A state in which they leave behind bind into pairs so strongly that the material opens a gap and stops conducting – not because of its chemistry, but because the pairs have all settled together into one shared, collective state. Telling this apart from an ordinary distortion of the crystal is notoriously difficult.
Going deeper
If the binding energy of an exciton exceeds the overlap between the bands, electrons and holes pair up spontaneously and the material opens a gap on its own. The difficulty is that a lattice distortion of the same symmetry produces an identical-looking gap, so the two have to be told apart by how they behave, not by the gap alone.
A gap that the electrons make themselves
Consider a in which conduction and overlap only slightly, or a whose gap is smaller than the binding energy of an . Then creating an electron–hole pair costs less energy than it gains from binding, and pairs form spontaneously until the system reorganises. The result, predicted in the 1960s, is an excitonic insulator: a state whose gap comes from electron–hole pairing rather than from chemistry, formally analogous to a with pairs of opposite charge instead of like charges.
Because the pairs are neutral, the state does not conduct like a superconductor; it insulates. Its interest lies in being a many-body ground state that can in principle be told apart from the ordinary band picture.
The impostor
Pairing an electron at one momentum with a hole at another produces a modulation at their difference – and that is exactly what a periodic lattice distortion produces. In the candidate materials, the two channels have the same symmetry, so the electronic condensate and a conventional -like instability open gaps that look the same in diffraction and in .
This is the core of the long arguments over Ta2NiSe5, where a flattened valence band at the transition was read as evidence of a condensate, and over -TiSe2, where the same data have been fitted by both pictures. Neither material settles the question by the size of its gap.
How the two are being separated
The experiments that can distinguish them look at dynamics and at tuning. measurements ask which order melts first after a laser pulse and how fast: an electronic condensate should respond on the timescale of the electrons, a lattice distortion on that of the . Pressure, and move the band overlap and the phonon energies differently. Isotope substitution changes only the lattice. Looking for a phase mode of the condensate, or for the fluctuation regime above the transition, provides further handles.
The careful conclusion so far is mixed: in most candidates the lattice takes part, and the statements that hold up are about how much each contributes rather than which one is right. For the attraction is that , strain and thinning give a way to move through the in one sample.
For specialists
A ground state predicted for a semimetal with small band overlap, or a semiconductor whose gap is smaller than the exciton binding energy, in which spontaneous exciton condensation reconstructs the bands and opens a gap. The experimental difficulty is that the transition is usually accompanied by a lattice distortion of the same symmetry, so photoemission, ultrafast and pressure experiments have to separate an electronic condensate from a conventional Peierls-like instability – the argument that surrounds Ta2NiSe5 and 1T-TiSe2.
Where this comes from
Excitonic insulatorJérome et al. · Physical Review 158, 462 (1967)cited by 790