Nanoscale electrostatic control in ultra clean van der Waals heterostructures by local anodic oxidation of graphite gates

TL;DR

This work demonstrates resist-free, nanoscale electrostatic control in ultra-clean all-van der Waals heterostructures by patterning sub-100 nm graphite gates with AFM-LAO and integrating them into a graphene QPC. The device enables precise tuning of edge confinement in both integer and fractional quantum Hall regimes, revealing clean edge-state transmission and revealing Coulomb-blockaded quantum dots formed by Coulomb-induced edge reconstruction. Tomographic Thomas-Fermi modeling confirms that fractional islands (e.g., $ u= frac{1}{3}$) can spontaneously emerge at gate-defined saddles, linking confinement smoothness to edge reconstruction. The approach opens routes to single-anyon control and coherent edge-state interferometry in vdW platforms, with broad implications for topological quantum devices and nanoscale quantum electronics.

Abstract

In an all-van der Waals heterostructure, the active layer, gate dielectrics and gate electrodes are assembled from two-dimensional crystals that have a low density of atomic defects. This design allows two-dimensional electron systems with very low disorder to be created, particularly in heterostructures where the active layer also has intrinsically low disorder, such as crystalline graphene layers or metal dichalcogenide heterobilayers. A key missing ingredient has been nanoscale electrostatic control, with existing methods for fabricated local gates typically introducing unwanted contamination. Here we describe a resist-free local anodic oxidation process for patterning sub 100nm features in graphite gates, and their subsequent integration into an all-van der Waals heterostructure. We define a quantum point contact in the fractional quantum Hall regime as a benchmark device and observe signatures of chiral Luttinger liquid behaviour, indicating an absence of extrinsic scattering centres in the vicinity of the point contact. In the integer quantum Hall regime, we demonstrate in situ control of the edge confinement potential, a key requirement for the precision control of chiral edge states. This technique may enable the fabrication of devices capable of single anyon control and coherent edge-state interferometry in the fractional quantum Hall regime.

Figures (15)

• Figure 1: Fabrication of a quantum point contact (QPC) device.(a) An exfoliated graphite flake is etched using atomic force microscope-actuated local anodic oxidation (AFM-LAO). (b) Topography of a graphite flake with two trenches patterned by AFM-LAO. (c) Exploded view of a graphene QPC heterostructure. (d) Topography of the same graphite flake as panel b after adhesion to an hBN crystal on a PDMS/PC dry-transfer stamp. Residue from AFM-LAO, visible in panel b, is not transferred into the heterostructure. (e) Optical micrograph of a completed device. We denote the four top gates isolated by trenches as north (N), south (S), east (E), and west (W); densities in the regions below these gates are controlled by the voltages $V_{N,S,E,W}$ and the bottom gate voltage $V_B$. Contacts to the graphene layer are labeled C1-C8. (f)$\sigma_{xx}$ and $\sigma_{xy}$ measured on the W side of the device while $\nu_{N} = \nu_{S} = \nu_{E} = 0$ and $V_B = 1V$.
• Figure 2: Quantum point contact operation in the integer quantum Hall regime.(a) Diagonal conductance $G_D$ plotted as a function of $V_{NS}$ and $V_{EW}$ at B=6 T and T=300 mK for $V_B=0.56$, (b)$V_B=-0.33$, and (c)$V_B=-1.22$. In panels a-c, $V_{NS}$ and $V_{EW}$ denote the voltages applied to north and south or east and west gates, respectively. The ranges of $V_{NS}$ and $V_{EW}$ are chosen such that the filling factor $\nu_{EW} = \nu_{E} = \nu_{W} \in [-6, 0]$ and $\nu_{NS} = \nu_S = \nu_N \in [-2, 1]$ for each conductance map in a-c. The range over which $\nu_{NS}=0$ is marked in each plot by the white bar. (d) Diagonal conductance plotted against $V_{EW} - V_B$. The trace in the multidimensional parameter space intersects the $G_D$ maps of panels a-c at the position marked I, II, and III (e) Schematic depiction of the filling factors within the QPC at point I in panel a, (f) point II in panel b, and (g) point III in panel c. For points I-III, the filling factor in the N/S/E/W regions is constant but the fringe fields vary with $V_B$, fully modulating transmission of the two outermost edge modes through the QPC.
• Figure 3: Selective partitioning of fractional quantum Hall edge modes.(a)$G_D$ map at fixed $\nu_{EW} = -\frac{5}{3}$. Both $V_{EW}$ and $V_B$ are varied along the y-axis, keeping $\nu_{EW}$ constant but varying $(V_B-V_{EW})$. The x-axis range corresponds to the full width of the $\nu=0$ plateau. (b)$G_D$ along the dashed white contour in panel a. Two fractional plateaus are highlighted, at $4/3$ and $5/3$. (c) Bias dependence of the $G_D = \frac{4}{3}$ plateau, along the dashed blue line shown in panel a. The tunneling conductance is suppressed at zero bias well into the plateau, a distinct signature of chiral Luttinger liquid behavior
• Figure 4: Coulomb blockade at a gate-induced saddle point.(a)$G_D$ at $V_B = -0.25$ V and B=13 T spanning zero to full transmission of a single IQH edge mode. Inset: simulated potential across the N-W boundary at the points marked I and II. $E_V/E_C\approx 0.4, 1.8$ for I and II respectively. (b) Two-terminal differential conductance $\mathop{}\!\mathrm{d} I/ \mathop{}\!\mathrm{d} V_{SD}$ measured across the QPC. Data are plotted as a function of $V_{SD}$ along the white contour in panel a, parameterized by $\Delta V = V_{NS} - V_{EW}$. Diamond-shaped conductance peaks are indicative of Coulomb blockade, consistent with resonant transmission of edge modes through a localized state at the center of the QPC, as depicted in the inset. (c)$\mathop{}\!\mathrm{d} I/ \mathop{}\!\mathrm{d} V_{SD}$ along the black contour in panel a. Resonant reflection is observed, consistent with backscattering of edge state through the localized state, depicted in the inset. (d) Zero-bias traces of (b) and (c) illustrate that the resonant transmission and resonant reflection regimes evolve from fractional plateaus at 1/3 and 2/3 respectively as $\Delta V = V_{NS} - V_{EW}$ is increased.
• Figure 5: Quantum dot position and polarizability.(a)$\mathop{}\!\mathrm{d} I/\mathop{}\!\mathrm{d} V_{SD}$ at $V_{SD}=0$ across several Coulomb blockade peaks, plotted as a function of $V_N$ and $V_S$ with other voltages held constant. Near $V_N=V_S$, $\mathop{}\!\mathrm{d} V_S/\mathop{}\!\mathrm{d} V_N\approx-1$ indicating that the dot is equidistant from the N and S gates. The peak follows a contour of positive curvature, indicating the dot is repelled by positive $V_N$ or $V_S$. (b) The same, but plotted in the $(V_W,V_E)$ plane. Again, $\mathop{}\!\mathrm{d} V_E/\mathop{}\!\mathrm{d} V_W\approx-1$ indicates that the dot is equidistant from the E and W gates. The curvature is negative, opposite to that in the $(V_N,V_S)$ plane, consistent with a dot trapped at a saddle point.