📃 semiconductor vs Mott insulator

Finally a nice picture for distinguishing the two:

“In a band insulator, as illustrated on the top-left figure, the valence band is filled. For N sites on the lattice, there are 2N states in the valence band, the factor of 2 accounting for spins, and 2N states in the conduction band. PES refers to “Photoemission Spectrum” and IPES to “Inverse Photoemission Spectrum”. The small horizontal lines represent energy levels and the dots stand for electrons. In a Mott insulator, illustrated on the top-right figure, there are N states in the lower energy band (Lower Hubbard band) and N in the higher energy band (Upper Hubbard band), for a total of 2N as we expect in a single band. The two bands are separated by an energy U because if we add an electron to the already occupied states, it costs energy U.

Perhaps the most striking difference between a band and a Mott insulator manifests itself when the Fermi energy EF is moved to dope the system with one hole. For the semiconductor, the Fermi energy moves, but the band does not rearrange itself. There is one unoccupied state right above the Fermi energy. This is seen on the bottom-left figure. On the bottom-right figure, we see that the situation is very different for a doped Mott insulator. With one electron missing, there are two states just above the Fermi energy, not one state only. Indeed one can add an electron with a spin up or down on the now unoccupied site. And only N−1 states are left that will cost an additional energy U if we add an electron. Similarly, N−1 states survive below the Fermi energy.”

arXiv:1310.1481 [cond-mat.supr-con] (2013)

💬 louder than words

We need a civilised world that goes on for all our grandchildren and beyond in which these guitars can be played and songs can be sung.

Pink Floyd guitarist David Gilmour auctioned off his guitars for $21.5 million and donated the money to public-interest environmental-law firm ClientEarth.

💡 iron fox challenge

An arctic fox made a record run from Svalbard to Canada in 2,5 months. The distance of 3,506 km was completed in only 76 days. The average daily distance the fox covered was 46 km. At most, the animal ran as much as 155 km per day.

Source: Norwegian Polar Institute

arctic fox
Image: Ann Kristin Balto / Norsk Polarinstitutt

map of route taken by arctic fox
Image: Arnaud Tarroux / NINA

📎 507 Mechanical Movements

This is an online edition of the classic technical reference Five Hundred and Seven Mechanical Movements by Henry T. Brown.

This site contains the original illustrations and text from the 21st edition of the book, published in 1908. It also includes animated versions of the illustrations, and occasional notes by the webmaster.