Chirality/Axiality-Induced Axiality/Chirality via Surface Polarization

Abstract

In condensed matter physics, a broad spectrum of physical characteristics, such as chirality, axiality, and polarity, arises as a direct consequence of the underlying symmetry of the system. We here theoretically investigate the effective coupling between chirality and axiality at their domain boundaries, mediated by polarity. Based on symmetry considerations and model analyses, we propose the concept of chirality-induced axiality via surface polarization, which refers to a phenomenon where the handedness of chirality selects an axial moment with a particular orientation by lowering its energy at the surface. We further establish the inverse process, termed axiality-induced chirality via surface polarization, whereby axiality in turn dictates the preferred chirality. These reciprocal couplings open a new pathway for stabilizing single-domain states of chirality and axiality. They further imply interfacial functionalities, including the selective adsorption of chiral and axial molecules.

Figures (4)

• Figure 1: (Color online) (a) Mutual relationships between the electric toroidal monopole $G_0$, electric toroidal dipole $\bm{G}$, and electric dipole $\bm{Q}$. (b,c) Schematic picture of single-domain selection in terms of (b) axial systems on the chiral substrate and (c) the chiral systems on the axial substrate along the $x$ direction. The green spheres, green arrows, and orange arrows stand for $G_0$, $G_x$, and $Q_x$.
• Figure 2: (Color online) (a) Chiral system interfaced with non-chiral sites. (b-d) Expectation values of (b) the electric toroidal monopole $G^{\rm (s)}_0$, (c) electric dipole $Q_x$, and (d) electric toroidal dipole $G^{\rm (s)}_x$ per site $i$.
• Figure 3: (Color online) (a) Chiral substrate interfaced with an axial site at $i=0$. (b) $h_{G_0}$ dependence of the energy difference between the states with $h_{G_x}<0$ and $h_{G_x}>0$, $\Delta E = E(h_{G_x}>0) - E(h_{G_x}<0)$, for different values of $h_{G_x}$ at $\mu=0.3$.
• Figure 4: (Color online) (a) Axial substrate interfaced with a chiral site at $i=0$. (b) $h_{G_x}$ dependence of the energy difference between the states with $h_{G_0}>0$ and $h_{G_0}<0$, $\Delta E = E(h_{G_0}>0) - E(h_{G_0}<0)$, for different values of $h_{G_0}$ at $\mu=-1.4$.