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For several decades now, ultra-high-mobility GaAs two-dimensional electronsystems (2DESs) have served as the hallmark platform for various branches ofresearch in condensed matter physics. Fundamental to this long-standing historyof success for GaAs 2DESs was continuous sample quality improvement, whichenabled scattering-free transport over macroscopic length scales as well as theemergence of a diverse range of exotic many-body phenomena. While the recentbreakthrough in the quality of GaAs 2DESs grown by molecular beam epitaxy ishighly commendable in this context, it is also important and timely toestablish an up-to-date understanding of what obstructs us from pushing themobility limit even further. Here, we present mobility data taken at atemperature of 0.3 K for a wide variety of state-of-the-art GaAs 2DESs,exhibiting a maximum, world-record mobility of $\mu\simeq57\times10^6$cm$^2$/Vs at a 2DES density of $n=1.55\times10^{11}$ /cm$^2$. We also providecomprehensive analyses of the collective scattering mechanisms that can explainthe results. Furthermore, based on our study, we discuss potential scenarioswhere GaAs 2DES mobility values exceeding $100\times10^6$ cm$^2$/Vs could beachieved.

Understanding limits to mobility in ultra-high-mobility GaAs two-dimensional electron systems: The quest for 100 million cm$^2$/Vs and beyond