Geometric distinctions between metals and insulators

Raffaele Resta has a very helpful review article The insulating state of matter: a geometrical theory.
It elegantly connects what to me are a rather disparate range of topics:
Kohn's classic 1964 characterisation of insulators, Berry's phase, Chern numbers, periodic versus open boundary conditions, quantum metrics, Anderson localization, Mott insulators, Quantum Hall insulators, ....

A central quantity defines the "localisation" associated with the ground state wavefunction.
In a 1999 PRL Resta and Sorella introduced this quantity and showed how it diverged at the quantum phase transition between a band insulator and a Mott insulator in a one-dimensional ionic Hubbard model.
In a 2006 J. Chem. Phys. paper Resta connects this localisation to Boy's localisation in quantum chemistry.

Comments

Post a Comment

Popular posts from this blog

Is it an Unidentified Superconducting Object (USO)?

If you look on the arXiv and in Nature journals there is a continuing stream of people claiming to observe superconductivity in some new material. There is a long history of this and it is worth considering the wise observations of Robert Cava , back in 1997, contained in a tutorial lecture. It would have been useful indeed in the early days of the field [cuprate superconductors] to have set up a "commission" to set some minimum standard of data quality and reproducibility for reporting new superconductors. An almost countless number of "false alarms" have been reported in the past decade, some truly spectacular. Koichi Kitazawa from the University of Tokyo coined these reports "USOs", for Unidentified Superconducting Objects , in a clever cross-cultural double entendre likening them to UFOs (Unidentified Flying Objects, which certainly are their equivalent in many ways) and to "lies" in the Japanese translation of USO.   These have caused g
Read more

What is Herzberg-Teller coupling?

Image
Is it something to do with breakdown of the Born-Oppenheimer approximation? In molecular spectroscopy you occasionally hear this term thrown around. Google scholar yields more than 3000 hits. But I have found its precise meaning and the relevant physics hard to pin down. Quantum mechanics in chemistry by Schatz and Ratner is an excellent book , but the discussion on page 204 did not help me. "Herzberg-Teller" never appears in Atkins' Molecular quantum mechanics. So here is my limited understanding. Herzberg and Teller wanted to understand why one observed certain vibronic (combined electronic and vibrational) transitions that were not expected, particularly some that were expected to be forbidden on symmetry grounds. " Intensity borrowing " occurred. Herzberg and Teller pointed out that his could be understood if the dipole transition moment for the electronic transition depended on the nuclear co-ordinate associated with the vibration. In the Franck-Condo
Read more

What should be the order of authors on a conference poster or talk?

I welcome discussion on this point. I don't think it is as sensitive or as important a topic as the author order on papers. With regard to paper authorship my general rule is that the person who does the bulk of the work, including actually writing the paper should be the first author. Doug Natelson has a good post on co-authorship , that I largely agree with. My only difference is that I am not really convinced that good practice prevails in the majority of circumstances. I fear there are increasing numbers of co-authors, particularly senior ones, with marginal contributions. But, what about conference talks and posters? Many of these are based on work that is already or about to be published. Should the author order be identical as the associated papers? I am not sure it should necessarily be. My tentative view is that the person who writes and submits the abstract and actually prepares and presents the post/talk should be the first author. Perhaps they should also highlig
Read more