Chiral-helical junctions in screened graphene

TL;DR

The work demonstrates that metal screening with Bi$_2$Se$_3$ enables a robust, gate-tunable graphene quantum Hall topological insulator (QHTI) with reproducible quantized helical edge transport at low magnetic fields. By introducing gate-defined chiral-helical junctions, the authors achieve mode-resolved control that selectively backscatters a single helical channel, providing direct evidence for helical edge states through spin-selective equilibration. They identify contact-induced doping as a universal source of quantization breakdown and show, via both experiments and Kwant-based simulations, that wide, well-equilibrated contacts restore quantization and that edge-channel equilibration is essential for robust QHTI behavior. A complementary model captures the observed plateaus and their dependence on filling factors, highlighting the interplay between screening, edge physics, and electrode design. The results establish metal-screened graphene as a gate-tunable, interaction-driven helical platform compatible with superconducting proximity for topological devices, while also outlining practical challenges related to contact engineering for scalable quantum technologies.

Abstract

Reproducibility and quantization in quantum spin Hall platforms is a persisting challenge, limiting their use in hybrid realizations of topological superconductivity. We report robust and reproducible quantized transport in a graphene quantum Hall topological insulator, stabilized at low magnetic fields by screening long-range Coulomb interactions with a metallic Bi$_2$Se$_3$ back gate. Beyond quantized resistance plateaus, we demonstrate mode-resolved control via gate-defined chiral-helical junctions that selectively transmit or backscatter a single helical channel, a capability inaccessible in time-reversal symmetric quantum spin Hall systems. Targeted experiments and simulations identify contact-induced doping, effectively creating unintended chiral-helical interfaces, as a generic mechanism for quantization breakdown, which is mitigated by large area contacts that enhance edge-channel equilibration. Our findings establish metal screened graphene as a gate-tunable, interaction-driven helical system with quantized transport, spatially separable helical channels, and compatibility with superconducting proximity for topological devices.

Figures (11)

• Figure 1: Metallic screening architecture for stabilizing the graphene quantum Hall topological insulator.a. Schematic of the device architecture. Monolayer graphene is encapsulated between thin bottom and thick top hBN layers, placed atop a metallic Bi$_2$Se$_3$ flake that serves as a proximal backgate to screen long-range Coulomb interactions. Planar Au/Cr contacts are fabricated by etching the top-hBN to avoid short-circuits through the thin hBN spacer. The device is equipped with a Pd top-gate. b. Schematic cross-section of the layered stack of graphene, hBN, and Bi$_2$Se$_3$. c. Transmission electron micrograph of a representative cross-section. Scale bar is 20 nm. d. Magnified electron energy loss spectroscopy (EELS) spatial map confirming the layer structure and planar contact to graphene. e. Optical image of a representative heterostructure, showing bubble-free interfaces. Scale bar is 2 $\upmu$m. f. False-color atomic force microscopy (AFM) images of the devices, with Au/Cr contacts in yellow and Pd top gates in grey. Scale bar is 2 $\upmu$m. e and f correspond to sample BK82 (see SI Table I).
• Figure 2: Helical edge transport in screened graphene.a. Two-terminal resistance of the Hall bar device in Fig. 1f (sample BK82) with top gate set to iso-density, plotted as a function of magnetic field and back-gate voltage at $T = 0.075$ K, showing quantized resistance plateau at charge neutrality associated with helical edge transport. b. Two-terminal resistance curves at the charge neutrality point (CNP) as a function of magnetic field at 0.075 K for the configurations in the inset. c. Two-terminal resistance at CNP measured at 4.2 K and 0.075 K, showing no temperature dependence of the QHTI plateau, and insulating behavior in the valley polarized phase.
• Figure 3: Selective backscattering and equilibration in chiral-helical junctions.a. Landau level dispersion for $N=0$ across a junction where the filling factor $\nu$ changes from 0 in the region with only the back gate to 2 in the region controlled by both back gate and top gate. At $\nu=0$, we assume a spin-split zeroth Landau level with spin-polarized helical edge states, while the gaps in the $\nu = 2$ region are negligible (the small lifting of the 4-fold degeneracy is just for visualization purpose). b. Schematic of a chiral-helical junction in a six-terminal Hall bar with top-gated region set to $\nu = 2$. Voltage probes $V_{1-4}$ and source-drain current leads $V_S$, $V_D$ are indicated. The backscattered hole-like helical mode equilibrates along the interface via spin-selective intermode scattering indicated by local tunneling bridges (dashed lines), thereby increasing conductance. c. Schematic of a chiral-helical junction with top-gated region set to $\nu = 6$. In addition to equilibration along the interfaces, spin-selective equilibration between the spin-down electron-like helical edge mode and the $N=1$ spin-down chiral modes is possible, inducing backscattering and increasing resistance. d. Colormap of the two-terminal resistance measured in the configuration shown in the inset at 1.8 T, as a function of the top-gated region filling factor $\nu_{\mathrm{TG}}$ and the back gate-only region filling factor $\nu_{\mathrm{BG}}$ for sample BK47 (see SI). The blue, orange, and green lines correspond to fixed back gate filling factors $\nu_{\mathrm{BG}}=0$, $\nu_{\mathrm{BG}}=+2$, and $\nu_{\mathrm{BG}}=-2$, respectively. e. Linecuts of the two-terminal resistance at fixed $\nu_{\mathrm{BG}}$ in panel d. Dashed lines indicate expected values for different filling factor combinations (see Methods).
• Figure 4: Asymmetric contact transmission due to induced dopinga. Deviation of the filling factor from $\nu = 0$ between the bulk and the contact vicinity, caused by n-type doping from the contact. b. Schematic illustrating the contact doping effect, which creates additional electron channel near the contact and prevents the hole-like helical edge mode from entering directly. Partial entry can occur via spin-selective inter-mode scattering (dashed lines), resulting in a transmission $t_{\rm h} < 1$. Electrons fully enter the contacts with transmission $t_{\rm e} = 1$. c. Two-terminal resistance at charge neutrality as a function of magnetic field, measured on the multi-terminal device BK41 shown in the inset (scale bar: 5 $\mu$m) with a bottom hBN spacer of 3.3 nm. The contact configurations are color-coded and illustrated in the inset schematics (black line connections between contacts indicate contacts shorted during fabrication). Dashed lines mark the expected resistance values for helical edge transport: $11/12 \times h/e^2$ for nearest-neighbor contacts (green and red curves) and $5/3 \times h/e^2$ for second-nearest neighbors (blue curve). d. Two-terminal resistance linecuts as a function of back-gate voltage for the configurations in panel c, measured at a fixed magnetic field of 2.4 T. e. Two-terminal helical edge resistance for nearest-neighbor (green) and second-nearest-neighbor (blue) contacts, calculated using the Landauer-Büttiker formalism (see Methods) as a function of hole transmission $t_{\rm h}$.
• Figure 5: Numerical simulations of edge equilibration along the contacts.a-c Six-terminal geometry with the scattering region of irregular shape and the electrical contacts represented by golden parallelograms. The scattering region is simulated with a tight-binding model of a graphene flake with Anderson disorder potential, chosen stronger at the contacts than in the bulk to simulate contact induced disorder (see Methods). a-c show the current density for a two terminal resistance experiment between the left- and right-most current leads (labeled 0 and 3, respectively) for three different voltage contact widths $w$. d. Disorder averaged two-terminal resistance $R$ between leads 0 and 3 as a function of the width of the voltage leads $w$, normalized by magnetic length $l_{B}$. The contact widths in a-c are indicated as vertical dashed lines in d. $R$ reaches the QSH value $3/2 \times h/e^2$ only when the contact width exceeds several tens of $l_B$.