Dataset DOI: 10.5061/dryad.m905qfvcm

Description of the data and file structure

Dataset for "Electrically controlled interlayer trion fluid in electron-hole bilayers". The dataset contains the underlying data for all the figure panels.

Evidence of interlayer trion formation in electron-hole bilayers is provided using optical spectroscopy. A monolayer MoS2 and a monolayer WSe2, separated by a thin hBN tunneling barrier, are encapsulated in hBN and gated by graphite gates on both sides. As the electron density and the hole density in the bilayer heterostructure is electrically tuned to commensurate ratios 1:2 or 2:1, layer-separated electrons and holes spontaneously bind into three-particle trion states. Such trions manifest in the optical spectrum as a higher-energy absorption peak with unique magnetic field dependence. This dataset contains the acquired optical spectra using a supercontinuum laser. 

Files and variables

The dataset data_files.zip consits of the following files:

Data from Figure 1

Optical spectroscopy of the e-h bilayer.

• Fig.1C n_e.dat: The measured electron density n_e, in units of 10^{12 cm}-2, in the MoS2 layer.
• Fig.1C n_h.dat: The measured hole density n_h, in units of 10^{12 cm}-2, in the WSe2 layer.
• Fig.1CDEF V_G.dat: The gate voltage (in Volts) applied on the heterostructure in Fig. 1C, D, E and F.
• Fig.1CF V_B.dat: The interlayer bias voltage (in Volts) applied on the heterostructure in Fig. 1C and F.
• Fig.1DE Energy.dat: The photon energy (in eV) for the optical spectra (vertical axis of Fig. 1D and E).
• Fig.1D dRdE.dat and Fig.1E dRdE.dat: Measured optical spectrum as functions of the gate voltage and photon energy. Data in arbitrary units.
• Fig.1F dRdE.dat: 2D map of the spectrum intensity at WSe2 X+ peak resonance as a function of gate and bias voltages.

Data from Figure 2

Spin-singlet pairing in the trion bound state revealed by helicity-resolved optical spectrum.

• Fig.2AB Energy.dat: The photon energy (in eV) for the optical spectra (vertical axis of Fig. 2A and B).
• Fig.2ABF B.dat: Out-of-plane magnetic field B applied (in Tesla) in Fig. 2A, B and F.
• Fig.2A dRdE.dat and Fig.2B dRdE.dat: Optical spectrum as a function of B measured using left-handed circularly polarized light.
• Fig.2DE Energy.dat: The photon energy (in eV) for the optical spectra (horizontal axis of Fig. 2D and E).
• Fig.2D dRdE.dat and Fig.2E dRdE.dat: Optical spectrum at B=0 for density ratio of 0:1 and 1:2.
• Fig.2D Fitted dRdE.dat and Fig.2E Fitted dRdE.dat: Fitting results for the measured spectra. The experimental data is fitted to the derivative of Fano line shapes. The fitting code is provided in multiFano_fitting.m.
• Fig.2F Spin ratio.dat: Spin occupation ratio (unitless) for the WSe2 holes as a function of B.

Data from Figure 3

Continuously tunable Bose-Fermi mixture.

• Fig.3A Energy.dat: The photon energy (in eV) for the optical spectra (vertical axis of Fig. 3A).
• Fig.3AB n_e.dat: Total electron density (in 10^{12 cm} -2) in the MoSe2 layer (horizontal axis of Fig. 3A and B).
• Fig.3A dRdE.dat: Optical spectrum as a function of electron density in the MoS2 layer, keeping the hole density 10^{12 cm} -2 constant.
• Fig.3B X+ oscillator strength.dat and Fig.3B X+ oscillator strength.dat: Fitted oscillator strength of the X+ peak and the P+ peak.
• Fig.3C n_t+.dat: Positive trion density, estimated using the P+ peak intensity, as a function of n_e (given in Fig.3C n_e.dat) and n_h (Fig.3C n_h.dat).

Data from Figure 4

High-order multiparticle states in the e-h bilayer under photoexcitation.

• Fig.4A Energy.dat: The photon energy (in eV) for the optical spectra (horizontal axis of Fig. 4A).
• Fig.4A dRdE ne=0.dat, Fig.4A dRdE ne=nh.dat, and Fig.4A dRdE ne=2nh.dat: Spectra at three different e-h density ratios 0:1, 1:1 and 2:1.
• Fig.4A Fitted dRdE ne=0.dat, Fig.4A Fitted dRdE ne=nh.dat, and Fig.4A Fitted dRdE ne=2nh.dat: Fitting results using sum of multiple Fano peaks.

Data from Figure S2, S3, and S4

Reproducing the main results in three other device, D2-D4. All the naming conventions and units are the same as described above.

• All files starting with Fig.S2: they are the same data as those described previously but acquired from device D2 (MoSe2/bilayer-hBN/WSe2).
• All files starting with Fig.S3: they are the same data as those described previously but acquired from device D3 (MoSe2/bilayer-hBN/WSe2).
• All files starting with Fig.S4: they are the same data as those described previously but acquired from device D4 (MoS2/bilayer-hBN/WSe2).

Data from Figure S5

X+ peak energy for different hBN thicknesses.

• Fig.S5 Num of hBN layers.dat: Number of hBN layers between the electron layer and the hole layer.
• Fig.S5 X+ energy shift at n_e=n_h.dat: X+ peak energy shift (in meV), compared to the n_e=0 case, at n_e=n_h.
• Fig.S5 X+ energy shift at n_e=2n_h.dat: X+ peak energy shift (in meV), compared to the n_e=0 case, at n_e=2n_h.

Data from Figure S6

Negative trion signatures from the MoS2 spectra.

• Fig.S6A V_G.dat and Fig.S6A V_B.dat: Gate and bias voltages (in Volts) applied.
• Fig.S6A dRdE.dat: 2D map of the spectrum intensity at MoS2 X- peak resonance as a function of gate and bias voltages.
• Fig.S6B Energy.dat: The photon energy (in eV) for the optical spectra (vertical axis of Fig. S6B).
• Fig.S6B n_h.dat: Total hole density (in 10^{12 cm} -2) in the WSe2 layer (horizontal axis of Fig. S6B).
• Fig.S6B dRdE.dat: Optical spectrum as a function of hole density in the WSe2 layer, keeping the electron density 10^{12 cm} -2 constant.
• Fig.S6C n_t-.dat: Negative trion density, estimated using the P- peak intensity, as a function of n_e (given in Fig.S6C n_e.dat) and n_h (Fig.S6C n_h.dat).

Data from Figure S7

X+ peak energy for different hBN thicknesses.

• Fig.S7A V_G.dat and Fig.S7A V_B.dat: Gate and bias voltages applied on the e-h bilayer
• Fig.S7A charge compressibility.dat: Charge compressibility, obtained from numerical derivative of net charge density with respect to the gate voltage, as a function of gate and bias voltages.
• Fig.S7B Num of hBN layers: Number of hBN layers between the electron layer and the hole layer.
• Fig.S7B Exciton binding energy.dat: Interlayer exciton binding energy, in units of meV.

Data from Figure S8

Thermal melting of interlayer trions.

• Fig.S8 T.dat: List of temperatures at which the data are acquired.
• Fig.S8A n_t+.dat: Positive trion density (in 10^{12 cm} -2) as a function of total electron density (given in Fig.S8A n_e.dat) for different temperatures. The hole density is kept at 10^12 cm -2.
• Fig.S8B n_t+.dat: Positive trion density (in 10^{12 cm} -2) as a function of hole density (given in Fig.S8B n_h.dat) for different temperatures. The e-h density ratio is kept at 1:2.

Data from Figure S9

Interlayer tunneling current.

• Fig.S9A V_G.dat and Fig.S9A V_B.dat: Gate and bias voltages applied on the e-h bilayer
• Fig.S9A Current.dat: Interlayer tunneling current (in Ampere) between the bilayer.
• Fig.S9B Current D1.dat, Fig.S9B Current D1.dat, Fig.S9B Current D1.dat, and Fig.S9B Current D1.dat: Interlayer tunneling current (in Ampere) as a function of e-h pair density (given in Fig.S9B Density.dat) for devices D1-D4.

Code/software

multiFano_fitting.m: Matlab code (version R2021b) used to fit the experimental optical spectrum to a sum of multiple Fano peaks.