Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene

Abstract

Trilayer graphene allows systematic control of its electronic structure through stacking sequence and twist geometry, providing a versatile platform for correlated states. Here we report magnetotransport in alternating twisted trilayer graphene with a twist angle of about 5$^{\circ}$. The data reveal an electron-hole asymmetry that can be captured by introducing layer-dependent potential shifts. At charge neutrality ($ν_{\mathrm{tot}}=0$), three low-resistance states appear, which Hartree-Fock mean-field analysis attributes to emerging spin-resolved helical edge modes similar to those of quantum spin Hall insulators. At $ν_{\mathrm{tot}}=-1$, we also observe suppressed resistance when the middle and bottom layers are each half filled while the top layer remains inert at $ν=-2$, consistent with an interlayer excitonic quantum Hall state. These results demonstrate correlated interlayer quantum Hall phases in alternating twisted trilayer graphene, including spin-resolved edge transport and excitonic order.

Figures (4)

• Figure 1: Landau level crossings and quantum Hall states in large-angle twisted trilayer graphene.(a) Schematic of the TTG with a $5^\circ$ twist heterostructure and the layer-resolved potential profile across the graphene layers at zero displacement field. (b) Color rendition of the longitudinal resistance $R_{xx}$ in the ($\nu_{\rm tot}$, $D/\varepsilon_{0}$) plane at $T = 1.5$ K and $B = 4$ T. (c) Calculated density of states in the $E$–$D/\varepsilon_{0}$ plane at $B = 4$ T. At $D = 0$, numbers in black boxes mark Landau level indices of the top and bottom layers, while numbers in blue boxes mark those of the middle layer. Black circles indicate Landau level crossings. (d) Schematic representation of (b). The green, blue, and red curves denote Landau levels of the top, middle, and bottom layers, respectively. Thicker curves indicate the lowest Landau levels, while thinner curves correspond to higher-index levels. Numbers in black boxes show the Landau level index $N$, and black circles indicate crossing points. The dashed line highlights the condition where Landau levels of the top and bottom layers have the same index.
• Figure 2: Evolution of interlayer helical edge states with displacement field.(a) Longitudinal resistance $R_{xx}$ as a function of $\nu_{\rm tot}$ and $D/\varepsilon_{0}$ at $B = 9$ T. Three regions of reduced resistance appear along $\nu_{\rm tot}=0$ (arrows). (b) Schematic representation of (a), showing the layer-resolved lowest Landau levels with the same color code in Fig. \ref{['Fig1']}d, and the vertical splittings reflect broken spin and valley degeneracies. Numbers in the colored boxes mark the layer filling factors. The gray-shaded areas are the low-resistance regions at $\nu_{\rm tot}=0$. (c) Hartree–Fock calculations of layer fillings at $\nu_{\rm tot}=0$ as a function of displacement field. Four stable configurations, labeled i–iv, appear as the displacement field is varied. (d) Edge channel configurations corresponding to the four regions in (c). Black vertical arrows denote spin polarization and horizontal arrows indicate chirality.
• Figure 3: Magnetic field dependence of helical edge states.(a) Contour map of longitudinal resistance $R_{xx}$ as a function of carrier density and displacement field at $B=11$ T. (b) Line traces of $R_{xx}$ as a function of displacement field at $n_{\rm tot}=5\times10^{10}\,\mathrm{cm}^{-2}$, taken along the green dotted line in (a), for magnetic fields between 12 T and 6 T. (c) Contour map of Hall resistance $R_{xy}$ measured under the same conditions as in (a). (d) Line traces of $R_{xy}$ corresponding to the green dotted line in (c), at $n_{\rm tot}=5\times10^{10}\,\mathrm{cm}^{-2}$ for fields between 12 T and 6 T.
• Figure 4: Interlayer coherence quantum Hall states at $\nu_{\rm tot}=-1$.(a) Longitudinal resistance $R_{xx}$ plotted as a function of $\nu_{\rm tot}$ and $D/\varepsilon_{0}$. (b) Schematic map of (a). Blue and red shading denotes filling of the middle and bottom layers, respectively, while the top layer remains fixed at $\nu_{\rm top}=-2$. The black solid line at $\nu_{\rm tot}=-1$ corresponds to integer quantum Hall states with $(\nu_{\rm mid},\nu_{\rm bot})=(0,1)$ and $(1,0)$. Dark red (blue) lines in the interval $-2<\nu_{\rm tot}<-1$ indicate fractional quantum Hall states of the bottom (middle) layer. The black dot marks a low-resistance region. (c) Evolution of $R_{xx}$ with displacement field at $\nu_{\rm tot}=-1$ for several magnetic fields. The arrow highlights resistivity minima. Curves are offset vertically and horizontally for clarity. (d) Line traces of $R_{xy}$ at various fixed $D/\varepsilon_{0}$ values indicated by (i-v) in panel (a).