Trion Hall effect in electron-hole double layers

Abstract: 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.

• The paper presents experimental observation and theoretical modeling of a distinct Hall effect for trions in MoSe₂/WSe₂ electron-hole double layers.
• It utilizes dual-gate engineering and low-temperature transport measurements to map phase diagrams and probe Bose-Fermi mixtures in van der Waals heterostructures.
• The study quantifies trion binding energies and temperature-driven transitions, paving the way for exploring trion quantum Hall states in 2D systems.

Trion Hall Effect in Electron-Hole Double Layers: Authoritative Summary

Introduction and Motivation

The study develops the theoretical and experimental framework for the Hall effect of trions—three-particle composite quasiparticles formed from additional electron or hole doping in exciton fluids—within MoSe$_2$/WSe$_2$ van der Waals heterobilayers. With significant prior investigations into equilibrium exciton fluids in Coulomb-coupled bilayer systems, this work extends the exploration to Bose-Fermi mixtures and transport phenomena of composite trion fluids under perpendicular magnetic fields ($B$). The main motivation arises from the expectation that charged trions, as composite particles, should exhibit a Hall response distinct from that of conventional free carriers.

Experimental Setup and Phase Diagram

The experimental double-layer platform comprises monolayer WSe$_2$ (hole layer) and bilayer MoSe$_2$ (electron layer), separated by a thin hBN barrier to suppress interlayer tunneling and maintain strong Coulomb coupling. Dual-gate engineering enables independent chemical potential control for electrons and holes, facilitating access to various carrier density regimes and tuning interlayer bias.

Temperature-dependent ($T\sim1.5\,\text{K}$) transport and optical measurements are performed under magnetic fields up to $B = 12\,\text{T}$, mapping the phase diagram in the space of electron and hole densities and bias voltages. The emergence and stabilization of trion fluids are confirmed by observing insulating behavior (diverging $R_{xx}$) in narrow regions centered at commensurate carrier densities.

Observation of Trion Hall Effect

The central result is the observation of a Hall effect for trions, evidenced in both Hall drag ($R_{xy}^{\rm drag}$) and standard Hall measurements ($R_{xy}$) on a single layer. Crucially, for negatively charged trions, anomalous electron-Hall effect signatures manifest in the hole-doped WSe$_2$0 monolayer, attributable to trion drag-induced transport. The explicit disappearance of the trion Hall effect with increasing temperature (trion ionization above $_2$1) or higher doping underscores the nontrivial thermodynamic stability of trion fluids.

Quantitatively, the Hall density deviates from expected hole density in the positive trion region, representing the loss of free holes due to trion and exciton formation. In the negative trion regime, the Hall response switches to negative, directly evidencing electron-Hall effect in the hole layer—a hallmark of trion-mediated conduction. The transition is well modeled by a four-component conductivity tensor, capturing the interplay between free carriers, excitons, and trions in the Bose-Fermi mixture.

Numerical estimates of trion binding energies ($_2$2) are obtained from injection threshold shifts in reflection contrast spectroscopy and corroborated by transport and Zeeman energy scales for trion ionization. The calculated temperature crossover supports the energetic stability range of trion fluids in these heterostructures.

Quantum Oscillation and Exciton Binding

In hole-doped regimes near charge neutrality, quantum oscillations in $_2$3 (vertical stripes) demonstrate the persistence of exciton binding. The work identifies the conditions required for genuine trion quantum oscillations and the potential realization of a trion quantum Hall effect—namely, low magnetic fields permitting cyclotron energies much smaller than trion binding energies and higher-quality samples with increased trion mobility.

Implications and Future Outlook

Theoretical implications are substantial: the measurement of Hall responses from composite, strongly correlated trion fluids establishes the feasibility of quantum transport studies for emergent quasiparticles in 2D systems. Practically, the ability to control and probe trion Hall physics expands the toolkit for manipulating Bose-Fermi mixtures and composite excitations in van der Waals heterostructures. These results pave the way for future studies targeting quantum oscillations and quantum Hall states of trions, which depend upon improved sample purity and optimized device engineering.

Additionally, the work provides a stringent benchmark for modeling many-body composite transport phenomena in Bose-Fermi mixtures, relevant for condensed matter systems exhibiting exotic superconductivity or correlated insulating behavior.

Conclusion

This paper provides experimental and theoretical confirmation of the trion Hall effect in Coulomb-coupled MoSe$_2$4/WSe$_2$5 electron-hole double layers, characterized by distinctive Hall transport from equilibrium trion fluids. The detailed phase diagram, temperature dependence, and anomalous Hall signatures highlight the interplay between free carriers and composite bound states, underscoring the role of trion stability and dynamics in quantum transport. The findings have significant implications for the study of emergent quasiparticles in 2D materials and set the stage for future exploration of trion quantum Hall physics and related strongly correlated phenomena.