July 2019
Abstracts of the QSIT Lunch Seminar, Thursday, July 4, 2019
Wigner-Crystal formation at filling factor 1/5 in a bilayer two-dimensional electron (2DEG) gas?
Jan Scharnetzky - Advanced Semiconductor Quantum Materials (Wegscheider group), ETH Zurich
Wigner [1] proposed that at low densities and low temperatures the electrons of any charge system crystallize to form a solid because the kinetic energy of the electrons becomes small compared to the Coulomb energy. While clear evidence for a crystalline structure is difficult to obtain experimentally, the transition into an electron solid has been seen in 2-dimensional electron and hole gases where strong perpendicular magnetic fields suppress the kinetic energy. It is well known that under this condition the Laughlin liquid state competes with the Wigner crystal and is energetically more favorable down to a filling fraction of 1/5 of the lowest Landau level and leads to the fractional quantum Hall effect (FQHE). The experimental observation of the FQHE has been verified by theoretical calculations predicting the Wigner Crystal (WC) as ground state only for filling factors below 1/5 [2].
We have studied the transition of high mobility 2-dimensional electron gases (2DEG) into an electron solid in devices where we could add a second charge layer close to the first one. With the help of both top and back gates we could vary the density in both layers. This allows adjusting nearly any ratio of filling factors in the two layers and measure the resulting magnetotransport. For most filling factor ratios, we find just the resistance expected for parallel layers of the respective fillings. However, if one of the layers is at 1/5 filling, then we observe always an insulating state of the combined layers. This insulating state persists even if densities and magnetic fields are changed as long as the 1/5 filling is conserved in at least one layer.
In this presentation I will review the experimental techniques including our novel ion implantation which made the simultaneous density tuning of the bilayer system possible. Additionally, I will explain the procedure to grow a high-mobility bilayer GaAs/AlGaAs heterostructure using our molecular beam epitaxy system. Then I will present the magnetotransport measurements at 50 mK over a wide density ratio in the two layers from which the combined insulated state is postulated. Finally, I will discuss the results in the light of the electron liquid to solid transition in bilayers.
[1] Wigner, E. (1934). Phys. Rev. 46, 1002.
[2] Lam, P.K and Girvin S.M. (1984). Phys. Rev. B 30, 473.
Practical tight-binding models for Twisted Bilayer Systems. Connection to ab-initio calculations.
Arkadiy Davydov – Condensed Matter Physics (Soluyanov group), University of Zurich
Twisted multilayer systems attract much attention after the discovery of the superconductivity in the Twisted Bilayer Graphene (TBG). Small angular twist gives rise to a peculiar electronic structure characterised by isolated flat bands, which results in occurrence of diverse physical phenomena, e.g., superconductivity, Mott transition, quantum Hall effect, etc. In particular, the measured phase diagram of TBG shows the competition between the Mott phase and superconducting phase, indicating the unconventional microscopic nature of superconductivity driven by strong correlations between electrons of flat-band states. Twisted multilayer materials form the so-called Moire lattices with many thousand atoms per unit cell, making ab-initio computational description rather impractical. In this talk we discuss possible paths of getting the electronic structure of the TBG, which could be applied to other Moire lattice systems, such as transition metal dichalcogenides or 2D Magnetic compounds. Our approach is based on the tight-binding model motivated by ab-initio calculations at smaller angles. Moreover, in the case of TBG, we make a projection onto a 12-band basis, resulting in a smaller Hamiltonian useful for an accurate calculation of topological invariants, and can serve as a starting point of many-body calculations.