Vafek Oskar, Kang Jian
National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA.
Department of Physics, Florida State University, Tallahassee, Florida 32306, USA.
Phys Rev Lett. 2020 Dec 18;125(25):257602. doi: 10.1103/PhysRevLett.125.257602.
We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated nonperturbatively. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian is determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step. We also calculate exactly the exciton energy spectrum from the Coloumb interactions projected onto the renormalized narrow bands. The resulting softening of the collective modes marks the propinquity of the enlarged ("hidden") U(4)×U(4) symmetry in the magic angle twisted bilayer graphene.
我们开发了一种两阶段重整化群，它将扭曲双层石墨烯在短于莫尔超晶格周期的长度尺度下的连续哈密顿量与仅在远长于莫尔周期的距离处有效的有源窄带哈密顿量联系起来。在第一阶段，库仑相互作用以抑制相同子晶格与相反子晶格隧穿比的方式重整费米速度和层间隧穿，从而趋近所谓的手征极限。在第二阶段，层间隧穿被非微扰处理。通过逐步数值消除远程能带，确定了类单粒子色散与有源窄带哈密顿量内相互作用的相对强度，从而量化了残余关联，并在最后一步证明了强耦合方法的合理性。我们还精确计算了从投影到重整化窄带上的库仑相互作用得到的激子能谱。集体模式的软化表明了魔角扭曲双层石墨烯中扩大的（“隐藏”）U(4)×U(4)对称性的临近。
