This RG discussion (thread) is an open teaching & learning talk about the use of the TB method in the solid-state.
TB has proven to be a very powerful no-relativistic quantum mechanical (NRQM) technic in order to match experimental data and theories in several branches of solid-state where quasiparticle excitations play the fundamental role, i. e., electrons and holes in metals, magnons and phonons, and Cooper pairs among other systems, it helps even in the physics of insulated systems where there is a gap between the conduction and the valence bands.
TB helps to understand more deeply into solids with respect to the free & nearly free electron models. The 3 methods create a wonderful picture of quasiparticles and interactions that take place in solids. In addition, with visualizing tools, TB becomes a very powerful method that can lead to important conclusions and give physical insight into STP complicated problems.
I learned the subject using the IV chapter (electron in a perfect lattice) of the classical book by Prof. Rudolph Peierls “Quantum Theory of Solids” – 1955 [1]. Later on, the subject of TB was popularized by another couple of classical books: Prof. Ziman’s book “Principles of the Theory of Solids” – 1972 [2] & Profs. Ashcroft and Mermin´s book “Solid State Physics” [3] - 1976. Finally, the TB method was magistrally exposed by Prof. W. A. Harrison, "Electronic Structure and Properties of Solids" [4] - 1980.
TB implies that electrons & holes which are eigenstates of the Hamiltonian are spread entirely on the crystal (like in the free & nearly free eh-models), but that they also are localized at lattice sites (free & nearly free e-models do have no such a requirement). This is a really important statement. In addition, the TB approach for example helps to understand the metal insulation transition by means of the Peierls instability & transition between metallic and insulating solid states [4].
Nowadays, there are important advances, both theoretical such as the one where using a TB approach Prof. Chris Nelson [7] still has the only model that predicted the frustration-based behavior of the structural glass transition in As2Se3, He used TB to fit experimental nuclear quadrupole resonance data (NQR). In addition, with TB there are ab initio ones using this powerful, rigorous but also, intuitive tool in the physics of the solid-state, please see for the latest news on Green functions and TB [8].
All RG community members are welcome to discuss and share teaching and research findings using the TB method. Thank you all in advance for your participation.
Main References:
[1] Rudolph Peierls: Quantum theory of Solids. Clarendon Press, Oxford, 1955.
[2] J.M. Ziman: Principles of the Theory of Solids, Cambridge University Press, London, 1972.
[3] N.W. Ashcroft and N.D. Mermin: Solid State Physics, HRW International Editions, 1976.
[5] W. A. Harrison, Electronic Structure and Properties of Solids, Dover, New York, 1980.
[6] Rudolph Peierls: More Surprises in Theoretical Physics. Vol. 105. Princeton University Press, 1991.
[7] W. A. Harrison
Article @ 1989 IUPAC Tight-binding theory of molecules and solids
[8] Chris Nelson, A frustration based model of the structural glass transition in As2Se3 201 Journal of Non-Crystalline Solids s 398–399:48–56
Article A frustration based model of the structural glass transition in As2Se3
[9] S. Repetsky, I. Vyshyvana, S. Kruchinin, and S. Bellucci. 2020. Tight-binding model in the theory of disordered crystals. Modern Physics Letters B Vol. 34, No. 19
TB methods used to study the electron transfer in solid-state materials devices .It is given best results for elec tron transfer rate .It is used in semiconductor-liquid interface and metal -liquid interface and others
Thank you so much for your post, Prof. Hadi Jabbar Alagealy
Very interesting to know that TB helps in the study & understanding of electron transfer in solid-state devices.
Best Regards.
There is more than one way to approach TB
Some think of it as simply discretizing the Schrodinger equation, but others prefer the Wannier function approach.
If simplicity is the idea, then it has many advantages
It can be used either time dependent or time independent.
A remarkably wide set of techniques are associated, like continued fractions or chain decimation.
Prof. Juan Weisz, thank you so much for your post about the ways TB can be approached, it is very interesting to know that by discretizing the Schrodinger equation, we can have a TB approach, I didn't know.
Also thank you for pointing out the associate mathematical techniques to TB: continued fractions & chain decimation.
Best Regards.
In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. https://en.m.wikipedia.org/wiki/Tight_binding
This physics is new to me and therefore I need to catch up with it by reading the references you posted sir.
Profs. Chinaza Godswill Awuchi & Kiprotich Kiptum
Thank you so much for your posts, references and comments, yes TB is a very simple and powerful method.
Best Regards.
Dear Dr. Pedro L. Contreras E. ,
¡MIS MÁS SINCERAS FELICITACIONES! // MY SINCEREST CONGRATULATIONS!
Prof. Juana Maria Arcelus-Ulibarrena
Thank you so much for your constant support.
Best Regards.
I was a student of Walt Harrison. I have used TB theory in almost all my work.
Thank you so much for your post, Prof. Chris Nelson
Could you share some experiences using TB with us? It will be very instructive since Prof. Harrison is a very well-known Solidist from Stanford U.
Best Regards.
Prof. Chris Nelson
Thank you so much for sharing your research experience using TB with us, and to provide interesting works dedicated to TB, very nice:
- A frustration-based model of the structural glass transition in As2Se3 by C.B. Nelson, Journal of Non-Crystalline Solids.
- A tight-binding model of the bond dissociation mechanism in thermochromic leuco dyes by C.B. Nelson et al. Journal of Molecular Structure.
- Optical Second Harmonic Generation from ZnO Nanofluids. A Tight Binding Approach in Determining Bulk χ(2), by C. B. Nelson, et al. J. Phys. Chem. C
Best Regards.
Thank you so much, Prof. Chris Nelson
I really enjoyed the reading of your article "A frustration based model of the structural glass transition in As2Se3"
Very instructive on how tight binding fits the glass state experimental parameters.
Best Regards.
I still have the only model that predicts the NQR dist. for this glass.
Prof. Chris Nelson
As you state for the case of a frustration-based model of the structural glass transition in As2Se3, using TB to fit experimental nuclear quadrupole resonance data (NQR), TB is a powerful technique.
Best Regards.
Yup. I'm currently using TB to explain the mechanism behind photo-darkening.
Very interesting, Prof. Chris Nelson thank you.
We are trying to use TB to explain some macroscopy properties in the unitary limit of two unconventional superconductors. We use the idea of a quantum phase distribution to map the parameters of TB.
My Best Regards.
I was thinking of getting into modellings Hi T superconductors using these methods. Is that what you are attempting?
DearProf . Pedro L. Contreras E. - No doubt interesting w.r.t electronic band strucrute withinin covalent solid as well as wave functional interpretation -https://www.ucl.ac.uk/~ucapahh/teaching/3C25/Lecture20s.pdf
Prof. Jaydip Datta
Yes, thank you for pointing it out, you see, let us take an atom of graphite [1] (4 available electrons), three electrons are bounded to the others and the TB parameter t (the hoping), controls the behavior of those, the last four one is controlled by the parameter EF (the ground state). i.e., remains free.
The free electrons model can not reproduce totally that behavior. I attach a drawn of the presentation you showed [2].
We ought to remember as well, that covalent bonding is a QM effect.
[1] Network Covalent Solids. (2016, January 26). https://chem.libretexts.org/@go/page/1551
[2] https://www.ucl.ac.uk/~ucapahh/teaching/3C25/Lecture20s.pdf
Best Regards.
Dear Prof . Pedro L. Contreras E. - Yes ,Hamiltonoan relationship as well as covalent energy interaction both I have noted . Many thanks for your reminder .
Yes, Prof. Jaydip Datta
With the ground state control parameter from the hamiltonian expectation value, a lot of interesting physics can be predicted without too much calculation effort.
Best Regards.
Interesting discussion, but more oriented towards molecular/chemistry point of view, rather than solid-state physics.
Thank you for the post, Prof. Muhammad Hamza El-Saba
I have done TB for solid-state, not for molecules, but going just to the following approximations:
- First & second Brillions zones.
- Without ab initio.
Reasons:
- I lack good computers in Venezuela and also lack permanent electricity, that is, I totally lack funding.
- I also lack ab initio programs.
Life's researcher is sad and not easy sometimes.
Best Regards :((
TB enriches its use in conection with Landauer-Butttiker quantum transport theory (short mesoscopic devices at low temperatures)
Profs. Chris Nelson and Juan Weisz look at this plot... un Asado venezolano con TB... con ayuda del Prof.
Eugeniy Beliayev
Profs. Rajesh Kumar, Chris Nelson & Juan Weisz thank you so much for your posts.
Very interesting approach to Quantum conductance of zigzag graphene, Prof. Chris Nelson. It is noticeable that you can calculate the self-energy, therefore probably you can calculate the scattering cross-section if it is modeled with TB?
Thank you for noticing the point, Prof. Juan Weisz
thank you all.
Profs. Chris Nelson & Juan Weisz
Please notice the way we approach High Tc by calculating the scattering cross-section in TB.
By now, we understand much more of what we have done.
Article Scattering Due to Non-magnetic Disorder in 2D Anisotropic d-...
The issue is that some preprints have to be understood fast...
Best Regards.
I can tunnel, with almost nothing more than 23 years of hard computer work!! Prof. Chris Nelson
P. from Venezuela
Yes, I can Prof. Chris Nelson, please contact me... I will verify with a question from your works.
Hi Dr Pedro L. Contreras E. . In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. See the link: https://en.m.wikipedia.org/wiki/Tight_binding
Also, see the following link: https://www.sciencedirect.com/topics/chemistry/tight-binding-method
Kindly see the following link too: http://www.physics.rutgers.edu/~eandrei/chengdu/reading/tight-binding.pdf
Thank you so much, Prof Aref Wazwaz
Profs. Chris Nelson & Juan Weisz is it possible to tunnel only with 0.04 meV?
Best Regards.
You are most welcome dear
Dr Pedro L. Contreras E.
Wish you the best always
Dr. Contreras,
Can you please email me at [email protected]? We can get in touch.
Dr. Nelson
Prof. Chris Nelson, I liked very much the last physics article on glass transition, looks like hard topis can be understood with TB faster ... I acknowledge them,
Best Regards.
An outstanding discussion about the use of the TB method in the solid-state. Congratulations.
You are most welcome, Dear Friend & Prof. Dang T. Nguyen, we appreciate your compliment.
Best Regards.
Dear readers & followers soon will appear another preprint related to this thread.
Best Regards,
P.
The preprint for the case of the 2 different families of the Wigner probability distributions for the gamma sheet and nodes position in strontium ruthenate have been finally published:
Preprint Quasi-point versus point nodes in Sr2RuO4, the case of a fla...
CC. Juan Weisz , Rajesh Kumar , Muhammad Hamza El-Saba
Thank you so much, Prof. Haifaa Abaas
We have added another preprint concerning this thread:
Preprint The two-dimensional density of states in normal and supercon...
also, we have added an article:
Deleted research item The research item mentioned here has been deleted
Best Regards
We have published a work that shows that the FS γ-sheet on Sr2RuO4 is in the unitary limit for most non-magnetic impurity concentrations nimp. using a Tight-Binding first neighbor model.
Article Non-magnetic tight binding disorder effects in the γ sheet of Sr2RuO4
A new version for our preprint concerning this thread has been published in arXiv and HAL.
The unitary tight-binding limit is the one that helps us to see where are the nodes in Sr2RuO4 located.
Referee comments are added since the publication will be Open Access.
Preprint Quasi-point versus point nodes in Sr2RuO4, the case of a fla...
We have just published a new preprint related to this thread. In this preprint, we explained some properties of the lightly doped strontium substituted lanthanum cuprates using Prof. Harrinson Tight Binding Theory among other tools.
CC Eugeniy Beliayev
Dianela Osorio
Preprint Coalescence of Impurity Strontium Atoms in Lightly-Substitut...
The tight Binding Theory of Prof. Walter Harrison, Emeritus Professor of Applied Physics at Stanford University is one of the most useful tools for analyzing and understanding the contemporary solid-state theory and condensed matter physics.
Today I honor him with his picture in this thread (from https://appliedphysics.stanford.edu/users/walter-harrison#profile-main).
Harrison, W. A.. "Tight-binding theory of molecules and solids" Pure and Applied Chemistry, vol. 61, no. 12, 1989, pp. 2161-2169.
https://doi.org/10.1351/pac198961122161
Article @ 1989 IUPAC Tight-binding theory of molecules and solids
Soon, we will publish a couple of papers, one already accepted, another in review.
Most useful order parameters in unconventional superconductors (OP)
A new research article related to this thread is coming soon, this time there was no preprint in repositories.
We just added a new publication related to this thread. Thank you so much to the Science Publishing Group "SciencePG" Editorial Team for their support:
Article Tight-Binding Superconducting Phases in the Unconventional C...
A new preprint related to this thread is available at:
Contreras, Pedro, Osorio, Dianela and Beliayev, Eugeniy, The Tight-Binding Flat Band Case in the Strontium-Substituted Lanthanum Cuprate. Available at SSRN: https://ssrn.com/abstract=4143305 or http://dx.doi.org/10.2139/ssrn.4143305
Best Regards.
A new important preprint substituting an old one will appear tomorrow here and on other open access platforms.
Best Regards and let the world decide, not only two people.
CC. Eugeniy Beliayev
,Dianela Osorio
A new work concerning this discussion thread has been posted in the SSRN Electronic Journal, the link to read is the DOI following the electronic publication
Article The Effect of Nonmagnetic Disorder in the Energy Gap at Zero...
It follows the zero temperature GF technique using a tight binding approach and particularly varies one parameter, the zero energy gap in a frequency window that allows seeing some interesting numerical results.
Best Regards.
CC Anjna Devi
A new preprint concerning this thread on unconventional superconductors and its DoS using the reduced phase space is available in the following arXiv link link and in RG platform:
Preprint The two-dimensional density of states in normal and supercon...
Kind Regards.
Good Morning All followers of this thread.
An article related to the subject of the preprint has finally appear on this subject & the DoS calculated from the elastic scattering cross section for two point group symmetries
Article The two-dimensional density of states in normal and supercon...
Kind Regards.
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