Recent experimental findings have demonstrated the occurrence of superconductivity in Bernal bilayer graphene when induced by a magnetic field.In this study,we conduct a theoretical investigation of the potential pair...Recent experimental findings have demonstrated the occurrence of superconductivity in Bernal bilayer graphene when induced by a magnetic field.In this study,we conduct a theoretical investigation of the potential pairing symmetry within this superconducting system.By developing a theoretical model,we primarily calculate the free energy of the system with p+ip-wave parallel spin pairing,p+ip-wave anti-parallel spin pairing and d+i d-wave pairing symmetry.Our results confirm that the magnetic field is indeed essential for generating the superconductivity.We discover that the p+ip-wave parallel spin pairing leads to a lower free energy for the system.The numerical calculations of the energy band structure,zero-energy spectral function and density of states for each of the three pairing symmetries under consideration show a strong consistency with the free energy results.展开更多
We consider the AB-(Bernal) stacking for the bi-layer graphene (BLG) system and assume that a perpendicular electric field is created by the external gates deposited on the BLG surface. In the basis (A1, B2, A2, B1) f...We consider the AB-(Bernal) stacking for the bi-layer graphene (BLG) system and assume that a perpendicular electric field is created by the external gates deposited on the BLG surface. In the basis (A1, B2, A2, B1) for the valleyKand the basis (B2, A1, B1, A2) for the valley K′, we show the occurrence of trigonal warping [1], that is, splitting of the energy bands or the density of states on the kx - ky plane into four pockets comprising of the central part and three legs due to a (skew) interlayer hopping between A1 and B2. The hopping between A1 - B2 leads to a concurrent velocity v3 in addition to the Fermi velocity vF. Our noteworthy outcome is that the above-mentioned topological change, referred to as the Lifshitz transition [2, 3], is entirely bias-tunable. Furthermore, the many-body effects, which is known to yield logarithmic renormalizations [4] in the band dispersions of monolayer graphene, is found to have significant effect on the bias-tunability of this transition. We also consider a variant of the system where the A atoms of the two layers are over each other and the B atoms of the layers are displaced with respect to each other. The Fermi energy density of statesfor zero bias corresponds to the inverted sombrero-like structure. The structure is found to get deformed due to the increase in the bias.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.12074130)the Natural Science Foundation of Guangdong Province (Grant No.2021A1515012340)。
文摘Recent experimental findings have demonstrated the occurrence of superconductivity in Bernal bilayer graphene when induced by a magnetic field.In this study,we conduct a theoretical investigation of the potential pairing symmetry within this superconducting system.By developing a theoretical model,we primarily calculate the free energy of the system with p+ip-wave parallel spin pairing,p+ip-wave anti-parallel spin pairing and d+i d-wave pairing symmetry.Our results confirm that the magnetic field is indeed essential for generating the superconductivity.We discover that the p+ip-wave parallel spin pairing leads to a lower free energy for the system.The numerical calculations of the energy band structure,zero-energy spectral function and density of states for each of the three pairing symmetries under consideration show a strong consistency with the free energy results.
文摘We consider the AB-(Bernal) stacking for the bi-layer graphene (BLG) system and assume that a perpendicular electric field is created by the external gates deposited on the BLG surface. In the basis (A1, B2, A2, B1) for the valleyKand the basis (B2, A1, B1, A2) for the valley K′, we show the occurrence of trigonal warping [1], that is, splitting of the energy bands or the density of states on the kx - ky plane into four pockets comprising of the central part and three legs due to a (skew) interlayer hopping between A1 and B2. The hopping between A1 - B2 leads to a concurrent velocity v3 in addition to the Fermi velocity vF. Our noteworthy outcome is that the above-mentioned topological change, referred to as the Lifshitz transition [2, 3], is entirely bias-tunable. Furthermore, the many-body effects, which is known to yield logarithmic renormalizations [4] in the band dispersions of monolayer graphene, is found to have significant effect on the bias-tunability of this transition. We also consider a variant of the system where the A atoms of the two layers are over each other and the B atoms of the layers are displaced with respect to each other. The Fermi energy density of statesfor zero bias corresponds to the inverted sombrero-like structure. The structure is found to get deformed due to the increase in the bias.
