Time For Phase Transitions

We all know what a phase transition is. A material at rest experiences a tiny change in external conditions and changes drastically into another state at rest. Like ice that, upon a minute rise in temperature above 0°C, turns into water. In materials science, however, materials at rest are not really useful. Usually, you do something to a material to exploit its technological merits. An electric voltage is applied to a transistor, for example, and a current begins to flow.

At a time when everything is moving ever faster, it is extremely important to know how long such a switching process takes and exactly how it progresses. And is it perhaps possible that, as switching speeds increase ever further, the nature of the switching process itself changes? For the functionality of a device, that would be extremely important to know.

Interestingly, there are materials where a tiny change in external conditions initiates a drastic change in their time-dependent properties. For example, its optical reflectivity changes exponentially with time, and after a minute rise of temperature this turns int an oscillatory reflectivity change. This is precisely what we observed in europium monoxide and is shown in the figure.

This resembles the discontinuity of a phase transition, but now in the time-dependent response and not in the material at rest, and so the term "non-Hermitian phase transition" is associated with it. Such an idea of a phase transition in the time dependence of a material may be acceptable - but just what the heck does "non-Hermitian" mean?

Imagine a coordinate system with the three axes x, y, and z. The axes are independent, and they are distinguished by angles of 90° from each other. So when I move an object along x, then y and z remain unaffected. Physics, especially quantum mechanics, usually describes phenomena in coordinate systems like that. However, when drastically time-dependent processes are considered, such coordinate systems get distorted - its axes get tilted, and the angle separating them is no longer 90°. Now a displacement in x may also cause a displacement in y or z. An extreme case is reached when the tilt of an axis reaches 90° because then two different axes may suddenly point in the same direction. If x becomes z, we no longer have a coordinate system in three dimensions (x, y, z), but only in two (x = z, y). The dimensionality changes and with it usually the materials properties. This moment of losing a dimension is termed as non-Hermitian phase transition because while "Hermitian" is a mathematical property that keeps the axes apart by 90° and thus independent, "non-Hermitian" indicates the loss of this separation and independence.

Non-Hermitian phase transitions have been observed in gases and certain carefully engineered systems, but never as an intrinsic property of a solid monolithic material. This has now changed with the observation in a europium oxide crystal. This discovery is not just important in its own right. In solid materials, the non-Hermitian phase transitions can exist along with the standard phase transition, where the material is at rest. The two types of phase transitions can influence each other.

This opens previously unimagined possibilities for engineering the properties of functional materials "in action", that is, while they are changing with time, as they do when operating a device. New ways of writing bits into computer memory, modulating the emission of laser light, or tuning electric circuits may ultimately become possible.