Strongly Enhanced Tunneling at Total Charge Neutrality in Double-Bilayer Graphene-${\mathrm{WSe}}_2$ Heterostructures

We report the experimental observation of strongly enhanced tunneling between graphene bilayers through a ${\mathrm{WSe}}_2$ barrier when the graphene bilayers are populated with carriers of opposite polarity and equal density. The enhanced tunneling increases sharply in strength with decreasing temperature, and the tunneling current exhibits a vertical onset as a function of interlayer voltage at a temperature of 1.5 K. The strongly enhanced tunneling at overall neutrality departs markedly from single-particle model calculations that otherwise match the measured tunneling current-voltage characteristics well, and suggests the emergence of a many-body state with condensed interbilayer excitons when electrons and holes of equal densities populate the two layers.

Figure 1

(a) Schematic of a double-bilayer graphene bilayer ${\mathrm{WSe}}_2$ heterostructure, with top and back gates and independent contacts to each graphene bilayer. (b) Optical micrograph of a heterostructure encapsulated in hBN. Dashed lines indicate top (red) and bottom (blue) bilayer graphene and interlayer ${\mathrm{WSe}}_2$ (yellow). (c) $I_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ at $V_{\mathrm{BG}}=-20\mathrm{V}$ for different $V_{\mathrm{TG}}$ and $T$ values. The data show resonance peaks and NDR that depend weakly on temperature.

Figure 2

Experimental (a) and calculated (b) $g_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ and $V_{\mathrm{TG}}$ at $V_{\mathrm{BG}}=-20\mathrm{V}$ and $T=1.5\mathrm{K}$. Regions in which data are missing due to NDR circuit instabilities are linearly interpolated in (a). The points labeled in (b) identify distinct tunneling regimes. (c) Relative alignment of top (red) and bottom (blue) bilayer graphene bands corresponding to the biasing conditions labeled in (b). The dashed lines mark the two layer Fermi levels. At point (vi) the carrier densities are equal and opposite in the two layers.

Figure 3

(a) $g_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ and $V_{\mathrm{TG}}$ at $V_{\mathrm{BG}}=-20\mathrm{V}$ and $T=1.5\mathrm{K}$, showing a strongly enhanced conductance in the vicinity of $n_T=-n_B$. The $g_{\mathrm{int}}$ range is reduced to better compare regions of low and high $g_{\mathrm{int}}$ values. (b) Experimental (solid black line) and calculated (dashed red line) $I_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ at $n_T=-n_B$ ($V_{\mathrm{TG}}=1.18\mathrm{V}$, $V_{\mathrm{BG}}=-20\mathrm{V}$) and $T=1.5\mathrm{K}$. The inset shows a magnified view of $I_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ data near $V_{\mathrm{int}}=0\mathrm{V}$. (c) $I_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ at $n_T=-n_B=7.4\times {10}^{11}{\mathrm{cm}}^{-2}$ measured at different temperatures, in the vicinity of $V_{\mathrm{int}}=0\mathrm{V}$. (d) Measured (symbols) and calculated (dashed line) $g_{\mathrm{int}}$ vs $T$ data at $V_{\mathrm{int}}=0\mathrm{V}$ and $n_T=-n_B=7.4\times {10}^{11}{\mathrm{cm}}^{-2}$, showing a strong experimental $g_{\mathrm{int}}$ increase with reducing $T$. Inset: Temperature dependence of $g_{\mathrm{int}}$ normalized to the $T=100\mathrm{K}$ value, at resonance (blue diamonds) and at the onset of unlike-band tunneling (green triangles), for $n_T\approx n_B=-1.7\times {10}^{12}{\mathrm{cm}}^{-2}$, showing a weak temperature dependence in agreement with calculations (dashed lines).

Figure 4

(a) $I_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ measured at $n_T=-n_B=7.4\times {10}^{11}{\mathrm{cm}}^{-2}$, and at different $B_{||}$ values, from 0 to 14 T in steps of 2 T. (b)–(e) $g_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ and $|n_T|-|n_B|$ near $n_T=-n_B$, at different $B_{||}$ values. The $g_{\mathrm{int}}$ enhancement is significantly suppressed in the presence of an in-plane magnetic field.

Figure 5

(a)–(c) $g_{\mathrm{int}}$ vs $V_{\mathrm{int}}$ and $|n_T|-|n_B|$ near $n_T=-n_B$, at different $n_B$. (d) Experimental (black triangles) and calculated (red dashed line) $g_{\mathrm{int}}$ vs $n_B$, at $n_T=-n_B$. The shaded regions indicate densities at which the experimental $I_{\mathrm{int}}$ onset is vertical to within experimental accuracy at $V_{\mathrm{int}}=0\mathrm{V}$. The black dashed lines are guides to the eye. The lower (upper) top $x$ axis shows the $d/r$ (${\mu }_B/\mathit{\Gamma }$) ratio.