Breakdown of the adiabatic Born-Oppenheimer approximation in graphene

The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics(1,2). ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur(3). The use of ABO to describe lattice motion in metals is, therefore, questionable(4,5). In spite of this, ABO has proved effective for the accurate determination of chemical reactions(6), molecular dynamics(7,8) and phonon frequencies(9-11) in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state(12,13), is a zero-bandgap semiconductor(14) that becomes a metal if the Fermi energy is tuned applying a gate voltage(13,15), V-g. This induces a stiffening of the Raman G peak that cannot be described within ABO.

自量子力学早期以来，绝热玻恩 - 奥本海默近似（ABO）一直是描述电子与原子核之间相互作用的标准假设（1,2）。ABO假定较轻的电子绝热地适应较重原子核的运动，在任何时刻都保持在其瞬时基态。当基态和激发态电子态之间的能隙大于核运动的能量尺度时，ABO是合理的。在金属中，能隙为零，会出现ABO之外的现象（例如由声子介导的超导性或由声子引起的电子性质的重整化）（3）。因此，使用ABO来描述金属中的晶格运动是有问题的（4,5）。尽管如此，ABO已被证明对于准确确定广泛的金属系统中的化学反应（6）、分子动力学（7,8）和声子频率（9 - 11）是有效的。在此，我们表明ABO在石墨烯中不适用。石墨烯是最近在自由态下被发现的（12,13），它是一种零带隙半导体（14），如果通过施加栅极电压\(V_g\)来调节费米能，它就会变成金属（13,15）。这会导致拉曼\(G\)峰的硬化，而这在ABO框架内是无法描述的。