tag:blogger.com,1999:blog-13869903.post3629402723682749325..comments2020-04-04T13:21:06.898-05:00Comments on nanoscale views: More about insulatorsDouglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-13869903.post-17803264956457946732009-01-14T15:41:00.000-06:002009-01-14T15:41:00.000-06:00Nice posts Doug. I'm trying to get up to speed he...Nice posts Doug. I'm trying to get up to speed here in my new academic career so I've missed most of this discussion. However, on the topic of insulators it might be worth mentioning the whole new idea of the "topological insulator". ( See for example http://www.nature.com/nature/journal/v452/n7190/abs/nature06843.html ). It turns out that band insulators can be very nontrivial -- and more recent work extends many of these ideas to interacting insulators as well. I don't know if this is unified with Anderson insulators though.Stevehttps://www.blogger.com/profile/14514301100480098429noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-23705970403023399252008-12-30T23:06:00.000-06:002008-12-30T23:06:00.000-06:00This paper provides a unifying view of Band and Mo...This paper provides a unifying view of Band and Mott insulators:<BR/><BR/>http://arxiv.org/abs/cond-mat/0301338<BR/><BR/>Ofcourse one needs to understand the more conventional way of looking too (which you provided) for getting a better understanding.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-53069467557289238662008-12-29T21:53:00.000-06:002008-12-29T21:53:00.000-06:00Doug wrote:>In the ideal (infinite periodic>...Doug wrote:<BR/><BR/>>In the ideal (infinite periodic<BR/>>solid) band insulator case, all <BR/>>(single-particle) electronic >states are extended,<BR/><BR/>But this goes back to what I wrote earlier.... Although this language is appropriate if one describes such systems in terms of Bloch functions, Kohn showed that this is not the essentially point. He showed that if one has a completely filled band (e.g. a "band" insulator) then one can write the many-electron wavefunction as a Slater determinant of EITHER delocalized Bloch waver OR localized Wannier functions. This is not possible for a partially filled band. There one must write it as Bloch waves.<BR/><BR/>Since the constituent wavefunction of a band insulator can be written using a complete set of local functions, localization is a ground state property of both Anderson and band insulators. In this sense band insulators are just as localized as Anderson insulators.<BR/><BR/>This point of view is not discussed in a textbook that I am aware of, but is more or less standard theory in the ferroelectric community. For instance the modern theory of polarization rests on the instrisic localization of wavefunctions... even in band insulators. Frankly, I was shocked the first time I learned about all this! :)<BR/><BR/>There are some nice pedagogical introductions by Raffaele Resta on this stuff.Peter Armitagehttps://www.blogger.com/profile/11567089164372083820noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-53133447561081636632008-12-29T12:43:00.000-06:002008-12-29T12:43:00.000-06:00Nice posts. I'm a high energy guy trying to learn ...Nice posts. I'm a high energy guy trying to learn some condensed matter theory. I've found your posts helpful and clear.Joshhttps://www.blogger.com/profile/15132332468165038669noreply@blogger.com