# Excitonic Insulator

The state of matter dubbed the excitonic insulator was first qualitatively discussed by Mott, Keldysh and Kopaev, and others and then expanded upon more systematically by Jerome, Rice and Kohn.

The excitonic insulating state can be considered from two normal states (pictured below). Either the system must be a small-gap semiconductor or a small indirect overlap semimetal. In fact, Mott had first considered the semimetallic limit, while Kohn and others had considered the semiconducting limit.

Intuitively, one can consider the following two heuristic arguments from the different limits, as presented in the article by Rossnagel, which was cited in the previous post:

1. Semiconducting limit: If one can somehow reduce the band gap energy, $E_G$, then at some point, the binding energy to form an exciton, $E_B$, will exceed $E_G$, and the system will unstable to the spontaneous formation excitons.
2. Semimetallic limit: In this case, one considers screening effects. If one decreases the band overlap, a characteristic energy, $E_1$, will be reached such that particle-hole pairs will be insufficiently screened, leading to a localization of the charge carriers.

Therefore, in the regime of $E_1$$E_G$ <$E_B$, the excitonic insulator state is expected. Properties of the excitonic insulator state are presented pedagogically in a Les Houches lecture by Kohn in this book, which is very difficult to find!

In a solid state context, it has been difficult to establish whether the excitonic insulator state has been realized because a lattice distortion is expected to accompany the transition to the excitonic insulator ground state. Therefore, it is difficult to isolate the driving mechanism behind the transition (this difficulty will be familiar to those who study high T-c superconductivity!).

There are a few materials suspected to possess excitonic insulator ground states in a solid state setting: 1T-TiSe$_2$, Ta$_2$NiSe$_5$ and TmSe$_{0.45}$Te$_{0.55}$. In my personal opinion, the case for 1T-TiSe$_2$ is probably the strongest purely because there have been far more experiments on this material than the other candidate materials.

Though this state of matter was considered almost 50 years ago, it still remains relevant today. As Landau once said,

Unfortunately, everything that is new is not interesting, and everything which is interesting, is not new.

### 2 responses to “Excitonic Insulator”

1. Pingback: This Condensed Life

2. Couldn’t find the ebook for “PROBLEME A N CORPS MANY-BODY PHYSICS”

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