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Abstract

For solid-state materials, the electronic structure is critical in determining a crystal’s physical properties. By experimentally detecting the electronic structure, the fundamental physics can be revealed. Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for directly observing the electronic structure with energy- and momentum-resolved information. Over the past few decades, major improvements in the energy and momentum resolution, alongside the extension of ARPES observables to spin (SpinARPES), micrometre or nanometre lateral dimensions (MicroARPES/NanoARPES), and femtosecond timescales (TrARPES), have led to important scientific advances. These advantages have been achieved across a wide range of quantum materials, such as high-temperature superconductors, topological materials, two-dimensional materials and heterostructures. This Primer introduces the key aspects of ARPES principles, instrumentation, data analysis and representative scientific cases to demonstrate the power of the method. We also discuss the challenges and future developments.