# Tag Archives: Excitonic Insulator

## A Rather Illuminating Experiment Using Ultrafast Lasers

Historically, in condensed matter physics, there have been generally two experimental strategies: (i) scattering/spectroscopy experiments such as angle-resolved photoemission or X-ray scattering, and (ii) experiments involving macroscopic variables such as specific heat, resistivity, or magnetization. In the past few decades, a qualitatively new frontier opened up. This consisted of experiments that involved kicking a system out of equilibrium (usually with a pulsed femtosecond laser) and monitoring its relaxation back to equilibrium.

The importance of this experiment requires a little background. There has been debate for a couple decades now in the literature as to whether excitonic correlations are driving the charge density wave transition in 1T-TiSe2. This experiment claims that one can non-thermally melt (with the ultrafast laser) the excitonic order while the lattice remains distorted. This is done by monitoring the optical response of the sample at time intervals after the intense pulsed laser hits the sample: zone-folded phonons are monitored as evidence of the lattice distortion while the plasmon peak energy is monitored as evidence of excitonic order. The conclusion that the authors come to is that it cannot be purely an excitonic mechanism that is responsible for the charge density wave in this material as the plasmon peak energy is drastically affected by the laser pulse, while the zone-folded phonons do not react.

There is one caveat in this otherwise quite solid piece of work, however. The authors have equated the shift in the plasmon peak frequency (immediately following the arrival of the ultrafast laser pulse on the sample) with the melting of excitonic order. While this interpretation is plausible, it is not necessarily correct considering that the laser is photo-exciting a large number of charge carriers.

Regardless of this last point, the paper is definitely worth the read and highlights the kinds of experiments that can be conducted with these techniques. To my mind, this is one of the more illuminating experiments conducted on 1T-TiSe2 as many other experiments have been quite inconclusive about the mechanism behind the CDW in this material. Despite the aforementioned caveat, this experiment quite definitively demonstrates that one cannot ignore the role that electron-phonon coupling plays in the formation of the CDW in 1T-TiSe2.

## 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.