A New Spin On Atomic Logic
Lead Research Organisation:
King's College London
Department Name: Physics
Abstract
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| Description | As a theoretical group, we have been working on a development of a new efficient method of calculating the Scanning Tunnelling Microscopy (STM) images. STM is the main tool used by the Nottingham experimental group in this project and it is essential that a proper theoretical support is provided to adequately interpret their images and workflow. In STM an atomically sharp tip is approached to the sample surface (with the distances between the two being between 2-10 Angstrems); when the bias is applied between the tip and surface, a current flows that is measured. By placing the tip at different lateral positions around the sample surface (its vertical position depends on the experimental mode used), a 2D image of the surface is made that in many cases has molecular and even atomic resolution. Currently, practically one method is being widely used for theoretical interpretation of experimental images, that is due to Tersoff and Hamann (TH). This method is cheap (which explains why it is so popular), as the whole STM image can actually be obtained from a single electronic structure calculation (made usually using a Density Functional Theory based code) of the surface under investigation, without using any tip model. Hence, the method provides a kind of "average" image over a range of possible tips. However, this method is highly approximate: it is not supposed to work at small tip-sample distances (if used in experiment) or at high voltages; basically, it is only expected to work in the limit of zero bias. As a consequence, the TH method gives often quantitatively, but also in many cases, qualitatively wrong results. The "exact" method of calculating the current roots in the Landauer formula derived using the Non-Equilibrium Green's Function (NEGF) method. This approach however has two main problems: (i) it requires a precise atomistic model of the tip; (ii) it is extremely computationally expensive as very costly current calculation should be done on a grid above the surface, basically hundreds or even thousands of such calculations are required. The latter point makes this method impractical. In this project we have been developing a new theoretical tool for calculating the STM images. The expectation is that it will be much more efficient computationally compared to the full NEGF method; however, it will bring much more precision in terms of the range of the tip-sample distances and the bias compared to the TH method. The tool is based on the exact Landauer formula for the tunnelling current, but makes a number of simplifications concerning the tip. As a result, each calculation required for the given tip position above the sample surface is greatly simplified, and hence the second difficulty mentioned above of the NEGF method is essentially relaxed, if not eliminated. With this method, we should be able to provide more realistic STM images at a wider range of tip-sample distances, voltages and even different temperatures (the TH method can only be applied at zero temperature). Currently: (i) the theoretical part of the method has been finished; (ii) it has been implemented in a code; (iii) a workflow has been created that enables one to run a CP2K code (relation to CP2K-UK award EP/K038222/1) in a script and extract the obtained wavefunctions and calculate the current; (iv) a workflow is being created for high throughput automatic simulations of STM images. We have also run a number of tests on the Au(111) surface with encouraging results. The method is versatile enough to include the spin into the consideration, i.e. the tip model can be, if desired, be spin-sensitive leading to different spin-up and spin-down current channels. The method requires a few parameters associated with the tip model, these can be obtained by fitting the current vs. tip height data obtained from experiment. 21.02.24 update: ^^^^^^^^^^^^^^^^^ Since the previous submission, the method has been significantly improved and the software has been substantially rewritten: (i) apart from the simple previous model in which the tip was modelled by a single "effective atom" with parameters to be fit to the experiment (or exact theory), now a hierarchy of methods has been implemented (5 in total), that enable one to perform simulations with increasingly better precision and more realistic models, albeit at increased cost; (ii) previously, CP2K wavefunctions needed to be used for the current calculation; in this new implementation Kohn-Sham and overlap matrices from CP2K are instead required, which is computationally more convenient and provides a better solution to the problem; (iii) the full workflow has been implemented in the TETR and LEV00 codes (already publicly available), as well as in additional codes that calculate the current from the CP2K matrices (not yet publicly available); (iv) both current modes (constant height and constant current) have been full implemented; (v) one can simulate spectroscopy curves as well as line scans in any direction apart from 2D STM images. The software has been tested more extensively. The full STM image was simulated for a benzene molecule on Au(111) surface, the results basically agree with experiment. The calculations were done both for non-relaxed and fully relaxed scenario; in the latter case it was found, to our surprise, that the molecule slightly rotates in response to the approaching tip during the imaging, which contributes to the image being even more smeared. We have also started applying the software to simulating spectroscopy experiments of Cu clusters on a Cu surface, for which the Nottingham group has obtained experimental results. |
| Exploitation Route | The code will become freely available (under the GNU General Public License (GPL)) for use by a wider scientific community. It will be placed on GitHub with full description, examples and a tutorial. Of course, when we are ready, we expect a number of scientific publications as well, both on the theory and applications to various systems including quantum corals. 21.02.2024 update: we would like to place the code on GitHub after finishing more tests and having a publication in which the code will be mentioned. The planned publication is on Cu clusters on a Cu surface. |
| Sectors | Aerospace Defence and Marine Chemicals Digital/Communication/Information Technologies (including Software) Education Electronics Energy Environment Manufacturing including Industrial Biotechology |
| Description | Nottingham |
| Organisation | University of Nottingham |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | our theory provides an input to experiments performed by this partner |
| Collaborator Contribution | experimental results from the partner serve as the basis for our theory |
| Impact | Two papers are ready for submission. The partner uses chemistry synthesis methods, we use physics methods. |
| Start Year | 2014 |
| Title | CP2K |
| Description | CP2K is a program to perform atomistic and molecular simulations of solid state, liquid, molecular, and biological systems. It provides a general framework for different methods such as e.g., density functional theory (DFT) using a mixed Gaussian and plane waves approach (GPW) and classical pair and many-body potentials. |
| Type Of Technology | Software |
| Year Produced | 2014 |
| Open Source License? | Yes |
| Impact | New functionality added and the website improved. |
| URL | http://cp2k.org |
| Title | NEGF method STM current calculation with CP2K+TETR+LEV00 |
| Description | An efficient method has been implemented for tunnel current calculations in an STM junction setup that allows one to calculate hundreds of values of the current at different tip positions in reasonable time. In particular, STM images can be routinely simulated which used to be unthinkable previously: the code is 10-20 times more efficient than the specialised codes such as Smeagol or TransSiesta based on Non-Equilibrium Green's Functions (NEGF) formalism. The method is based on a specific approximation to the Landauer formula within the NEGF formalism and a standard local basis set DFT simulations of the STM junction at different tip positions. The method can be used for small and large biases (the commonly used Tersoff-Hamann (TH) method can only be used for small biases), and takes account of the surface+tip relaxation at different tip positions; the method is not limited then to large tip-sample distances, also at variance with the TH method. Currently, the scripting structure implemented is based on CP2K DFT code to be used. However, other local basis set software can also be easily incorporated if required. The code is implemented within the TETR and LEV00 environments (URL provided) and contains some additional tools (no URL as yet). |
| Type Of Technology | New/Improved Technique/Technology |
| Year Produced | 2022 |
| Impact | This software enables one to calculate, at a reasonable cost, STM currents in tunnel molecular junctions using realistic surface and tip models. It is much more efficient than the standard software and hence makes it possible to calculate the tunnel current at multiple tip positions, e.g. to simulate whole STM images of realistic systems including the constant current mode, at a reasonable cost. Real atomistic tips are used in the simulations, this is at variance with the commonly used TH method in which a model point-like tip is used. The really exciting point is that we can now perform STM image simulations using an advanced proper non-equilibrium NEGF theory. |
| URL | https://nms.kcl.ac.uk/lev.kantorovitch/codes/lev00/index.html |