A Study on the Utilization Plan for Functionally Lost Reservoirs: Focused on Daegu and Gyeongbuk

Abstract

We report on integer and fractional quantumHall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, we suppress single particle tunneling between both bilayers. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulomb interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in an orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling -3/2. Our observations suggest a unique edge reconstruction involving both electrons and chiral pwave composite fermions.Recent advances in twistronics [1] have enabled the exploration of an extremely diverse set of quantum phases. They include unconventional superconducting ground states, correlated insulating phases as well as integer and fractional Chern insulating states [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. These phases form due to strong correlations in a flat band environment that possesses non-trivial topological characteristics and offers a pool of nearly degenerate electronic states. Such flat bands can be engineered in the absence of a magnetic field by twisting two layers with the so-called magic angle [2,3]. However, there is also a more traditional alternative route to end up with topologically non-trivial flat bands in 2D systems in the presence of a perpendicular magnetic field that breaks time reversal symmetry. Landau quantization produces Landau levels with a macroscopic degeneracy equal to the number of flux quanta that pierce the sample. They are characterized by their orbital index N that acts as a Chern number and determines the shape of the wave function of the states the Landau level hosts. Correlations in this highly degenerate environment again produce a wide variety of ground states including for instance fractional quantum Hall states, Wigner crystal as well as bubble and stripe charge density wave phases [19].