The Quantum Hall (QH) effect allows the exploitation of the quantum coherence of electrons for various applications, from metrology to quantum computing. QH interferometry is a convenient tool that provides an archetypal platform for achieving fractional QH state braid statistics. However, phase coherence along the length of the interferometer and the suppression of the Coulomb charge energy are required to observe fractional statistics.
Study: Hall quantum interferometry in triangular domains of marginally twisted bilayer graphene. Image credit: Neon_dust / Shutterstock.com
In a recent article in the journal Nano Letters, a marginally twisted bilayer graphene-based QH interferometer was manufactured with a rotation angle (θ) of 0.16 degrees. The operations of the device in the QH regime gave rise to the unique characteristics of the magnetothermopower, including the oscillations of Aharonov-Bohm (AhB) and Fabry-Pérot (FP) in the phase of density-magnetic field, where the filling factors of the Landau level (ν) were 4, 8.
QH interference effects were limited to the triangular AB / BA domains in marginally twisted bilayer graphene and showed lower Coulomb loading effects. The overall results demonstrated the coherent phase interference of the QH mode without the need for an additional complex architecture, defined by a logic gate in twisted bilayer graphene material.
QH interferometry in triangular domains and twisted bilayer graphene
The hierarchy of quasiparticle excitations can be investigated by interfering between fractional and integer QH modes. This method can help to observe the non-abelian braid statistics of the quasiparticle in the fractional QH regime. However, it is difficult to achieve this phenomenon experimentally due to the inevitable Coulomb repulsion of quasiparticles, which are spatially limited, changing the effective area of the interferometer accordingly.
The additional load effect of the interferometer prevents the robustness of the braiding statistics. However, increasing the dimensions of the device can prevent the impact of an additional load on the interferometer at the expense of the phase coherence that allies the interfering paths. As a result, several device architectures were designed and materials were designed to suppress Coulomb repulsion without affecting the phase coherence of the quasiparticle.
The physical properties of twisted bilayer graphene depend on the angle of rotation between the two layers of these two-dimensional (2D) materials. Twisted bilayer graphene has a rotation angle close to 1.1 degrees. This 2D twisted two-layer graphene material shows phase transitions from a conductive system to a correlated insulating phase, a ferromagnetic phase, and a superconductivity phase.
The present study discussed a new QH interferometer operation based on marginally twisted bilayer graphene. The band structure of the two-layer graphene moire lattice twisted around the magic angle (θm) of 1.1 degrees can facilitate a wide range of new phases such as superconductivity, magnetism, and correlated insulators.
However, at the twisted angle of the twisted bilayer graphene below θm, the atomic registers of the moire lattice are altered due to the relaxation effects, resulting in the mosaic structure of triangular regions with alternating stacking AB and BA , separated by domain walls. However, the separation of the AB or BA regions from the twisted bilayer graphene due to the vertical displacement field results in a one-dimensional (1D) network that conducts channels housed by the domain walls.
Triangular domains of marginally twisted bilayer graphene
Here, thermoelectric and electrical measurements were performed on slightly twisted bilayer graphene with θ of 1.6 degrees in full QH regime and in insignificant displacement fields. Here, the thermoelectric coefficient provided the fundamental characterization of the electronic state due to the sensitivity of the charge carrier to the dispersion dynamics.
In addition, quasiparticle excitations led to entropy in the QH regime. In this regime, magnetothermopower provided a view of the spectrum of quasiparticles. In addition, under appropriate conditions, thermoelectric measurements helped to explore the statistical properties of the non-abelian quasiparticle due to the higher entropy of any person than that of Abelian. In the QH regime, several characteristics of the interference effect were investigated by correlating the thermal voltage and the magnetic field (B) together with the gate-induced density (n).
Conclusion
In summary, magnetothermoenergetic transport of marginally twisted bilayer graphene was measured by θ of approximately 0.16 degrees. Periodic oscillations of the B in thermovoltage were in concurrence with the electronic interference FP and AhB between the trajectories of the charge carriers closing a magnetic flux limited to a temperature below 3 kelvin in twisted bilayer graphene.
Thermotension measurements showed periodic oscillations, which were absent in conventional resistance measurements. The resonance pattern emerged in the QH regime at ν of 4 and 8. The loop obtained from the periodicity of the AhB oscillations was like the size of the moiré lattice.
Overall results indicated that the load carriers at the local Landau level are within the triangular domains AB / BA. In addition, QH modes interfered across AA stacked regions. The native QH interference effect on marginally twisted bilayer graphene could serve as a new platform to achieve any statistics in the QH regime.
Reference
Mahapatra, PS, Garg, M., Ghawri, B., Jayaraman, A., Watanabe, K., Taniguchi, T., Ghosh, A et al. (2022). Hall quantum interferometry in triangular domains of marginally twisted bilayer graphene. Nano letters. https://pubs.acs.org/doi/10.1021/acs.nanolett.2c00627
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