An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature superconductors^1,2,3,4,5,6. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due to their gapping^{7,8,9,10,11,12,13,14,15,16,17,18}. Here, we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates^{19,20,21,22,23,24}, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket^{25,26,27,28,29,30,31,32}. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime^{7,8,9,10,11,12,13,14,15,16,17,18}.

了解伪间隙状态下缺少的反节点电子激发对于揭示低掺杂的铜酸盐高温超导体^1,2,3,4,5,6的物理性质至关重要。然而，迄今为止进行的大多数高温实验都无法辨别反节点状态是否由于其阻尼而变得不可观察，或者由于其间隙^{7,8,9,10,11,12,13}而消失。^{，14,15,16,17,18}。在这里，我们通过使用量子振荡来检查这两种情况之间的区别，以检查在掺杂不足的铜酸盐中，小的费米表面口袋是否仅占据了布里渊区的2％^{19,20,21,22,23,24}存在于横跨波腹的大多数完全空隙密度的状态中，或者是否热力学耦合到无空隙的非结状态的背景上，存在β1。我们发现，与小的费米表面腔相关的量子振荡显示出一个孤立的二^维费米表面^{腔25、26、27、28、29、30、31、32}的特征性锯齿波形特征。这一发现表明，反结点状态被遍布整个布里渊区的硬间隙所破坏，这在伪间隙制度^7,8,9中几乎对整个布里渊区的准粒子消失的剧烈潜在成因施加了强大的约束^{， 10,11,12,13,14,15,16,17,18}。