Trion gas on the surface of a failed excitonic insulator

TL;DR

The authors reveal an equilibrium trion gas localized at the surface of Ta$_2$NiS$_5$, stabilized by surface band bending in a quasi-1D material. Using ARPES and 2PPE, they detect a sharp in-gap state at $\sim$165 meV below $\epsilon_F$ with strong 1D confinement and show that its energetics support a trion (electron–exciton) bound state rather than a single exciton or impurity band. A minimal 1D lattice model and spectral-function calculations reproduce the observed feature, and controlled surface doping tunes the trion population, underscoring a robust, equilibrium many-body surface state. This work positions Ta$_2$NiS$_5$ as a unique platform to study interaction-driven surface quasiparticles and their controllability in low-dimensional systems.

Abstract

Trions, three-body bound states composed of an exciton and an additional charge, are typically fragile and require external excitation to form. Here, we report the spontaneous emergence of a stable trion gas at the surface of the layered semiconductor Ta2NiS5, revealed through angle-resolved photoemission spectroscopy. We observe a sharp, highly localized in-gap feature that cannot be explained by conventional band-theory. Instead, we argue that it arises from the formation of negative trions, stabilized by surface-induced band bending and the material's quasi-one-dimensional geometry. Unlike excitons, these trions form without optical pumping and persist at equilibrium, marking a rare example of an interaction-driven surface state in a nominally conventional semiconductor. Our findings establish Ta2NiS5 as a unique platform for exploring many-body physics at surfaces and open new avenues for studying and controlling collective excitations in low-dimensional systems.

Figures (10)

• Figure 1: Sulfur substitution in the excitonic insulator candidate $\mathrm{Ta_2Ni(Se_{1-x}S_x)_5}$:(A) Brillouin zone of $\mathrm{Ta_2Ni(Se_{1-x}S_x)_5}$, with high-symmetry points indicated. The $\Gamma$--$X$ direction corresponds to the quasi-1D chain direction shown in panel (B). (B) Simplified crystal structure of $\mathrm{Ta_2Ni(Se_{1-x}S_x)_5}$. Each unit cell contains one Ni atom (blue) and two Ta atoms (red), coordinated by Se/S atoms. The atoms are arranged in chains along the crystallographic $a$-axis, giving rise to a quasi-one-dimensional structure (C) Schematic illustration of the band structure evolution in $\mathrm{Ta_2Ni(Se_{1-x}S_x)_5}$ as sulfur gradually replaces selenium, highlighting the transition from a semimetallic to a semiconducting state. (D) ARPES image of the top of the valence band in Ta$_2$NiSe$_5$, exhibiting the characteristic "M"-shaped dispersion commonly associated with an excitonic insulator seki_excitonic_2014. (E) ARPES image of the fully sulfur-substituted compound Ta$_2$NiS$_5$, showing a shift of the valence band to higher binding energies. A faint in-gap feature is observed at approximately $165\,\mathrm{meV}$. (F) Schematic phase diagram of an excitonic insulator (adapted from jerome_excitonic_1967). In the semiconducting regime, increasing the band gap reduces the excitonic condensation temperature until a critical point is reached at which the exciton binding energy equals the band gap $(E_g = E_{ex}^b)$, resulting in $T_c = 0$.
• Figure 2: Characterization of the in-gap state in Ta$_2$NiS$_5$:(A) ARPES spectrum measured with 22 eV photons along the chain direction ($\Gamma$–X), revealing a faint and compact in-gap state located $\sim165$ meV below the Fermi level. The intensity in the marked region (white dotted line) is enhanced by a factor of 40 for visibility. The overlaid curve shows the dispersion of the in-gap state along k$_x$, as extracted from panel (C). (B) Energy distribution curve (EDC) at the $\Gamma$ point, clearly showing the in-gap state energetically separated from both the valence band and the Fermi level. The binding energies of the in-gap state and valence band maximum are indicated by dashed lines. (C) Dispersion of the in-gap state along k$_x$, extracted by fitting the EDC peaks. Error bars represent the uncertainty in the extracted peak positions. A clear hole-like dispersion is observed, with spectral weight abruptly vanishing beyond $\pm0.2$ Å$^{-1}$. Data are shown only where the fits are reliable. (D) ARPES spectrum along $\Gamma$–Y (50 eV photons, linear horizontal polarization), i.e., perpendicular to the chains. The spectrum is shown on a logarithmic scale and has been FFT-filtered for clarity. The same in-gap state is present but remains completely flat, underscoring its strong one-dimensional character. (E) Binding energy of the in-gap state measured at various momenta across multiple Brillouin zones. Energies are extracted from Gaussian fits to the EDCs; error bars indicate fitting uncertainties. The dispersion remains flat within experimental resolution. (F) EDCs corresponding to the momentum points shown in panel (E). The valence band exhibits a clear dispersion, while the in-gap state remains fixed in energy. Dashed vertical lines mark the valence band peak positions, and the shaded gray band highlights the energy range of the in-gap state.
• Figure 3: Photoemission process and energetics:(A) Schematic of the photoemission process involving a trion. Left: Initial ground state where an exciton and a conduction-electron form a trion bound state. Right: upon photon absorption, one electron is emitted, breaking the trion and leaving behind a neutral exciton. (B) The 6.4eV ARPES spectra showing the top of the valence band, combined with the 6eV 2PPE spectra showing the bottom of the conduction band. The solid lines are fits to the data using a simple model. More details about the model can be found in the SM. (C) Illustration of the band structure and the the in-gap feature resulting from the exciton remaining after breaking a trion. Conduction band (red), valence band (blue) and in-gap feature (magenta). The excitonic binding energy ($E_{ex}^b$) and the electron-exciton binding energy ($E_{ex-e}^b$) are indicated. (D) Calculated spectral function obtained in the presence of a single trion, in a system of $N=40$ unit cells, due to photoemission of a conduction electron obtained using Exact diagonalisation (ED) on the minimal model presented in the SM. To mimic the finite temperature and resolution of the ARPES measurement we use convolution with a Gaussian of width $20$meV. Here model parameters are $U_0/a=0.7$eV, screening length $\xi/a=6$, $E_\text{g}=0.4$eV, and tight binding hopping amplitudes $t_c=0.78$eV and $t_f=1.09$eV, fixed by the effective masses of the conduction and valence bands respectively.
• Figure 4: Surface doping dependence of the in-gap state:(A–C) ARPES spectra along the $\Gamma$–X direction measured over time using 6.4 eV photons. (A) Two hours, no in-gap state is visible. (B) After 8 hours in vacuum, a faint in-gap feature begins to emerge. (C) After 12 hours, the spectral weight of the in-gap state increases significantly. (D) Time evolution of the valence band maximum (blue) and the spectral intensity of the in-gap state(magenta). Shaded lines serve as guides to the eye. EDCs at the $\Gamma$ point as a function of time used here are shown in the SM. Dashed vertical lines indicate the time points at which panels A–C were measured. Intensity values are normalized to the intensity of the peak of the valence band. (E–G) Controlled potassium surface doping of Ta$_2$NiS$_5$. (E–F) ARPES spectra along the $\Gamma$–X direction, taken with 43 eV photons and horizontal polarization, measured before (E) and after 20 seconds of potassium deposition (F). (G) Extracted dispersion of the in-gap state from panel (F) (red), overlaid with the dispersion from Fig. \ref{['fig:kxyz']}(C) (black) for comparison. (H) Schematic illustration of the effect of surface doping: band structure shifts downward, and once the condition in Eq. \ref{['E_C']} is satisfied, trion formation becomes energetically favorable.
• Figure S1: Full momentum range fitting result of the in-gap state. Top: peak amplitude as a function of $k_x$. Bottom: peak positions over the full range.