Linear exciton Hall and Nernst effects in monolayer two-dimensional semiconductors

TL;DR

This work addresses whether linear exciton Hall and Nernst effects can arise in monolayer 2D semiconductors and how exciton Berry curvature influences them. It develops a semi-classical transport framework and derives the exciton Berry curvature $\, ext{Omega}^{ex}(oldsymbol{k})$ for general inhomogeneous 2D systems, applying the theory to monolayer TMDs and black phosphorus (BP). The key findings show that Berry-curvature–driven linear responses are forbidden by symmetry in these materials (e.g., cancelation in TMDs and vanishing near Γ in BP), yet strong in-plane anisotropy in BP produces a sizable linear Hall current without Berry curvature. This reveals the possibility of significant Berry-curvature–free exciton Hall/Nernst signals in 2D materials, offering new avenues for optoelectronic applications and experimental exploration under controlled symmetry and anisotropy conditions.

Abstract

This paper focuses on the study of linear exciton Hall and Nernst effects in monolayer two-dimensional (2D) semiconductors, employing the semi-classical transport theory. By deriving the exciton Berry curvature in momentum space for a general inhomogeneous 2D system, we establish its dependence on the Berry curvature and the effective mass of electron and hole. As illustrative examples, the exciton Hall effect in monolayer transition metal dichalcogenides (TMDs) and black phosphorus (BP) are calculated. For these materials, we demonstrate that a linear Hall (Nernst) exciton current with the non-zero Berry curvature is strictly forbidden by the symmetries. This finding aligns with earlier experimental observations on the exciton Hall effect in MoSe$_2$. In contrast, a strong anisotropy in BP leads to a net linear Hall current of excitons, exhibiting a relatively large value and resembling an anomalous Hall effect rather than a valley Hall effect. Our work reveals that the specific symmetry of 2D materials can induce a significant linear exciton Hall (Nernst) effect even without Berry curvature, which is normally forbidden with non-zero Berry curvature in the monolayer 2D material. This observation holds promise for future optoelectronic applications and offers exciting possibilities for experimental exploration.

Figures (3)

• Figure 1: (Color online) (a) Top panel: Schematic of the atomic structure of a monolayer TMD. Bottom panel: Schematic of the band edge near these high symmetric points ($\pm K$ valley) in the first BZ of a monolayer TMD. The possible valley excitons are also shown within the black dashed circle. (b) The similar plot to (a) but for monolayer BP.
• Figure 2: (Color online) (a) Numerical calculation of $\sigma _{xx}^{1}-\sigma _{yy}^{1}$ in Eq. (\ref{['Hall']}) for $H_{\mathrm{BP}}$ [Eq. (\ref{['H_B']})], with respect to the the temperature $T$. (b) The Similar plot of $\alpha _{xx}^{1}-\alpha _{yy}^{1}$ in Eq. (\ref{['Hall']}) for BP, which has the same y-axis index as (a). $\mu =-0.01\,\mathrm{eV}$ and $\tau =1\,ps$ for all plots.
• Figure 3: (Color online) (a) Numerical calculation of $f_{\sigma _{y}}$ in Eq. (\ref{['Hall']}) for $H_{\mathrm{BP}}$ [Eq. (\ref{['H_B']})] at different values of $\boldsymbol{k}=(k_{x},k_{y})=k(cos\varphi ,sin\varphi )$, with respect to the the temperature $T$. (b) The Similar plot of $f_{\alpha _{y}}$ in Eq. (\ref{['Hall']}) for BP, which has the same y-axis index as (a). $X_{BP}=\pi /4.58$ means the half width of the first Brillouin zone of BP in $x$ direction. $\mu =-0.01\,\mathrm{eV}$ and $\tau =1\,ps$ for all plots.