# Exotic Insulators

According to band theory, an insulator is characterized by an energy gap for electronic excitations. In most insulators (let us call them call “conventional insulators”), the gap is fixed by the valence of atoms and the atomic potential. However, there is another route to create a gap in the electronic spectrum. In the limit where where the coulombienne interaction is much stronger than the kinetic energy, a band metal is indeed an insulator: this is the physics of the Mott insulator. This physics has been intensively discusses in the last twenty year especially in the context of the high T_{c} superconductor.

During the last few years, two new classes of “unconventional inulators” have emerged.

**Topological insulators** which have attracted much attention in the two last years are the first class. A topological insulator resembles an ordinary insulator in its bulk electronic band structure , with the Fermi level falling between the conduction and valence bands. On the surface of a topological insulator, there are special states which fall within the bulk energy gap and allow conduction. The peculiar topology of the bulk band structure leads to the existence of these remarkable surface state. These surface state are protected by quantum mechanics from backscattering and are analogue to the edge state in the quantum Hall effect regime.

Anothe new class of insulators is generated by magnetic frustration. In some frustrated compounds, in spite of significant magnetic exchange J, the system doesn’t show any long range order down to the lowest accessible temperature. This kind of system may host original magnetic ground states, such as a **spin liquid** [1]. This new ground state is characterized by a peculiar low energy excitation spectrum.

One way to probe it is to study the entropy transport. One recent example is the case of the 2D S=1/2 triangular lattice EtMe3Sb[Pd(dmit)2]2. In this system, Prof. Yuji Matsuda’s group resolved a fermionic contribution to the thermal conductivity [2]. From entropy transport point of view, everything happened as if there are fermionic carriers in spite of the fact that the system is an insulator! Recently, we started to investigate the entropy transport in other frustrated systems.

Reference :

[1]Patrick A. Lee , Science, VOL 321,1306 (2008)

[2] Minoru Yamashita et al.,Science 4 June 2010 328: 1246-1248 (2010)