crystal surface imaging and electrical property analysis technology, it can not only obtain the structure and electronic information of the material to the atomic scale, but also move and replace individual atoms. Scanning tunneling spectrum measurement can be carried out while imaging the sample morphology at the atomic level, which plays an important role in the analysis of state density, band gap, work function and topological properties. By measuring the Fermi velocity while imaging the target sample at the atomic level, it is expected that the target sample processing steps can be greatly reduced, and the Fermi velocity measurement can be achieved with faster efficiency.

[0040] This embodiment provides a method for measuring the Fermi velocity of a two-dimensional Dirac material.

[0041] See also Figure 1 , the figure shows that the method includes step S100, step S200, step S300, step S400, step S500, step S600 and step S700.

[0042] S100, using a scanning tunneling microscope to perform atomic-level imaging of the area to be measured of the target sample to obtain the crystal structure and unit cell parameters, and verifying whether the area to be measured is the desired target sample by analyzing and comparing the crystal structure and unit cell parameters.

[0043] It can be understood that in this step, this comparison process is a commonly used method in materials science to verify the consistency and purity of samples, where STM, as a high-resolution surface analysis tool, provides strong support for this type of verification, and through precise imaging and parameter recording, researchers can ensure the accuracy and reliability of their experimental results. Use a scanning tunneling microscope to perform atomic-level imaging of the area to be measured of the target sample to obtain a first crystal structure and a first unit cell parameter as well as a second crystal structure and a second unit cell parameter. By comparing the first crystal structure and the second crystal structure and comparing the first unit cell parameter and the second unit cell parameter, it is verified whether the area to be measured is the desired target sample, wherein the first crystal structure and the first unit cell parameter are the first crystal data obtained from the material of the target sample itself, and the second crystal structure and the second unit cell parameter are the second crystal data obtained from the moiré superlattice caused by the target sample and the substrate.

[0044] S200 , setting scanning parameters of current and voltage according to the target sample, measuring the tunnel current spectrum of the scanning area where the target sample is located, and obtaining current-voltage spectrum data of the scanning area.

[0045] It is understandable that, in this step, when measuring the tunnel current spectrum of the scanning area where the target sample is located, the constant height mode of the scanning tunneling microscope needs to be turned on for measurement.

[0046] S300, measuring the scanning area of ​​the target sample to obtain a first current-height spectrum, and simultaneously obtaining a second current-height spectrum of a calibration material with a known work function, and obtaining the distance between the probe and the target sample by comprehensively analyzing the first current-height spectrum and the scanning parameters of the current and voltage set for the target sample.

[0047] It is understandable that in this step, when measuring the scanning area of ​​the target sample to obtain a first current-height spectrum and simultaneously obtaining a second current-height spectrum of a calibration material with a known work function, the constant voltage mode of the scanning tunneling microscope needs to be turned on for measurement.

[0048] S400, using the current-voltage spectrum data of the scanning area, the differential conductivity spectrum of the target sample is measured by the measurement system, and the linear dispersion characteristics of the two-dimensional Dirac material are obtained by analyzing the linear relationship between the state density of the target sample and the bias voltage.

[0049] It can be understood that in this step, the measurement system for measuring the differential conductance spectrum of the target sample through the measurement system includes a scanning tunneling microscope and a digital lock-in amplifier, wherein the digital lock-in amplifier needs to add a sinusoidal signal when measuring the current-voltage spectrum to obtain the differential conductance spectrum.

[0050] It should be noted that the linear dispersion characteristics of the two-dimensional Dirac material obtained by analyzing the linear relationship between the state density of the target sample and the bias voltage does not need to be calculated. It only needs to look at the differential conductivity spectrum, such as Figure 4 As shown, as long as a straight line is found at each end of the Dirac point, it can be determined that the material has linear dispersion.

[0051] S500, according to the distance between the probe and the target sample, combined with the comparison results of the first current-height spectrum and the second current-height spectrum, calculate the work function difference between the target sample and the calibration material, and obtain the work function of the target sample, and then calculate the average work function of the probe and the target sample.

[0052] It can be understood that the step S500 includes S501, S502 and S503, wherein the step of calculating the work function difference of the target sample and obtaining the work function of the target sample, and then calculating the average work function of the probe and the target sample, includes:

[0053] S501, analyzing the current-height differential spectrum of the calibration material with known work function, and using the current-height differential spectrum as the calibration value;

[0054] S502, processing the current-height differential spectrum of the target sample, calculating the difference with the calibration value, and obtaining the work function of the target sample;

[0055] S503 , combining the work functions of the target sample and the probe, and then calculating an average value of the probe and the target sample.

[0056] It should be noted that in step S503, the work function of the target sample and the work function of the probe are added and divided by 2 to obtain their average value. This average value can be used to analyze the electron exchange and interaction between the sample and the probe, and to further understand the interaction between the probe and the sample, such as the charge transfer that may occur during the contact process. This step can accurately determine the electronic properties of the material, which is very important for understanding the electronic behavior of the material and designing new electronic devices.

[0057] S600. Based on the unit cell parameters and linear dispersion characteristics, the energy-momentum relationship in momentum space is used to obtain the functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the bias voltage.

[0058] It can be understood that in this step, by verifying the linear dispersion relation in step S400, Figure 6The straight line change shown is the linear change relationship between the parallel component of the Fermi wave vector relative to the point in momentum space and the energy; then the energy-momentum relationship, that is, the functional relationship formula, can be obtained. The unit cell parameters of the target material are required here, and the premise of linear dispersion must be ensured. Substituting this formula into the current-voltage function, the calculation formula of the differential conductivity spectrum containing the Fermi velocity is simplified. Here is the first parameter, a value that can be obtained by fitting the formula. The first parameter has a functional relationship with the Fermi velocity and the average work function of the probe and the sample, so the Fermi velocity can be calculated by the first parameter.

[0059] S700. According to the functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the bias voltage, the differential conductivity spectrum of the target sample is analyzed, and the first parameter related to the Fermi function is extracted. The Fermi velocity of the target sample is finally obtained by calculation based on the distance between the probe and the target sample, the average work function of the probe and the target sample, and the first parameter.

[0060] It can be understood that the calculation formula for fitting the first parameter in this step is as follows:

[0061]

[0062] Where: is the current, is the differential conductivity spectrum corresponding to the density of states, is a constant value, k is the Boltzmann constant, T is the temperature, e is the charge of the elementary charge, V s is the sample bias voltage, V D is the bias position of the Fermi level relative to the Dirac point, For natural numbers Second power, represents the natural logarithm calculation, is the hyperbolic cosine function.

[0063] It should be noted that the calculation formula of the first parameter in step S700 is as follows:

[0064]

[0065] In the formula, b is the fitting parameter, m is the effective mass of the electron, is the reduced Planck constant, is the distance from the probe to the target sample, is the average work function of the probe and the target sample, e is the charge of the elementary charge, V s is the sample bias voltage, is pi, a is the unit cell parameter, v F is the Fermi speed.

[0066] In some embodiments of the present application, based on the aforementioned scheme, for the convenience of description, the present application will take graphene as an example to describe in detail the method disclosed in the embodiments of the present application.

[0067] like Figure 1 As shown, a method for measuring the Fermi velocity of a two-dimensional Dirac material comprises the following steps:

[0068] Step S1. Obtain the crystal structure and unit cell parameters of the target sample to confirm whether the crystal structure and unit cell parameters of the measurement area are consistent with the target sample. If they are consistent, the measurement area is confirmed to be the target sample. If not, continue the comparison analysis.

[0069] It should be noted that the confirmation of the target sample is the basis of the measurement of this application. Only when the measured area is confirmed to be the target sample, the subsequent measurement and analysis are meaningful. Since graphene does not exist alone, its property measurement and Fermi velocity adjustment must be placed on other substrates. In the embodiment of this application, graphene is placed on a molybdenum disulfide substrate to form a graphene / molybdenum disulfide heterojunction. Atomic-level imaging can be obtained by adjusting the current, voltage and other parameters of the scanning tunneling microscope. According to Figure 3 Figure (a) Atomic resolution of graphene and (b) Moiré superstructure formed by graphene / MoS2 heterojunction, Figure (c) Schematic diagram of the fast Fourier transform 5° rotation angle corresponding to the scanning tunneling microscope image of graphene / MoS2 heterojunction, confirming that the surface of the measurement area is graphene, and obtaining the crystal structure parameter a=0.246 nm of the target sample graphene. In addition to the atomic structure, the large periodicity image comes from the moiré fringes formed by the 5° rotation of graphene and MoS2, which can correspond to the high symmetry point angle difference of different periodic structures in the fast Fourier transform image.

[0070] Step S2. According to the graphene region identified in step S1, current-voltage spectrum data of the region is measured.

[0071] It should be noted that the current-voltage spectrum measurement requires setting different starting current and voltage parameters, and keeping the relative height between the probe and the sample unchanged during the measurement process;

[0072] Step S3. Based on the scanning area of ​​step S2, measure the current-height spectrum of the area, then measure the current-height spectrum of the calibration material with a known work function, compare the scanning parameters of the current-voltage spectrum of the target sample in step S2, and process to obtain the distance from the probe to the target sample; it should be noted that the current-height spectrum needs to be measured under different bias conditions to ensure the uniformity of the data. In this embodiment, Au (111) is used as the calibration sample, and the current-voltage spectrum data of graphene and Au (111) under the constant height mode and the same bias conditions are compared to calculate the distance from the probe to the target sample.

[0073] Step S4. Connect the lock-in amplifier and the scanning tunneling microscope, apply a modulation signal, and measure Figure 5 The differential conductivity spectrum shown in Figure 1 determines the linear dispersion characteristics of the two-dimensional Dirac material. It should be noted that since the differential conductivity spectrum measures the state density of the material and the two-dimensional Dirac material has linear dispersion, the differential conductivity spectrum of graphene is as follows: Figure 4 The curve shows a "V" shape. In addition, the density of states of the molybdenum disulfide substrate in the energy range of -0.9 eV to 0.45 eV is zero, indicating that it will not affect the electrons near the Dirac point of graphene in this energy range, which is the key basis for the experiment to measure.

[0074] Step S5. Drawing Figure 5 As shown in dln( I )and z The relationship between the change of Au(111) samples and the dln( I )and z The relationship and work function are calculated, the difference with the calibration sample is calculated, the work function of the target sample is obtained, and finally the average work function of the work function of the target sample and the probe is calculated. The average work function of the platinum-iridium alloy probe and the sample in this embodiment is 4.5 eV.

[0075] Step S6. Through the unit cell parameters and linear dispersion characteristics verified in the above steps S1 and S4, Figure 7 As shown, according to the parallel component of the Fermi wave vector in momentum space K II The relationship between the change in energy and the two-dimensional Dirac material state density (i.e., differential conductivity spectrum) and the bias voltage is obtained as a function. It is worth noting that the scanning tunneling microscope is based on the quantum tunneling theory, so the tunneling current measured is expressed as:

[0076]

[0077] In the formula, is the current, e is the charge of the elementary charge, V s is the sample bias, E is the energy, is the state density of the sample, is the state density of the probe, k is the inverse decay constant, is the relative distance from the probe to the sample, and dE is the derivative of energy. In the momentum space of a two-dimensional Dirac material, the inverse decay constant k is closely related to the parallel component of the Fermi wave vector, which can be specifically expressed as:

[0078]

[0079] In the formula, is the inverse decay constant, m is the effective mass of the electron, is the reduced Planck constant, is the average work function of the probe and the target sample, e is the charge of the elementary charge, V s is the sample bias voltage, eV is the energy of the electron relative to the Fermi level, K II for Figure 6 The Fermi wave vector in the medium momentum space is relatively The Fermi wave vector is parallel to the point. The parallel component of the point has the following relationship with the lattice constant of hexagonal honeycomb structures such as graphene:

[0080]

[0081] In this case, a is the unit cell parameter, is pi, k is the parallel component of the Fermi wave vector relative to point K in momentum space. For graphene with a linear dispersion relation, the relationship between k and energy E is: ,here is the reduced Planck constant, v F is the Fermi speed.

[0082] Combining the above formulas, we can see that the measured current-voltage spectrum corresponds to the following functional relationship:

[0083]

[0084] In the formula, is the current, e is the charge of the elementary charge, V s is the sample bias, E is the energy, is the state density of the sample, is the state density of the probe, m is the effective mass of the electron, is the reduced Planck constant, is the relative distance from the probe to the sample, is the average work function of the probe and the target sample, eV is the energy of the electron relative to the Fermi level, is pi, a is the unit cell parameter, dV is the derivative of the bias voltage, v F is the Fermi speed.

[0085] Simplifying the relationship between current and voltage, we can get the following formula:

[0086]

[0087] In the formula, is the current, is a constant value, V s is the sample bias, V is the bias voltage, b is the fitting parameter related to the Fermi velocity, represents the bV power of a natural number, dV is the derivative of the bias voltage, and e is the charge of the elementary charge.

[0088] At this point, the differential conductivity spectrum can also be simplified to the following formula:

[0089]

[0090] In the formula, is the current, is the differential conductivity spectrum corresponding to the density of states, is a constant value, V s is the sample bias voltage, bV represents natural numbers s Power.

[0091] Step S7. Based on the relationship obtained in step S6 above, the graphene differential conductivity spectrum obtained in step S4 is processed. The result of this embodiment is It should be noted that, by combining the formula in step S6 above, the differential conductivity is convolved with the derivative of the Fermi-Dirac distribution to obtain the formula:

[0092]

[0093] In the formula, is the current, is the differential conductivity spectrum corresponding to the density of states, is a constant value, k is the Boltzmann constant, T is the temperature, e is the charge of the elementary charge, V s is the sample bias voltage, represents the natural logarithm calculation, is the hyperbolic cosine function.

[0094] For the case where the Dirac point is not at the Fermi level:

[0095]

[0096] In the formula, is the current, is the differential conductivity spectrum corresponding to the density of states, is a constant value, k is the Boltzmann constant, T is the temperature, e is the charge of the elementary charge, V s is the sample bias voltage, V D is the bias position of the Fermi level relative to the Dirac point, For natural numbers Second power, represents the natural logarithm calculation, is a hyperbolic cosine function. In this embodiment, the Dirac point is located at V D = -70 meV.

[0097] It should be noted that, in order to avoid the influence of the substrate on the key electronic states of graphene, the fitting value range needs to avoid the region where the electronic state density of the substrate is not zero. Therefore, the energy interval of this embodiment can be selected from -0.9 eV to 0.45 eV in step S4.

[0098] Step S8. Calculate the Fermi velocity of the target sample by combining the probe-sample distance, average work function and fitting parameter b calculated in the above steps S3, S5 and S7. .

[0099] It should be noted that, in combination with the relevant formulas in step S6 and step S7, the expression of the fitting parameter b and the Fermi level is:

[0100]

[0101] Wherein, b is the fitting parameter in the above step S6, m is the electron effective mass, is the reduced Planck constant, is the distance from the probe to the target sample, is the average work function of the probe and the target sample, e is the charge of the elementary charge, V s is the sample bias voltage, is pi, a is the unit cell parameter, v F is the Fermi velocity. According to the measured parameters, the fitting parameter b in this embodiment can be simplified to , A is a constant.

[0102] Embodiment 2:

[0103] Corresponding to the above method embodiment, this embodiment also provides a device for measuring the Fermi velocity of a two-dimensional Dirac material. The device for measuring the Fermi velocity of a two-dimensional Dirac material described below and the method for measuring the Fermi velocity of a two-dimensional Dirac material described above can refer to each other.

[0104] Figure 2 FIG. 8 is a block diagram of a device 800 for measuring the Fermi velocity of a two-dimensional Dirac material according to an exemplary embodiment. Figure 2 As shown, the device 800 for measuring the Fermi velocity of two-dimensional Dirac materials includes: a processor 801 and a memory 802. The device 800 for measuring the Fermi velocity of two-dimensional Dirac materials also includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0105] The processor 801 is used to control the overall operation of the device 800 for measuring the Fermi velocity of a two-dimensional Dirac material, so as to complete all or part of the steps in the above-mentioned method for measuring the Fermi velocity of a two-dimensional Dirac material. The memory 802 is used to store various types of data to support the operation of the device 800 for measuring the Fermi velocity of a two-dimensional Dirac material, such as instructions for any application or method operated on the device 800 for measuring the Fermi velocity of a two-dimensional Dirac material, and application-related data, such as contact data, sent and received messages, pictures, audio, video, etc. The memory 802 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, disk or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touch screen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signal may be further stored in the memory 802 or sent via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. The I / O interface 804 provides an interface between the processor 801 and other interface modules, and the above-mentioned other interface modules can be a keyboard, a mouse or a button, etc. These buttons can be virtual buttons or physical buttons. The communication component 805 is used for wired or wireless communication between the device 800 for measuring the Fermi speed of two-dimensional Dirac materials and other devices. Wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G or 4G, or a combination of one or more of them, so the corresponding communication component 805 can include: a Wi-Fi module, a Bluetooth module or an NFC module.

[0106] In an exemplary embodiment, the device 800 for measuring the Fermi speed of two-dimensional Dirac materials can be implemented by one or more application specific integrated circuits (ASIC), digital signal processors (DSP), digital signal processing devices (DSPD), programmable logic devices (PLD), field programmable gate arrays (FPGA), controllers, microcontrollers, microprocessors or other electronic components to perform the above-mentioned method for measuring the Fermi speed of two-dimensional Dirac materials.

[0107] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided, and when the program instructions are executed by a processor, the steps of the method for measuring the Fermi velocity of a two-dimensional Dirac material are implemented. For example, the computer-readable storage medium may be the memory 802 including the program instructions, and the program instructions may be executed by the processor 801 of the device 800 for measuring the Fermi velocity of a two-dimensional Dirac material to complete the method for measuring the Fermi velocity of a two-dimensional Dirac material.

[0108] Embodiment 3:

[0109] Corresponding to the above method embodiment, a readable storage medium is also provided in this embodiment. The readable storage medium described below and the method for measuring the Fermi velocity of a two-dimensional Dirac material described above can refer to each other.

[0110] A computer program is stored on the readable storage medium, and when the computer program is executed by the processor, the steps of the method for measuring the Fermi velocity of a two-dimensional Dirac material in the above method embodiment are implemented.

[0111] In summary, the present invention measures the Fermi velocity based on a scanning tunneling microscope, has a spatial resolution as low as the atomic scale, avoids quasi-particle interferometry measurement, omits the operation of artificially introducing scattering centers, greatly reduces the sample processing steps, and improves measurement efficiency.

[0112] The readable storage medium may specifically be a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, or other readable storage medium that can store program codes.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0114] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for measuring the Fermi velocity of a two-dimensional Dirac material, characterized in that: include: Step S1, using a scanning tunneling microscope to perform atomic-level imaging of the area to be measured of the target sample to obtain the crystal structure and unit cell parameters, and verifying whether the area to be measured is the desired target sample by analyzing and comparing the crystal structure and unit cell parameters; Step S2, setting scanning parameters of current and voltage according to the target sample, turning on the constant height mode of the scanning tunneling microscope to measure the tunnel current spectrum of the scanning area where the target sample is located, and obtaining current-voltage spectrum data of the scanning area; Step S3, turning on the constant voltage mode of the scanning tunneling microscope, measuring the scanning area of ​​the target sample to obtain a first current-height spectrum, and simultaneously obtaining a second current-height spectrum of a calibration material with a known work function, and obtaining the distance between the probe and the target sample by comprehensively analyzing the first current-height spectrum and the scanning parameters of the target sample set current and voltage; Step S4, using the current-voltage spectrum data of the scanning area, measuring the differential conductance spectrum of the target sample through the measurement system, and obtaining the linear dispersion characteristics of the two-dimensional Dirac material by analyzing the linear relationship between the state density of the target sample and the bias voltage; The measurement system comprises a scanning tunneling microscope and a digital lock-in amplifier, wherein the digital lock-in amplifier adds a sinusoidal signal during current-voltage spectrum measurement to obtain a differential conductance spectrum; Step S5, according to the distance between the probe and the target sample, combined with the comparison results of the first current-height spectrum and the second current-height spectrum, calculate the work function difference between the target sample and the calibration material, and obtain the work function of the target sample, and then calculate the average work function of the probe and the target sample; These include: Analyze the current-height differential spectrum of the calibration material with known work function, and use the current-height differential spectrum as the calibration value; Processing the current-height differential spectrum of the target sample, calculating the difference from the calibrated value, and obtaining the work function of the target sample; Combining the work functions of the target sample and the probe, an average value of the probe and the target sample is calculated; Step S6, based on the unit cell parameters and the linear dispersion characteristics, using the energy-momentum relationship in the momentum space, deriving the functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the bias voltage; Step S7, according to the functional relationship between the differential conductivity spectrum of the two-dimensional Dirac material and the bias voltage, the differential conductivity spectrum of the target sample is analyzed and fitted, and the first parameter related to the Fermi function is extracted. The Fermi velocity of the target sample is finally obtained by calculation based on the distance between the probe and the target sample, the average work function of the probe and the target sample, and the first parameter.

2. The method for measuring the Fermi velocity of a two-dimensional Dirac material according to claim 1, characterized in that: The calculation formula for fitting the first parameter in step S7 is as follows: In the formula, is the current, is the differential conductivity spectrum corresponding to the density of states, is a constant value, k is the Boltzmann constant, T is the temperature, e is the charge of the elementary charge, V s is the sample bias voltage, V D is the bias position of the Fermi level relative to the Dirac point, For natural numbers Second power, represents the natural logarithm calculation, is the hyperbolic cosine function.

3. The method for measuring the Fermi velocity of a two-dimensional Dirac material according to claim 1, characterized in that: In step S7, the calculation formula of the first parameter is as follows: In the formula, b is the fitting parameter, m is the effective mass of the electron, is the reduced Planck constant, is the distance from the probe to the target sample, is the average work function of the probe and the target sample, e is the charge of the elementary charge, V s is the sample bias voltage, is pi, a is the unit cell parameter, v F is the Fermi speed.

4. A device for measuring the Fermi velocity of a two-dimensional Dirac material, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the method for measuring the Fermi velocity of a two-dimensional Dirac material as claimed in any one of claims 1 to 3 when executing the computer program.

5. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for measuring the Fermi velocity of a two-dimensional Dirac material according to any one of claims 1 to 3 is implemented.

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