Gate-defined wires in twisted bilayer graphene: From electrical detection of intervalley coherence to internally engineered Majorana modes

Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as (i) a tool for revealing the nature of correlated insulators and (ii) a platform for Majorana-based topological qubits. We show that the band structure of a gate-defined wire immersed in an intervalley coherent correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the wire by a superconducting TBG region on one side and an intervalley coherent correlated insulator on the other further enables the formation of Majorana zero modes—possibly even at zero magnetic field depending on the precise symmetry-breaking order present. Our proposal not only introduces a highly gate-tunable topological qubit medium relying on internally generated proximity effects but can also shed light on the Cooper-pairing mechanism in TBG.

Figure 1

(a) Gate-defined twisted bilayer graphene (TBG) wire architecture, not to scale. (b)–(d) Schematic flat-band occupations when the wire borders (b) trivial insulators at $\nu =-4$ and correlated intervalley coherent (IVC) insulators at (c) $\nu =0$ and (d) $\nu =-2$

Figure 2

Band structure, conductance $G$, and density of states for a gate-defined twisted bilayer graphene (TBG) wire immersed in (a) and (b) trivial band insulators and (c)–(j) intervalley coherent (IVC) orders. Insets: Top view of wire and proximate phases. All plots include spin-orbit coupling (SOC) except dashed-line band structures. The upper and lower halves respectively correspond to zero and nonzero in-plane magnetic fields. Proximate IVC order facilitates bandgaps (shaded rectangles) that manifest as conductance dips and associated density of states features within chemical potential windows indicated by gray bars on the $\mu$ axes. The energy window (vertical axis) shown in each top panel is equal to the chemical potential interval (horizontal axis) plotted in the corresponding bottom panel.

Figure 3

Phase diagram for a wire bordered on one side by a superconducting TBG region and on the other by (a) $\nu =0$ singlet IVC order and (b) $\nu =\pm 2$ AFM IVC order. The color scale shows the wire's excitation gap. ‘Topo’ indicates topological superconductivity hosting unpaired Majorana zero modes. Grey bars on the $\mu$ axis of (a) correspond to odd-channel regimes highlighted in Fig. 2, which give way to Majorana modes even at $B=0$. The crosses on the $\mu$ axis of (b) label the energies at which the Kramers-enforced band crossings occur at $B=0$ in Fig. 2. Supplemental Material, Section E presents additional phase diagrams illustrating the dependence on ${\mathrm{\Delta }}_{1,2}$ [53].