Tunable helical crystals

TL;DR

This paper explores a tunable topological helical crystal formed by tunnel-connected holes in a 2D topological insulator, demonstrating controllable band structure, Dirac points, and potential for topologically protected qubits for quantum computing.

Contribution

It introduces a novel tunable helical crystal with controllable Dirac points and multicritical behavior, and proposes topologically protected qubits for quantum computing applications.

Findings

Band structure controlled by gates and magnetic field.

Dirac points appear at specific flux values and become massive otherwise.

Defects can host topologically protected qubits unaffected by temperature.

Abstract

We consider a superlattice formed by tunnel-connected identical holes, periodically placed in a two-dimensional topological insulator. We study tunneling transport through helical edges of these holes and demonstrate that the band structure of such helical crystal can be controlled by both gate electrodes and external magnetic filed. For integer and half-integer values of dimensionless magnetic flux through the holes, the spectrum possesses Dirac points whose positions and velocities can be tuned by gates. The deviation of magnetic flux from these special values by $\delta \phi$ makes the Dirac cones massive, with the gap value $\Delta \propto |\delta \phi|$. At certain gate-dependent values of $\delta \phi$ different Dirac points converge to a double Dirac point and then disappear with further increase of $\delta \phi.$ Interaction between carriers may lead to strong renormalization of parameters $\alpha$ and $\beta$ controlling total tunnel coupling between holes and spin flip tunneling processes, respectively. We plot the renormalization flow in the plane $(\alpha,\beta)$ and demonstrate multicritical behavior of the crystal -- there is a multicritical fully unstable fixed point separating three different phases: independent rings, independent shoulders, and perfect spin-flip channels. We also find that defects in the crystal may lead to a formation of topologically protected qubits which are not destroyed by temperature and can be also manipulated both by gates and by magnetic field. The possibility of purely electrical high-temperature control of the qubits opens a wide avenue for applications in the area of quantum computing.