Monte Carlo Studies of Twisted Bilayer Graphene: Strain and Thermal Fluctuations

Abstract

We study the phase diagram of twisted bilayer graphene at charge neutrality as a function of twist angle $\theta$, uniaxial heterostrain $\varepsilon$, and temperature $T$ using sign-problem-free quantum Monte Carlo simulations. At $T=0$ and zero strain, we find a continuous transition from a Dirac semimetal to a gapped Kramers inter-valley coherent (KIVC) phase as $\theta$ decreases toward the magic angle. With finite strain, the KIVC phase undergoes a further continuous transition at smaller $\theta$ into an anisotropic semimetal with gapless excitations near the center of the moir\'{e} Brillouin zone. In the KIVC regime, the entropy rises sharply with temperature and plateaus at $15\,\text{K} \lesssim T \lesssim 40\,\text{K}$ near the value expected from a Mott-like regime of localized electrons with nearly uncorrelated spin, valley, and orbital degrees of freedom, despite the topological obstruction preventing a localized tight-binding description of the active bands. The spectral function evolves continuously with $\theta$: at low $T$, a gap opens at the $K$ points and the minimal gap shifts to $\Gamma$ as $\theta$ decreases; at intermediate $T$, the spectral function smoothly interpolates between a Dirac semimetal spectrum with coherent $K$-point quasiparticles and a spectrum with gapless $\Gamma$-centered quasiparticles near the magic angle. The later can be a anisotropic or a Mott semimetal and we discuss how to distiguish them in experiment.