Optical Detection and Manipulation of Pseudospin Orders in Wigner Crystals

Abstract

In Wigner-crystal states of two-dimensional electrons, the spin ordering remains poorly understood. The small energy differences between candidate spin orders make theoretical studies less reliable, and probing magnetic order at a nonzero wave vector is experimentally challenging. In modern realizations of Wigner crystals, the electronic spin degree of freedom is often replaced by a valley pseudospin associated with nonzero Berry curvature. The resulting anomalous velocity couples the electrons' pseudospin texture to their orbital vibration. We show that this mechanism enables optical detection of pseudospin orders in Wigner crystals by producing sharp signatures in the terahertz optical conductivity. For example, antiferromagnetic pseudospin order enables light to excite collective electronic vibrations at the ordering wave vector, generating a characteristic absorption peak. Based on the same principle, we further show that a strong optical drive generates an effective potential that reshapes the pseudospin energy landscape, inducing phase transitions to stripe antiferromagnetic states. These results point to a route for optical detection and control of spin order via its coupling to orbital motion.

Figures (2)

• Figure 1: Optical detection of the pseudospin order. (a) Schematic of the electronic displacements in a triangular-lattice Wigner crystal driven by a dynamical uniform electric field. Because of the different anomalous velocities associated with different pseudospins, the forced motion of the electrons are not uniform, which distorts the lattice. (b) Its phonon dispersion in the limit of zero Berry curvature. (c) The real part $\sigma_1(\omega)$ of the optical conductivities of a Wigner crystal for different pseudospin configurations, where the background Drude peak is not shown. For ferromagnetic order, $\sigma_1$ vanishes at nonzero frequencies in the absence of external disorder because of an effective Galilean invariance. In contrast, an antiferromagnetic order generates characteristic peaks at phonon frequencies $\omega_{\text{L/T}}(q)$ corresponding to the ordering wave vector $q$ (purple line for stripe antiferromagnet and orange line for 120° Néel anti-ferromagnetism), which is a direct spectroscopic signature for experimental identification. In a spin liquid phase (blue line), the conductivity spectrum closely resembles the phononic density of states. We used the carrier density $n=10^{11}\,\mathrm{{cm}^{-2}}$, the effective mass $m=0.5 m_e$ and Berry curvature $\Omega=10\,\mathrm{\mathring{A}^2}$ motivated by those in monolayer MoSe$_2$smolenski_signatures_2021zhou_bilayer_2021, and the phononic damping rate $\gamma=0.1 \,\mathrm{THz}$.
• Figure 2: Light manipulated pseudospin order. (a) Schematic illustration of the pump light switching the ferromagnetic Wigner crystal to a strip antiferromagnetic state. (b) The energy landscape $E_{\text{G}}(q)$ of the stripe antiferromagnetic state as a function of its ordering momentum $\mathbf{q}$ (in units of $q_M=2\pi/(\sqrt{3}a)$) under the $x$-polarized driving field $E=2\times10^{5} \,\mathrm{V/cm}$ at the driving frequency $\omega=3.1 \,\mathrm{THz}$. The global energy minimum corresponds to the optimized ordering momentum which locates along the $q_y$ direction. (c) Cross-sectional cuts of $E_{\text{G}}(q)$ along the gray line in (b) for three different pump fields, showcasing the pump induced phase transition. (d) The zero temperature phase diagram on the plane of driving frequency $\omega$ and electric field $E$, with the color scale encoding the pseudospin ordering wave vector $q_y$. The gray dashed line marks the critical field $E_c$ required to drive the phase transition. The other parameters used are $\gamma=0.3 \,\mathrm{THz}$, $n=10^{11}\,\mathrm{cm^{-2}}$, $J=5 \,\mathrm{\mu eV}$ and $\Omega=10\,\mathrm{\mathring{A}^2}$, consistent with those in MoSe$_2$smolenski_signatures_2021zhou_bilayer_2021.