In some crystals, electrons are not spread uniformly but arrange themselves into a strict checkerboard: one cell has more electrons, the neighboring cell has fewer. Such a pattern is called charge order, and for a long time it was considered something frozen, like a pattern on frosty glass. But recently it turned out that this pattern can be flipped, just as magnetic order is flipped by a current pulse. What remained unclear was how an electric field makes the electron checkerboard change the color of all cells at once.
To figure this out, physicists reduced the complex picture to a simple model. Each site of the crystal lattice can be either empty or occupied by two electrons. These two states are denoted as an arrow pointing up or down, called a pseudospin. In this notation, charge order looks like an antiferromagnet: arrows on neighboring sites point in opposite directions. And if the arrows start to oscillate, their collective motion is described by the same equations as the swaying of magnetic arrows in an antiferromagnet.
Then the electric field comes into play. It acts on the pseudospins as a staggered field, pulling arrows on one sublattice in one direction and on the other sublattice in the opposite direction. As long as the field is weak, the arrows only tilt slightly and return back. But if the field exceeds a threshold, the collective oscillation loses stability: one of the modes starts to grow on its own, and the entire pattern flips over. Calculations for typical parameters give a threshold field of about one million volts per centimeter, and the oscillation frequency is about three and a half terahertz, that is, trillions of oscillations per second.
Numerical modeling confirms the picture. When the field is slightly above the threshold, the longitudinal component of the pseudospin oscillates and eventually transitions from a positive value to a negative one, meaning the charge order changes polarity. The transverse component first grows due to the instability and then decays. If a small uniform field is added, for example due to deviation from half filling, the trajectory acquires an additional jitter, similar to the nutation of a spinning top.
Thus, charge order ceases to be a static picture and turns into a controllable dynamic system. Previously, there was no microscopic theory linking an electric field to the switching of a charge pattern, unlike magnetic order, where such a theory has long been developed. Now this link is established: charge order can be described as a pseudospin antiferromagnet, and the electric field as a handle that flips the entire checkerboard. This opens the way to devices where information is stored and processed by switching charge order, much as is done today with magnetic bits.
The frequency of collective pseudospin excitations of charge order lies in the terahertz range, that is, about a trillion oscillations per second. This is a million times faster than the typical frame rate in movies.