DOI: 10.5061/dryad.612jm64km
title: Orbital dependent Coulomb drag in electron-hole bilayer graphene heterostructures

description: We report Coulomb drag studies in an electron-hole bilayer graphene
 heterostructure in a magnetic field, where the orbital, spin, and valley
 degrees of freedom are lifted by the combined effects of exchange
 interaction, Zeeman energy, and vertical displacement field. Our device
 enables the application of a large vertical displacement field in both
 layers. In addition to the well-established strong Coulomb drag between
 the Landau levels with an orbital quantum number N = 0, we observe a
 Coulomb drag signal between the N = 1 Landau levels under a suitable
 vertical displacement field. As the displacement field increases further,
 the Coulomb drag signal between N = 1 Landau levels weakens, and a Coulomb
 drag signal emerges between the N = 0 and N = 1 Landau levels. These
 findings suggest the important role of the orbital index and vertical
 displacement field in interlayer Coulomb interaction within the quantum
 Hall regime of coupled bilayer systems.
description: # Orbital dependent Coulomb drag in electron-hole bilayer graphene
 heterostructures Dataset DOI:
 [10.5061/dryad.612jm64km](https://doi.org/10.5061/dryad.612jm64km) This
 Dryad package contains the source data (plain-text *.txt*) used to
 generate the main-text and Supplemental Material figures in the associated
 Physical Review Letters article “Orbital-Dependent Coulomb Drag in
 Electron-Hole Bilayer Graphene Heterostructures.” --- ## 1. Experiment and
 measurement overview **Device:** an electron–hole (e–h) double-layer
 system formed by two bilayer graphene sheets separated by an insulating
 hBN barrier (~3.5 nm). Carrier densities in each bilayer are tuned by top
 gate voltage (*V~t~*) and bottom gate voltage (*V~b~*). An interlayer bias
 (*V~interlayer~*) is applied between the two bilayer graphene sheets.
 **Coulomb drag measurement:** an AC current *I~drive~* = 1 nA at 17 Hz is
 driven through the drive layer (top bilayer graphene). Voltages are
 measured in the drag layer (bottom bilayer graphene) using lock-in
 techniques. * Longitudinal drag resistance: R~xx~^drag^ = V~xx~ / I~drive~
 * Hall drag resistance: R~xy~^drag^ = V~xy~ / I~drive~ **Magnetic-field
 regime:** The main drag maps shown in Figs. 2–4 are taken in the quantum
 Hall regime at B = 10 T and T ≈ 10 mK. Some Supplemental characterization
 data are taken at other fields (noted below per figure). **Vertical
 displacement field:** Many phenomena discussed are organized by the
 effective vertical displacement field D (in V/nm). In Fig. 4 the
 approximate D value used for each panel is given in the panel label. ---
 ## 2. File structure All source data are contained in: **File:**
 `Source_data.zip` The zip archive contains two top-level directories: *
 `Main Figures/` * `Supplemental Materials Figures/` Each directory
 contains subfolders for individual figures, named by the figure
 number/caption. --- ## 3. Data format conventions ### 3.1 Line-plot files
 (2 columns) * **Column 1:** x-axis values * **Column 2:** y-axis values
 ### 3.2 Two-dimensional (2D) color-plot files (3 or 4 columns) Most 2D
 maps are stored as lists of points: * **Column 1:** x-coordinate *
 **Column 2:** y-coordinate * **Column 3 (and sometimes Column 4):**
 measured value(s) to be plotted as color scale Units: * Voltages (*V~t~*,
 *V~b~*, *V~interlayer~*) are in V * Displacement field *D* is in V/nm *
 Resistances are in kΩ, unless stated otherwise --- ## 4. Main-text figures
 ### Figure 2 — Landau-level structure and global drag maps (B = 10 T, T ≈
 10 mK, V~interlayer~ = 0.2 V) Figure 2 introduces the orbital
 (Landau-level) structure of bilayer graphene under a vertical displacement
 field and connects it to Coulomb drag signatures. Panels (a)–(b) are
 schematic/expected patterns. Panels (c)–(d) show the measured longitudinal
 and Hall drag resistance maps over a broad (*V~b~*, *V~t~*) range. **Data
 file:** `Main Figures/Figure 2/Fig.2 raw data.txt`\ Two-dimensional color
 plots of longitudinal and Hall drag as functions of gate voltages. *
 Column 1: *V~b~* (x-axis) in V * Column 2: *V~t~* (y-axis) in V * Column
 3: R~xx~^drag^ (color scale for Fig. 2c) * Column 4: R~xy~^drag^ (color
 scale for Fig. 2d) --- ### Figure 3 — Zoom-in of two N = 1 Hall-drag
 features and line cuts (B = 10 T, T ≈ 10 mK, V~interlayer~ = 0.2 V) Figure
 3 zooms into two circled regions from the global Hall-drag map (Fig. 2d)
 where strong negative Hall drag appears when both layers occupy N = 1
 Landau levels at specific filling-factor combinations. * Panels (a) and
 (c) are zoomed 2D maps centered at (νb, νt) = (1.5, −0.5) and (3.5, −0.5),
 respectively. * Panels (b) and (d) are horizontal line cuts through (a)
 and (c), showing the Hall-drag peak amplitude along the indicated dashed
 lines. Insets indicate the relevant N = 1 LLs responsible for the signals.
 **Data files:** `Main Figures/Figure 3/` * `Fig.3a raw data.txt` (2D map
 near (1.5, −0.5)) * Column 1: *V~b~* (V) * Column 2: *Vt* (V) * Column 3:
 R~xy~^drag^ * `Fig.3b raw data.txt` (line cut of Fig. 3a) * Column 1:
 *V~b~* (V) * Column 2: R~xy~^drag^ * `Fig.3c raw data.txt` (2D map near
 (3.5, −0.5)) * Column 1: *V~b~* (V) * Column 2: *V~t~* (V) * Column 3:
 R~xy~^drag^ * `Fig.3d raw data.txt` (line cut of Fig. 3c) * Column 1:
 *V~b~* (V) * Column 2: R~xy~^drag^ --- ### Figure 4 — Evolution of Hall
 drag with increasing interlayer bias / displacement field D (B = 10 T, T ≈
 10 mK) Figure 4 tracks how the Hall-drag landscape evolves as the
 effective vertical displacement field D is increased. * Panels (a)–(e) are
 2D color plots of R~xy~^drag^(V~b~, V~t~) at increasing *V~interlayer~* =
 0.2, 0.4, 0.6, 0.8, 1.0 V (with approximate D ≈ 0.19, 0.38, 0.57, 0.75,
 0.94 V/nm, respectively, as labeled in the figure). * The strong N = 1 ↔ N
 = 1 Hall-drag features weaken with increasing D, and at larger D a new
 Hall-drag feature emerges consistent with drag between N = 1 and N = 0
 Landau levels. **Data files:** `Main Figures/Figure 4/`\ For all files
 below: * Column 1: *V~b~* (V) * Column 2: *V~t~* (V) * Column 3:
 R~xy~^drag^ * `Fig.4a raw data.txt` — Fig. 4a, *V~interlayer~* = 0.2 V (D
 ≈ 0.19 V/nm) * `Fig.4b raw data.txt` — Fig. 4b, *V~interlayer~* = 0.4 V (D
 ≈ 0.38 V/nm) * `Fig.4c raw data.txt` — Fig. 4c, *V~interlayer~* = 0.6 V (D
 ≈ 0.57 V/nm) * `Fig.4d raw data.txt` — Fig. 4d, *V~interlayer~* = 0.8 V (D
 ≈ 0.75 V/nm) * `Fig.4e raw data.txt` — Fig. 4e, *V~interlayer~* = 1.0 V (D
 ≈ 0.94 V/nm) --- ## 5. Supplemental Material figures ### Figure S1 —
 Layer-resolved longitudinal resistance maps and line cuts (device
 characterization) Figure S1 provides device characterization for the
 individual bilayer graphene layers: longitudinal resistance maps versus
 gate voltages, along with representative line cuts. **Data files:**
 `Supplemental Materials Figures/Figure S1/` * `Fig.S1a.txt` — 2D map of
 top bilayer graphene longitudinal resistance vs (*V~b~*, *V~t~*) * Column
 1: *V~b~* (V) * Column 2: *V~t~* (V) * Column 3: longitudinal resistance
 (top layer) * `Fig.S1b.txt` — vertical line cut of Fig. S1a at *V~b~* = −2
 V * Column 1: *V~t~* (V) * Column 2: longitudinal resistance (top layer) *
 `Fig.S1c.txt` — 2D map of bottom bilayer graphene longitudinal resistance
 vs (*V~b~*, *V~t~*) * Column 1: *V~b~* (V) * Column 2: *V~t~* (V) * Column
 3: longitudinal resistance (bottom layer) * `Fig.S1d.txt` — horizontal
 line cut of Fig. S1c at *V~t~* = −2 V * Column 1: *V~b~* (V) * Column 2:
 longitudinal resistance (bottom layer) --- ### Figure S2 — Landau fan
 diagram of the top bilayer graphene Figure S2 shows a Landau fan diagram
 (longitudinal resistance vs gate voltage and magnetic field) for the top
 bilayer graphene. **Data file:** `Supplemental Materials Figures/Figure
 S2/Fig.S2 raw data.txt` * Column 1: *V~t~* (V) * Column 2: magnetic field
 *B* (T) * Column 3: longitudinal resistance (top layer) --- ### Figure S3
 — Longitudinal and Hall resistance of the bottom bilayer graphene at B = 1
 T Figure S3 provides a 1D transport characterization of the bottom bilayer
 graphene: longitudinal and Hall resistance as a function of bottom-gate
 voltage at B = 1 T. **Data file:** `Supplemental Materials Figures/Figure
 S3/Fig.S3 raw data.txt` * Column 1: *V~b~* (V) * Column 2: longitudinal
 resistance (bottom layer) * Column 3: Hall resistance (bottom layer)