Trion Hall Effect in TMDs

• Trion Hall effect is the phenomenon where charged composite trions, carrying finite Berry curvature, drive a Hall voltage in TMD systems.
• In photo-induced configurations, valley-polarized trions generate a zero-field Hall response, directly modifying the conductivity tensor unlike neutral excitons.
• In electron–hole double layers, equilibrium trion fluids under a perpendicular magnetic field exhibit unique Hall and Hall-drag signals, highlighting tunable transport behavior.

Searching arXiv for the specified papers and closely related work on the trion Hall effect and valley Hall effect in TMDs. First, locating the 2017 paper on the microscopic origin of the valley Hall effect in TMDs. Now locating the 2026 paper on the trion Hall effect in electron-hole double layers. The trion Hall effect denotes Hall transport in which trions, rather than only elementary electrons or holes, are the operative charged quasiparticles. In the transition-metal dichalcogenide literature summarized here, the term refers to two distinct but conceptually linked regimes. In monolayer and few-layer TMDs, valley-polarized trions can contribute directly to a zero-field photo-induced Hall voltage because they are charged composite quasiparticles with finite Berry curvature (Ubrig et al., 2017). In Coulomb-coupled electron-hole double layers, equilibrium trion fluids in MoSe$_2$/WSe$_2$ heterobilayers exhibit a Hall effect under perpendicular magnetic field through the Lorentz force acting on the trions themselves, with signatures in both standard Hall and Hall-drag measurements (Chaturvedi et al., 17 Jun 2026).

1. Definition, quasiparticle content, and conceptual scope

A trion is a three-particle bound state of two like charges and one opposite charge. In the double-layer setting, the relevant species are the negative trion, consisting of two electrons and one hole, and the positive trion, consisting of two holes and one electron (Chaturvedi et al., 17 Jun 2026). In the optical valley-transport setting, trions are described as charged excitons that bind an additional electron or hole and inherit a Berry curvature from the electron and hole band states out of which they are formed (Ubrig et al., 2017).

This charge distinguishes trions sharply from neutral excitons. Neutral excitons may possess Berry curvature, but they do not directly influence the conductivity tensor because they are neutral (Ubrig et al., 2017). Trions, by contrast, can either contribute an off-diagonal conductivity at $B=0\ \mathrm{T}$ when a valley polarization is optically prepared, or undergo a conventional Lorentz-force deflection under finite magnetic field because they carry net charge (Ubrig et al., 2017, Chaturvedi et al., 17 Jun 2026).

A central conceptual point is therefore that the trion Hall effect is not a single mechanism. One form is a Berry-curvature-mediated zero-field response of valley-polarized charged composite quasiparticles. Another is a magnetic-field Hall response of equilibrium trion fluids. The common element is that Hall transport is attributed to the trions themselves rather than being reduced to a response of independent free carriers.

2. Trions in the photo-induced valley Hall effect

In monolayer TMDs, the two valleys $K$ and $K'$ carry equal and opposite Berry curvature, so their Hall contributions cancel in equilibrium. A Hall voltage transverse to the current flow can nevertheless appear if a net valley polarization is generated, that is, if the electronic states in the two valleys are populated differently; this is the valley Hall effect (Ubrig et al., 2017). Circularly polarized light is crucial because orbital selection rules for optical inter-band transitions allow valley-selective excitation, whereas linearly polarized light induces transitions in the $K$ and $K'$ valleys with equal probability and causes no valley imbalance (Ubrig et al., 2017).

The 2017 study argues that the observed photo-induced valley Hall effect in TMDs is not best understood as arising from a valley-unbalanced population of independent electrons and holes created by interband transitions. That interpretation is described as questionable because the relevant optoelectronic phenomena become visible upon illumination at the wavelength corresponding to the energy of excitons $X_0$ or trions $X_\pm$, an energy much smaller, by $0.5\ \mathrm{eV}$ or more, than the energy needed to cause interband transitions (Ubrig et al., 2017). The proposed microscopic origin is instead resonant generation of composite quasiparticles.

Within that framework, trions provide the most direct route to a Hall response. Upon stationary illumination with circularly polarized light, trions can develop a finite valley polarization and contribute an off-diagonal term to the conductivity tensor. Because they are charged, this term can produce a finite Hall voltage at $_2$0 when a current is forced through the system (Ubrig et al., 2017). The trion Hall effect in this sense is a constituent of the photo-induced valley Hall effect.

3. Exciton-mediated and trion-mediated channels

The optical valley-Hall literature separates two microscopic channels. For excitons, the mechanism is indirect. Valley-polarized excitons should not lead to a measurable valley Hall effect by direct transport because they are neutral, but in the presence of a strong electric field they may split and release free electrons and holes. If the valley polarization is preserved during this splitting process, those released carriers can generate a measurable Hall response (Ubrig et al., 2017). The paper associates this with exciton dissociation near metal contacts, where the electric field is sufficiently strong.

For trions, the mechanism is different. Trions are already charged, so they directly modify the conductivity tensor. The measured Hall response does not require prior dissociation into free carriers (Ubrig et al., 2017). This distinction is the basis for the paper’s reinterpretation of photo-induced valley Hall measurements at sub-gap wavelengths.

The experimental discrimination strategy is wavelength-dependent spatial mapping of the Hall voltage. When the wavelength is tuned to the exciton absorption energy, the Hall signal is expected to be maximum when the laser is focused next to the edge of the current-injecting contact, because the excitons must reach the interface with the metallic contact and split there. When the wavelength is tuned to photo-generate trions, the photo-induced charged trions directly cause a change in the local conductivity tensor, so the signal is largest when the laser spot is focused in the center of the Hall probes (Ubrig et al., 2017). The resulting spatial fingerprints are asymmetric and contact-centered for the exciton-mediated channel, but symmetric and centered between the Hall probes for the trion-mediated channel.

This spatial separation has a further implication. For the trion contribution, the detection of a Hall signal attributable to resonantly generated trions directly implies that trions in TMDs possess a non-trivial Berry curvature (Ubrig et al., 2017). The inference is experimental: the Hall voltage appears at the trion absorption wavelength, and its spatial profile is consistent with transport by a charged mobile species rather than neutral-exciton splitting alone.

4. Equilibrium trion fluids in electron-hole double layers

A second realization of the trion Hall effect appears in Coulomb-coupled electron-hole double layers formed from a monolayer WSe$_2$1 hole layer and a bilayer MoSe$_2$2 electron layer, separated by a thin hBN barrier of about $_2$3–$_2$4 in the active channel (Chaturvedi et al., 17 Jun 2026). The barrier strongly suppresses interlayer tunneling while preserving strong interlayer Coulomb interaction. The device is dual-gated, and the reported control parameters are $_2$5, which controls the overall doping density, $_2$6, which controls the perpendicular electric field, and $_2$7, applied to the Mo-layer to tune electron doping and chemical potential (Chaturvedi et al., 17 Jun 2026).

Because tunneling is quenched but Coulomb coupling remains strong, the two layers can form equilibrium bound states. When the interlayer charge gap is reduced enough that

$_2$8

where $_2$9 is the exciton binding energy, the system spontaneously forms an equilibrium exciton fluid (Chaturvedi et al., 17 Jun 2026). Doping that exciton fluid with extra electrons or holes then yields an equilibrium trion fluid.

The trion state is reported in narrow regions of the phase diagram centered around the commensurate conditions

$B=0\ \mathrm{T}$0

for negative trions and

$B=0\ \mathrm{T}$1

for positive trions, where $B=0\ \mathrm{T}$2 is the electron density in the Mo-layer and $B=0\ \mathrm{T}$3 is the hole density in the W-layer (Chaturvedi et al., 17 Jun 2026). The favored trions are noted to be spin-singlet because the two like carriers occupy opposite valleys due to spin-valley locking. The state is visible through large $B=0\ \mathrm{T}$4, strong Coulomb drag, optical signatures in reflection contrast, and Hall signatures (Chaturvedi et al., 17 Jun 2026).

5. Magnetic-field trion Hall transport and Hall drag

In the double-layer platform, the trion Hall effect arises from a Lorentz force on trions under a perpendicular magnetic field. The reported picture is direct: trions drift under the applied electric field, the magnetic field deflects them sideways, and a transverse voltage appears (Chaturvedi et al., 17 Jun 2026). This response is manifested in both Hall drag measurements and standard Hall measurements on one of the semiconductor layers.

The transport analysis is formulated through a $B=0\ \mathrm{T}$5-by-$B=0\ \mathrm{T}$6 conductivity tensor containing free electrons, free holes, excitons, and trions, with conductivities $B=0\ \mathrm{T}$7, $B=0\ \mathrm{T}$8, $B=0\ \mathrm{T}$9, and $K$0, and magnetic-field-dependent Drude-like terms involving cyclotron frequencies $K$1, $K$2, and $K$3 (Chaturvedi et al., 17 Jun 2026). The measured Hall and drag resistances follow from solving these tensor equations under open-circuit Hall conditions in the W-layer and Coulomb-drag conditions with current driven in the Mo-layer.

Several transport signatures are emphasized. Inside the trion regions, $K$4 and $K$5 become large; outside the trion regions, the drag Hall signal is negligible (Chaturvedi et al., 17 Jun 2026). The Hall-drag response changes sign between positive and negative trion regions, consistent with opposite trion charge. The effective Hall density is defined as

$K$6

and at $K$7 it deviates strongly from the expected hole density: it drops below the free-hole line in the positive trion region, approaches zero near charge neutrality, becomes negative in the negative trion region, and returns to free-hole behavior outside the trion regime (Chaturvedi et al., 17 Jun 2026).

One of the most striking observations is the appearance of an electron Hall effect in a hole-doped WSe$K$8 monolayer in the negative trion regime. The reported interpretation is that the Hall signal is not determined by free holes alone; it includes trion drags and bound-state contributions from the coupled bilayer, so an effective electron-like Hall signal can appear even though the layer is hole-doped overall (Chaturvedi et al., 17 Jun 2026). In the hole-trion case, the Hall response simplifies approximately to that of the free holes, whereas in the electron-trion case it mixes free-electron and trion contributions and can produce the observed sign reversal.

6. Stability, disappearance, and broader significance

The trion Hall effect depends on trion stability. In the double-layer system, the reported Hall signatures emerge below about $K$9. At higher temperature, $K'$0 becomes negligible and the standard Hall response reverts toward that of free holes, consistent with thermal ionization of trions into free carriers (Chaturvedi et al., 17 Jun 2026). The crossover temperature is stated to provide an estimate of the trion binding energy.

A second route to disappearance is high carrier density. At large $K'$1, roughly $K'$2 in the reported calibration, screening weakens the interlayer Coulomb attraction and ionizes the bound states, so excitons and trions are destroyed and the Hall signal again becomes that of a conventional free-carrier layer (Chaturvedi et al., 17 Jun 2026). A third route is strong magnetic field: above about $K'$3 in the reported device, the trion regions shrink and disappear because the valley Zeeman splitting overwhelms the trion binding energy (Chaturvedi et al., 17 Jun 2026). From the threshold shift in optical spectroscopy, the trion binding energy is estimated to be

$K'$4

corresponding to roughly $K'$5 near charge neutrality (Chaturvedi et al., 17 Jun 2026).

Across both research directions, the significance is that composite quasiparticles participate directly in Hall transport. In the optical zero-field case, the trion contribution is taken as experimental evidence that trions possess finite Berry curvature (Ubrig et al., 2017). In the double-layer magnetic-field case, the observation of Hall drag and standard Hall signatures establishes that charged composite bound states in equilibrium can undergo Hall transport as such (Chaturvedi et al., 17 Jun 2026). The 2026 work further states that this opens the door for realizing quantum oscillations and the quantum Hall effect for trions, while also noting that the present quantum oscillations seen in $K'$6 are not yet true trion quantum oscillations. The stated requirements for bona fide trion quantum oscillations or a trion quantum Hall effect are lower magnetic field satisfying

$K'$7

and/or cleaner samples with higher trion mobility (Chaturvedi et al., 17 Jun 2026).

A recurring misconception in this area is to treat all Hall signatures under optical or coupled-bilayer conditions as if they were necessarily responses of independent carriers. The papers summarized here argue for a more specific interpretation. In photo-induced valley Hall measurements, neutral excitons act indirectly through splitting at contacts, whereas charged trions act directly through their own Berry-curvature-mediated transport (Ubrig et al., 2017). In electron-hole double layers, the magnetic-field Hall signal can be dominated by trion drag and trion motion, so even the sign of the Hall response need not match the naive expectation from the nominal doping of an individual layer (Chaturvedi et al., 17 Jun 2026).