Ab initio modeling of electronic and magnetic properties of small Wigner crystals.- (Daniele Lagasco LPT / These). -20/10/2026, 2 p.m.

PhD defense

Daniele Lagasco LPT, Salle de conférence, Bat. 3R4 – 2 p.m.

Abstract:
Wigner crystallization, proposed in 1934, predicts that in an electronic liquid at sufficiently low density — where the Coulomb potential dominates over the kinetic energy — the electrons arrange themselves into an ordered structure. This work is motivated by a recent observation of few-electron Wigner crystals in a quasi-one-dimensional system. The objective of the thesis is to calculate the charge distribution and the magnetic exchange coupling of N electrons in a one-dimensional system using ab initio methods. In the first method, we obtain an analytical expression for the exchange coupling of a two-electron Wigner dimer confined to a one-dimensional space in the low-density limit, using two complementary approaches. The first consists of the analytical solution of the Schrödinger equation for two electrons, assuming the center of mass of the two particles to be fixed. Under this approximation, the original problem reduces to a second-order differential equation, which is solved in terms of Whittaker functions. The second approach is based on the quasiclassical, or Wentzel-Kramers-Brillouin (WKB), approximation. The two approaches yield compatible results in their overlapping region of validity. In the second method, we model the N-electron liquid in order to reproduce the experimental setup we aim to interpret. We adopt a full configuration interaction approach to capture electron correlation. With this approach, we obtain accurate electronic density profiles of small one-dimensional Wigner crystals with N = 2 to N = 4 electrons, which clearly show the localization of the electrons. Finally, we present a simple approach for obtaining the exchange coupling constant by mapping our ab initio results onto a Heisenberg Hamiltonian.