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Angle-resolved photoemission spectroscopy

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.

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Fig. 1: ARPES basic principles and experimentation.
Fig. 2: Sample preparation and controls in ARPES measurements.
Fig. 3: Schematic drawing of the ARPES endstation.
Fig. 4: Basic principles and schematic drawing of ARPES variations.
Fig. 5: ARPES data analysis.
Fig. 6: ARPES examples on cuprates and iron-based superconductors.
Fig. 7: ARPES results on topological materials.
Fig. 8: 2D materials and heterostructures.

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Acknowledgements

H.Z. and S.Z. are supported by the National Key R&D Program of China (grant numbers 2021YFA1400100 and 2020YFA0308800), the National Natural Science Foundation of China (grant no. 11725418) and the Tohoku–Tsinghua Collaborative Research Fund. T.P. is supported by the Alexander von Humboldt Stiftung with the Alexander von Humboldt Fellowship. R.E. is supported by the Max Planck Society, the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program (grant numbers ERC-2015-CoG-682843 and H2020-FETOPEN-2018-2019-2020-01) and OPTOLogic (grant no. 899794). C.J. is supported by the Advanced Light Source, a US DOE Office of Science User Facility (contract no. DE-AC02-05CH11231). T.K. is supported by the JSPS KAKENHI (grant numbers JP21H04439 and JP19H00651), by MEXT Q-LEAP (grant no. JPMXS0118068681), and by MEXT under the “Program for Promoting Researches on the Supercomputer Fugaku” (Basic Science for Emergence and Functionality in Quantum Matter Innovative Strongly Correlated Electron Science by Integration of “Fugaku” and Frontier Experiments) (project ID hp200132). T.S. is supported by JST-CREST (grant no. JPMJCR18T1) and JSPS (KAKENHI grant no. 21H04435).

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Authors and Affiliations

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Contributions

Introduction (H.Z., C.J. and S.Z.); Experimentation (H.Z., T.P., C.J., T.K., T.S. and S.Z.); Results (H.Z., T.P., C.J., T.K., R.E., T.S. and S.Z.); Applications (H.Z., T.P., C.J., T.K., T.S. and S.Z.); Reproducibility and data deposition (H.Z., T.P., R.E. and S.Z.); Limitations and optimizations (H.Z., T.P., C.J., T.K., R.E., T.S. and S.Z.); Outlook (H.Z., T.P., C.J., R.E. and S.Z.); and Overview of the Primer (all authors).

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Correspondence to Shuyun Zhou.

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Nature Reviews Methods Primers thanks Guang Bian, Dong Qian and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Glossary

Photoelectric effect

Release of electrons from a material surface upon irradiation with light.

Photoelectrons

Electrons released from the material surface by the photoelectric effect.

Work function

Minimum energy required to remove an electron from a solid surface to a distance such that all interactions with the solid are negligible.

Topological insulators

Topological insulators are materials with a bulk bandgap, like ordinary insulators, but on their edge or surface they also have protected conducting states, known as topological states. Topological states are induced by the combination of time-reversal symmetry and spin–orbit coupling.

Inelastic collisions

A scattering process in which the energy of the individual particles is not conserved.

Inelastic mean free path

Mean distance that electrons can travel before suffering an inelastic collision process; it is material- and energy-dependent.

Hemispherical analyser

An electron kinetic energy analyser that produces circular orbits with hemispherical capacitors; the radii of the electron orbits depend on their kinetic energy, mapping it linearly to a position at the exit of the hemispheres.

Time-of-flight (TOF) analyser

An electron kinetic energy analyser. Kinetic energy is resolved by measuring the electron drift time through a long field-free section of the electron optics. Short-pulsed sources are required to time the electron’s start, along with fast electron detectors to time the electron’s arrival.

Quasiparticle

A quasiparticle is an emergent quantum excitation of a many-body system that can be treated as a non-interacting particle, given a suitable renormalization of its properties.

Plasmarons

Composite quasiparticles formed by charges and plasmons, which can modify the electronic dispersion.

Fermi–Dirac distribution function

Also called the Fermi function. For a certain temperature, it provides the probability of energy-level occupancy by fermions.

Pump–probe measurements

Stroboscopic method of observing non-equilibrium electronic distributions and their dynamics. A pulsed pump beam excites the electrons, followed by a delayed pulse that produces photoemission. This routine is repeated for multiple pump–probe delays, mapping the dynamical evolution.

Free-electron approximation

This assumes, in the context of photoemission, that the photoelectrons obey the parabolic dispersion relationship between energy and momentum of free electrons, ignoring long-range interactions between the emitted electron and the solid.

Energy distribution curve

A common lower-dimensionality (1D) subset of angle-resolved photoemission spectroscopy data used in data analysis, consisting of the photoemission intensity distribution versus energy at a fixed momentum value.

Momentum distribution curve

A common lower-dimensionality (1D) subset of angle-resolved photoemission spectroscopy data used in data analysis, consisting of the photoemission intensity distribution versus momentum at a fixed energy value.

Phonons

Quasiparticles describing collective excitations of atomic vibrations in a crystal.

Magnons

Quasiparticles describing a collective excitation of spin order, that is, a quantization of a spin-wave.

Plasmons

Quantization of collective oscillations of charge carriers in a solid, arising when electromagnetic fields act on a conducting surface.

Kramers–Kronig relation

A mathematical relation between the real and imaginary parts of a complex function, like the energy-dependent electron self-energy.

Brillouin zone

A primitive cell in reciprocal (k) space; the first Brillouin zone consists of a set of points in k-space, which is the set of points that can be reached from the origin without crossing any Bragg plane.

Wannier function

Element of a complete set of localized orthogonal functions, which are a convenient representation when describing highly localized wavefunctions or local properties of a wavefunction in a solid.

Bloch state

An electronic state of electrons in a periodic potential crystal, which is described as periodic wavefunction multiplied by a plane wave with a specific wavevector.

Berry curvature

A geometrical property of the electron wavefunctions in the parameter space, which is critical for the electronic properties of materials such as topological materials.

Cooper pairing

Pairing of two electrons at low temperature to form a bound state with the character of a boson, the condensation of which is the foundation for Bardeen–Cooper–Schrieffer superconductivity.

Bardeen–Cooper–Schrieffer (BCS) superconductors

Superconductors that can be well explained by Bardeen–Cooper–Schrieffer (BCS) theory developed in 1957, in which electron–phonon interaction plays a critical part in the superconductivity.

Excitons

Bound states of electrons and holes in an insulator or semiconductor. These many-body states, bound by electrostatic Coulomb attraction, can be treated as single quasiparticles.

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Zhang, H., Pincelli, T., Jozwiak, C. et al. Angle-resolved photoemission spectroscopy. Nat Rev Methods Primers 2, 54 (2022). https://doi.org/10.1038/s43586-022-00133-7

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