Quantum-Hall Spectroscopy of Elliptically Deformed Graphene Nanobubble Qubits

TL;DR

Graphene's gapless spectrum complicates electrostatic confinement, motivating strain-induced pseudo-magnetic fields to define quantum dots. The authors model elliptically deformed graphene nanobubbles and analyze SQD and DQD spectra using quantum-Hall channel spectroscopy, showing that $σ_y$-driven deformation mainly tunes SQD levels while $σ_x$-driven deformation modulates DQD coupling and energy splitting; a PMF-mediated complex inter-dot hopping yields a Berry-phase-like switching, captured by a reduced three-QD model with a PMF-flux phase of about $\pi/4$. They demonstrate that the qubit energy gap $\Delta$ scales with the aspect ratio $σ_x/σ_y$, increasing for $σ_x>σ_y$ and decreasing for $σ_x<σ_y$, while larger nanobubbles sharpen Fano resonances, indicating weaker coupling to the quantum-Hall channels. Overall, the work establishes strain engineering of elliptically deformed graphene nanobubbles as a practical knob to tune qubit transition energies and decoherence pathways, enabling programmable graphene-based quantum devices.

Abstract

With recent advances in strain-engineering technology of graphene and 2D materials, graphene quantum dots (QDs) defined by the strain-induced pseudo-magnetic fields (PMFs) have been of interest, with the feasibility of tunable graphene qubits. Here, we theoretically investigate how the electronic states of the nanobubble QDs are influenced by the geometrical anisotropy of the elliptical-shape nanobubbles. We examine the energy levels of the single QD (SQD) and double QD (DQD) spectra by varying the elliptical deformation in the $x$ and $y$ axes, respectively. We found that the SQD and DQD show distinguished behavior with respect to the direction of the elliptical deformation. While the SQD levels are substantially affected by the $y$-directional deformation, the DQD levels are largely shifted by the $x$-directional deformation.

Figures (6)

• Figure 1: (a) Spatial distribution of the pseudo-magnetic field (PMF) for representative elliptic nanobubbles for various $\sigma_{x}$ and $\sigma_{y}$ values. All plots are displayed with the same PMF strength range, $-360~\mathrm{T}<B_{z}<+360~\mathrm{T}$. (b) The maximum PMF strength versus $\sigma_{x}$ and $\sigma_{y}$, for $h_{0}=17a$.
• Figure 2: (a) Schematics of quantum-Hall spectroscopy used to probe the localized states of the nanobubble QD. The two sides of the p-n junction are tuned to filling factors $\nu=\pm1$ by the anti-symmetric potential step defined in Eq. (\ref{['eq:pnjnc']}). The distance between the quantum-Hall channel and the nanobubble center is denoted by $d$. (b) Color map of the quantum-Hall conductance $G_{H}$ as a function of Dirac fermion energy $E$ and deformation parameter $\sigma_{x}$ for fixed $\sigma_{y}=30a$. (c) Analogous map $G_{H}$ versus $E$ and $\sigma_{y}$ for fixed $\sigma_{x}=30a$. Fano resonances arising from SQD and DQD bound states are indicated by solid arrows. A spectra are calculated with $h_{0}=17a$.
• Figure 3: (a) Quantum-Hall conductance maps showing how the resonances evolve as the relative distance between the quantum-Hall channels and the nanobubble, $d$, and $\sigma_{x}$; the minor-axis width is fixed at $\sigma_{y}=30a$. (b) Analogous data obtained by varying $\sigma_{y}$ at fixed $\sigma_{x}=30a$. The primary and secondary SQD resonances are labeled SQD1 and SQD2; the corresponding DQD resonances are labeled DQD1, DQD2.
• Figure 4: (a) Fano-resonance switch for the DQD2 states in the $Q_{H}$ spectra corresponding to the highlighted area in Fig. \ref{['fig:QDlevels-spatial']}(a). Green and red dashed lines represent the Fano-resonance energies for the anti-symmetric and symmetric configurations of the DQD2, respectively. (b) and (c) probability current density maps corresponding to the Fano resonances for the circular and elliptical nanobubble DQD2. (d) Calculated results of the reduced transport model through the side-coupled DQD with complex inter-dot hoppings. Here, we set $h_{0}=17a$ and $\sigma_{y}=30a$.
• Figure 5: (a) Schematics of the gate-defined modulation of a graphene nanobubble qubit. The position of the quantum-Hall channel is shifted relative to the nanobubble by an electrostatic detuning parameter $\delta$. (b-e) $Q_{H}$ maps for the DQD1 branch, showing the characteristic avoided crossing that defines the qubit energy gap under four representative elliptic deformations: (b) $\sigma_{x}=27a$, $\sigma_{y}=30a$; (c) $\sigma_{x}=33a$, $\sigma_{y}=30a$; (d) $\sigma_{x}=30a$, $\sigma_{y}=27a$; (e) $\sigma_{x}=30a$, $\sigma_{y}=33a$. The energy splitting $\Delta$ at the anti-crossing corresponding to the qubit transition frequency when the two QDs are maximally superposed.