Interlayer exciton condensates between second Landau level orbitals in double bilayer graphene

Abstract

We present Coulomb-drag measurements on a heterostructure comprising two Bernal-stacked bilayer graphene (BLG) sheets separated by a 2.5 nm hexagonal boron nitride (hBN) spacer in the quantum Hall (QH) regime. Using top and bottom gate control, together with an interlayer bias, we independently tune the two BLG layers into either the lowest (N = 0) or second (N = 1) Landau level (LL) orbital and probe their interlayer QH states. When both layers occupy the N = 0 orbital, we observe both interlayer exciton condensates (ECs) at integer total filling and interlayer fractional QH states, echoing the results in double monolayer graphene. In contrast to previous studies, however, when both BLG layers occupy the N = 1 orbital, we also observe quantized drag signals, signifying an interlayer exciton condensate formed between the second LLs. By tuning the layer degree of freedom, we find that this N = 1 EC state arises only when the N = 1 wavefunction in each BLG is polarized toward the hBN interface to maximize the interlayer Coulomb interaction.

Figures (23)

• Figure S1: a, Device picture with dashed lines denoting the original flake placement. The semi-transparent region is covered by contact gates. b, Schematic of the double layer structure and device configuration. c, Illustration of valley and orbital flavor of the zero-energy Landau levels in BLG. Spin flavor is not included. Valley flavor is tied with layer polarization. d, Drive resistance $R_{\text{xx}}^{\text{drive}}$ (bottom layer) as a function of displacement field $D_{\text{bot}}$ and filling factor $\nu_{\text{bot}}$. e, Schematic of the main features in d.
• Figure S2: a,$R_{\text{xx}}^{\text{drive}}$ and b,$R_{\text{xx}}^{\text{drag}}$ as a function of $\nu_{\text{top}}$ and $\nu_{\text{bot}}$. c,$R_{\text{xx}}^{\text{drag}}$ near $(\nu_{\text{top}}, \nu_{\text{bot}})=(0.5, 2.5)$ at $B = 16$ T. The colormap limits are chosen to highlight drag resistance and suppress spurious signals due to contact quality.d, same as c but with $B = 25$ T. e,$R_{\text{xx}}^{\text{drag}}$ near $(\nu_{\text{top}}, \nu_{\text{bot}})=(0.5, 0.5)$ at $B = 16$ T. f, Line cuts across the EC state in c showing $R_{\text{xx}}^{\text{drag}}$, $R_{\text{xy}}^{\text{drag}}$ and $R_{\text{xy}}^{\text{drive}}$.
• Figure S3: a,$R_{\text{xx}}^{\text{drive}}$ as a function of $\nu_{\text{top}}$ and $\nu_{\text{bot}}$ at $V_{\text{int}}=0.07$ V. Dashed squares mark interlayer states formed by N = 0 orbitals. Dashed circles mark interlayer states formed by $N = 1$ orbitals. b, The corresponding drag signal $R_{\text{xx}}^{\text{drag}}$. The top insets show cartoons illustrating the two types of interlayer states formed by coupling $N=$ 0 and 1 LL orbitals. c,$R_{\text{xx}}^{\text{drag}}$ and e,$R_{\text{xy}}^{\text{drag}}$ near $(\nu_{\text{top}}, \nu_{\text{bot}})=(1.5, 0.5)$ at $V_{\text{int}}=0.1$ V. d and f, Line cuts across the state showing all other transport channels. Dashed lines denote the state location and quantization value.
• Figure S4: a,$R_{\text{xx}}^{\text{drive}}$ at fixed $\nu_{\text{bot}}=3.5$ as a function $D_{\text{top}}$ and $\nu_{\text{top}}$. b,$R_{\text{xx}}^{\text{drag}}$ in the same range, showing clearly interlayer QH states. c,$R_{\text{xx}}^{\text{drive}}$ at fixed $\nu_{\text{bot}}=1.5$. d, Schematic of the features in the resistance data. This shows the $N=1$ interlayer QH states form only when the second LL component in the $N=1$ orbitals are in proximate layers.
• Figure S1: Left, schematic of the gating configuration for a double layer graphene device. Right, the corresponding capacitance network circuit model.