DOI: 10.5061/dryad.m905qfvcm
title: Electrically controlled interlayer trion fluid in electron-hole bilayers

description: The combination of repulsive and attractive Coulomb interactions in a
 quantum electron(e)-hole(h) fluid can produce correlated phases of
 multiparticle charge complexes such as excitons, trions, and biexcitons.
 We report an experimental realization of an electrically controlled
 interlayer trion fluid in van der Waals heterostructures. In strongly
 coupled electron-hole bilayers, electrons and holes spontaneously form
 three-particle trion bound states. The interlayer trions can assume 1e-2h
 and 2e-1h configurations. We show that the two holes in 1e-2h trions form
 a spin-singlet with a ~1meV spin gap. By electrostatic gating, the
 equilibrium state can be continuously tuned into an exciton fluid, a trion
 fluid, an exciton-trion mixture, or a trion-charge mixture. Our work
 demonstrates a unique platform to study correlated phases of tunable
 Bose-Fermi mixtures.
description: # Electrically controlled interlayer trion fluid in electron-hole bilayers
 Dataset DOI: [10.5061/dryad.m905qfvcm](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.