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arXiv:2512.24153

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

Weilong Guo, Lianguo Li, Qingjun Tong, Ci Li

cond-mat.mes-hallquant-phSubmitted Dec 30, 2025• Announced Dec 31, 2025
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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.

Comments
8 pages, 3 figures

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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 MoSe2_22​. 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.
Valley-layer coupling (VLC) two-dimensional (2D) materials define a distinct class of quantum systems in which valleys are related by crystal, rather than time-reversal (T\mathcal{T}T) symmetry, enabling gate-controlled valley-contrasted layer polarization. Here we extend this concept to excitons. Using TiSiCo as a prototype VLC material, we show that a perpendicular electric field E⊥E_{\perp}E⊥​ controls exciton- dispersion anisotropy and thereby generates unconventional linear transverse exciton transport in both monolayer and twisted bilayer structures. In the monolayer, this response is characterized by anisotropy-induced transverse conductivities, arising from the antisymmetric combination of diagonal elements in the conductivity tensor and strongly tunable by E⊥E_{\perp}E⊥​. In the twisted bilayer, symmetry additionally permits transverse responses from the symmetric part of the conductivity tensor. Since intralayer excitons in different layers are connected by the Förster coupling, these symmetric and antisymmetric responses coexist and compete with the recently proposed T\mathcal{T}T-even layer Hall and Nernst exciton counterflow. This interplay is highly tunable by twisted angle, temperature, and the direction of the in-plane driving force, providing a route to disentangle distinct transverse exciton transport signals experimentally. Our results establish E⊥E_{\perp}E⊥​ as a powerful knob for controlling exciton transport via VLC and identify VLC 2D materials as a promising platform for engineered excitonic phenomena.
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.
Excitons in anisotropic two-dimensional (2D) materials, defined by direction-dependent effective masses, are of pronounced interest for their roles in excitonic and magneto-optical phenomena. A perpendicular magnetic field complicates the separation of center-of-mass (c.m.) and relative motions, especially when electron and hole masses are comparable. Conventional theories often employ an approximate c.m. separation using factorized wave functions, modifying magnetic Hamiltonian terms and possibly introducing inaccuracies in magnetoexciton energy predictions. This work develops an exact analytical framework for c.m. and relative motion separation in anisotropic 2D magnetoexcitons, without resorting to the stationary-c.m. approximation. Starting from the full electron-hole Hamiltonian in a homogeneous magnetic field, the formalism uses the conserved pseudomomentum to derive a relative-motion Hamiltonian, revealing new anisotropy-dependent couplings and magnetic coefficients absent in approximate models. The resulting Schrödinger equation is treated via the Feranchuk-Komarov operator method and Levi-Civita transformation, allowing non-perturbative, systematically convergent solutions. Application to monolayer black phosphorus and titanium trisulfide, both freestanding and encapsulated in hexagonal boron nitride, yields magnetoexciton energies, diamagnetic coefficients, and probability densities for the ten lowest states across considerable magnetic-field ranges. The results demonstrate the significant influence of anisotropy-dependent coupling on magnetic response in systems with strong mass anisotropy. This formalism is generalizable to other anisotropic 2D semiconductors, establishing a foundation for advanced magneto-optical studies.
Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically-doped WSe2_22​ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out-of-plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly-bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.
The realization of Coulomb coupled electron-hole double layers in 2D semiconductor heterostructures has enabled the thermodynamic and transport studies of equilibrium exciton fluids without a magnetic field. By doping the exciton fluid with additional electrons/holes, an equilibrium fluid of trions - three particle bound states of electrons and holes - further emerge, providing the platform to explore new transport phenomena associated with such composite particles. Here we report the observation of a Hall effect for trions in MoSe2/WSe2 heterobilayers, which support Coulomb-coupled electron and hole fluids with tunable densities. The Hall effect arises from a Lorentz force on trions under a perpendicular magnetic field. It is manifested in both Hall drag measurements and standard Hall effect measurements on just one of the semiconductor layers. For negatively charged trions, an electron Hall effect is observed even in a hole doped WSe2 monolayer due to the presence of trion drags. The trion Hall effect also disappears when the trions are ionized at elevated temperatures and/or high trion densities. Our work opens the door for realizing quantum oscillations and the quantum Hall effect for trions.
Direct evidence of exciton condensation in semiconductor heterostructures remains elusive. Here we propose charge transport of doped carriers as a probe of exciton condensation in transition-metal dichalcogenide heterostructures and identify distinct experimental signatures. First, condensation suppresses the phase space for carrier scattering, leading to a reduction in resistivity, that provides a general diagnostic of exciton condensation. Second, in heterostructures with a tunable solid-state Feshbach resonance, condensate-induced hybridization between doped carriers and trion bound states qualitatively modifies transport. In particular, near resonance, this hybridization yields a negative effective mass and a corresponding sign reversal of the Hall resistivity. These results establish charge transport as a promising route for detecting and characterizing exciton condensation in semiconductor heterostructures.