How to Flip an Electronic Chessboard ✛ ✎

Original: "Pseudospin Dynamics of Charge Order"
· Ping Tang
arXiv:2608.30381v1 · 2026-08-31 · arXiv non-exclusive · independent analysis · 2 min
An electric field can switch charge order the way a current switches magnetic order.

In some crystals, electrons are not distributed evenly but alternate: one atom has more, the neighboring one has fewer. The result is a pattern resembling a chessboard. Such a pattern is called charge order. It was once thought to be static, but recently it turned out that an electric field can flip it, just as a current flips magnetic order. The only remaining question was how exactly the field does this.

Physicists came up with a simple way to describe the situation. Each atom in the crystal can be either empty or occupied by two electrons at once. These two states were labeled with an arrow pointing up or down, and the label was called a pseudospin (not a real spin, just a convenient tag). In this description, charge order looks like an antiferromagnet: arrows on neighboring atoms point in opposite directions. And the electric field acts on these arrows as if pulling them in different directions.

If the field is weak, the arrows only wobble slightly and return to their original positions. But if the field exceeds a threshold, the collective oscillation loses stability, and all arrows tip over at once. Then the charge order changes polarity: sites that had many electrons now have few, and vice versa.

This discovery makes it possible to control charge order with an electric field. Previously, this was not possible because there was no theory linking the field to the switching of the pattern. Now charge order can be used for storing and processing information, much like magnetic bits are used today.

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.

H_{\rm eff} = \sum_{\langle ij\rangle} \left( J_z \tau_i^z \tau_j^z - J_\perp (\tau_i^x \tau_j^x + \tau_i^y \tau_j^y) \right) - h_z \sum_i \tau_i^z
The energy of the system is expressed in terms of pseudospin operators: Jz sets the antiferromagnetic Ising coupling (stabilizes charge order), J⊥ sets the ferromagnetic transverse coupling (provides coherent pair transfer), and hz is a uniform longitudinal field (deviation from half filling).
E_c = -\frac{Z N_0 (J_z - J_\perp)}{p_0}
The threshold electric field at which transverse fluctuations become unstable and charge order switches. Here Z is the coordination number, N0 is the equilibrium length of the charge-order vector, and p0 is the effective dipole moment.
\Omega_{\rm CO}^2 = \frac{[p_0 E + Z N_0 (J_z - J_\perp)][p_0 E + Z N_0 (J_z + J_\perp)]}{\hbar^2}
The square of the frequency of transverse oscillations of the charge-order vector in the absence of a uniform field. It depends on the electric field and exchange parameters, allowing frequency control by an external field.
Scientists
Charles-Augustin de CoulombJames Clerk MaxwellEnrico FermiPaul DiracWolfgang PauliJohn Henry Poynting
Concepts
spin current antiferromagnetic order spintronics spin transport magnetic order altermagnetism magnetic state stochastic self organization law of conservation of electric charge entropy driven self assembly charge separation alternating magnetism electric field electronic structure electromagnetism Faraday's law of electromagnetic induction landau level power electronics power grid stabilization disorder