AI 中文总结
研究承载狄拉克费米子的晶体膜中两个低能部分的耦合，通过发展低能场论，分析了长波长平坦相及有限波长不稳定时的情况，利用临界指数表征转变、确定畸变并表明速度锁定，涉及多种普适类。
AI 中文摘要
以石墨烯为典型例子的承载狄拉克费米子的晶体膜，结合了两个具有截然不同动力学的低能部分：非相对论性弯曲声子和类相对论性狄拉克准粒子。我们在电荷中性时发展了这个耦合系统的低能场论，并确定这种动力学失配如何控制两个部分之间的耦合。在长波长平坦相中，旋转对称性将主导局部标量应变 - 密度耦合的重整化与尺度依赖的弯曲刚度联系起来，导致其无量纲强度对数下降。同时，弯曲模式在参数上比狄拉克费米子慢，所以由此产生的费米子反馈作为幂次消失。因此，这个平坦相对于这种微扰是稳定的。当弹性相互作用或电子软化在有限波长使膜不稳定时，物理情况会改变，选择由±Q 模式形成的涟漪图案。对于一对孤立的有序波矢，若可公度性诱导的相位钉扎无关紧要，转变由玻色子威尔逊 - 费舍尔不动点控制，而狄拉克费米子保持旁观者状态。当对称性允许质量型狄拉克双线性项共享涟漪的动量和量子数，包括水平反射宇称时，会出现真正的混合电子 - 结构临界点。然后，转变由手征 - XY 格罗斯 - 内夫 - 汤川普适类描述。利用已知的单圈临界指数，我们对这个转变进行了表征，确定了诱导的二次弹性畸变，并表明费米子和玻色子速度在各向同性连续极限中锁定。
英文摘要
Crystalline membranes hosting Dirac fermions, with graphene as the paradigmatic example, combine two low-energy sectors with sharply different dynamics: nonrelativistic flexural phonons and relativistic-like Dirac quasiparticles. We develop the low-energy field theory of this coupled system at charge neutrality and determine how this dynamical mismatch controls the coupling between the two sectors. In the long-wavelength flat phase, rotational symmetry ties the renormalization of the leading local scalar strain--density coupling to the scale-dependent bending rigidity, causing its dimensionless strength to decrease logarithmically. At the same time, flexural modes become parametrically slower than the Dirac fermions, so the resulting fermionic feedback vanishes as a power law.The flat phase is therefore stable against this perturbation. The physics changes when elastic interactions or electronic softening destabilize the membrane at a finite wavelength, selecting a ripple pattern formed by modes at $\pm\mathbf{Q}$. For an isolated pair of ordering wavevectors, provided that commensurability-induced phase pinning is irrelevant, the transition is governed by the bosonic Wilson--Fisher fixed point, while the Dirac fermions remain spectators. A genuinely hybrid electronic--structural critical point arises instead when symmetry permits a mass-type Dirac bilinear to share the ripple's momentum and quantum numbers, including horizontal-reflection parity. The transition is then described by the chiral-XY Gross--Neveu--Yukawa universality class. Using the known one-loop critical exponents, we characterize this transition, determine the induced secondary elastic distortion, and show that the fermionic and bosonic velocities lock in the isotropic continuum limit.
