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Introduction

Crystalline solids are conventionally described in terms of periodic structures, yet the properties of real materials are frequently determined by deviations from this idealized picture. Single lattice imperfections, or point defects, influence electronic and ionic transport, optical behavior, structural stability, and chemical reactivity, and the study of point defects has developed into a substantial field spanning physics, chemistry, and materials science. As point defect research approaches a century of development, measured from Frenkel’s field-launching work [Z. Physik 35, 652 (1926)], it is timely to consider how the field has evolved and, in particular, the role played by the journals of the American Physical Society (APS).

The APS journals have provided important venues for many of the experimental, theoretical, and methodological advances that have shaped our present understanding of defects in solids. Across the portfolio, the journals have accommodated different formats and approaches, from concise conceptual and methodological advances in Physical Review Letters and landmark studies in Physical Review X, through detailed investigations in Physical Review B, Physical Review Materials, Physical Review Applied, PRX Energy, and Physical Review Research to field-spanning overviews in Reviews of Modern Physics.

The continuity of the APS literature across the decades has supported the cumulative development of insight into individual defects and defect complexes, in which contemporary studies frequently build upon measurements and interpretations reported several decades previously. Modern studies of defects can be considered directly alongside the work reported in the Physical Review during the latter half of the twentieth century. This has contributed to the development of defect physics as a coherent discipline in which new methods can be assessed against an extensive body of established experimental and theoretical results.

Now a century into its development, the study of point defects is entering a period of substantial change, driven both by methodological advances and by growing interest from interdisciplinary research communities. Machine-learned interatomic potentials are extending the spatial and temporal scales accessible to atomistic simulation, while developments in finite-temperature thermodynamics and configurational sampling are allowing defects to be considered beyond static, zero-temperature structures. The dynamical behavior of defects in structurally soft and disordered materials presents additional challenges, with particular attention devoted to promising materials for next-generation solar cells and other emerging technologies. At the same time, applications in quantum information increasingly require individual defects to be understood and controlled as functional elements, rather than treated solely as sources of undesirable behavior.

In this Collection, our editors share an overview of the development of the field of point defects, seen through the lens of APS publications. In a historical Foundational Works section, we chart the landmark developments that ignited further insight and progress, while a Modern Perspectives section seeks to predict where point defects will influence the next generation of research and technology.

This retrospective Collection brings together research previously published across the APS portfolio. These papers, selected by our editors for their contribution to the field, have all undergone our standard peer-review process.

We thank John Lyons (Indiana University), Michael Scarpulla (University of Utah), Izabela Szlufarska (University of Wisconsin–Madison), and Filip Tuomisto (University of Helsinki) for their assistance with the selection of the Foundational Works.

The curation of this Collection represents the work of many individuals. Part of the filtering and organization was assisted by Claude (Anthropic); final manuscript selections were made by our editors.

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Foundational works

Color centers and lattice imperfections

The earliest APS contributions to the defect physics of insulators and semiconductors addressed color centers in alkali halide crystals, providing a coherent theoretical framework for phenomena that had previously been considered across several distinct experimental and chemical traditions.

Color Centers in Alkali Halide Crystals
Frederick Seitz
Rev. Mod. Phys. 18, 384 (1946)

Color Centers in Additively Colored Alkali Halide Crystals Containing Alkaline Earth Ions
Frederick Seitz
Phys. Rev. 83, 134 (1951)

Early implications for semiconductor performance

Early studies of carrier recombination in semiconductors revealed that structural imperfections decreased the charge-carrier lifetime. Physical Review papers from Hall and from Shockley and Read quantified how point defects influence the recombination of injected charge carriers, an insight that proved foundational to the development of semiconductor devices.

Electron-Hole Recombination in Germanium
R. N. Hall
Phys. Rev. 87, 387 (1952)

Statistics of the Recombinations of Holes and Electrons
W. Shockley and W. T. Read, Jr.
Phys. Rev. 87, 835 (1952)

Experimental identification of defects

The post-war decades were characterized by atomic-scale identification of semiconductor defects through experimental techniques including electron paramagnetic resonance, electron-nuclear double resonance, and photocapacitance. These measurements established the microscopic structures, charge states, and symmetry distortions of specific defects, providing an experimental foundation against which later theoretical developments would be tested.

Defects in Irradiated Silicon: Electron Paramagnetic Resonance of the Divacancy
G. D. Watkins and J. W. Corbett
Phys. Rev. 138, A543 (1965)

Defects in Irradiated Silicon: Electron Paramagnetic Resonance and Electron-Nuclear Double Resonance of the Si-E Center
G. D. Watkins and J. W. Corbett
Phys. Rev. 134, A1359 (1964)

Nonradiative capture and recombination by multiphonon emission in GaAs and GaP
C. H. Henry and D. V. Lang
Phys. Rev. B 15, 989 (1977)

Trapping characteristics and a donor-complex (DX) model for the persistent-photoconductivity trapping center in Te-doped AlxGa1−xAs
D. V. Lang, R. A. Logan, and M. Jaros
Phys. Rev. B 19, 1015 (1979)

First-principles defect theory

Beginning in the late 1970s, Green’s-function and scattering-theoretic approaches demonstrated that the electronic structure of an isolated defect in a real crystal could be treated self-consistently. This period established the theoretical infrastructure on which subsequent density-functional-theory-based defect calculations would be built and produced a major comprehensive review in the field.

Scattering-theoretic method for defects in semiconductors. I. Tight-binding description of vacancies in Si, Ge, and GaAs
J. Bernholc and Sokrates T. Pantelides
Phys. Rev. B 18, 1780 (1978)

Self-Consistent Green’s-Function Calculation of the Ideal Si Vacancy
G. A. Baraff and M. Schlüter
Phys. Rev. Lett. 41, 892 (1978)

The electronic structure of impurities and other point defects in semiconductors
Sokrates T. Pantelides
Rev. Mod. Phys. 50, 797 (1978)

Density functional theory, corrections, and benchmark studies

The adoption of density functional theory within a periodic supercell framework during the late 1980s and 1990s transformed defect calculations into a widely used approach across solid-state physics and materials chemistry. The chemical-potential-dependent formation-energy formalism introduced during this period underpins much of the modern computational treatment of point defects. Subsequent decades saw studies published in APS journals challenge established interpretations of defect behavior in a range of semiconductors, identify the limitations of standard exchange-correlation functionals for defect calculations, and develop the correction schemes required for quantitative treatment of charged defects.

Theory of the Atomic and Electronic Structure of DX Centers in GaAs and AlxGa1−xAs Alloys
D. J. Chadi and K. J. Chang
Phys. Rev. Lett. 61, 873 (1988)

Chemical potential dependence of defect formation energies in GaAs: Application to Ga self-diffusion
S. B. Zhang and John E. Northrup
Phys. Rev. Lett. 67, 2339 (1991)

Microscopic Origin of the Phenomenological Equilibrium “Doping Limit Rule” in n-Type III-V Semiconductors
S. B. Zhang, S.-H. Wei, and Alex Zunger
Phys. Rev. Lett. 84, 1232 (2000)

Hydrogen as a Cause of Doping in Zinc Oxide
Chris G. Van de Walle
Phys. Rev. Lett. 85, 1012 (2000)

Intrinsic n-type versus p-type doping asymmetry and the defect physics of ZnO
S. B. Zhang, S.-H. Wei, and Alex Zunger
Phys. Rev. B 63, 075205 (2001)

Native point defects in ZnO
Anderson Janotti and Chris G. Van de Walle
Phys. Rev. B 76, 165202 (2007)

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs
Stephan Lany and Alex Zunger
Phys. Rev. B 78, 235104 (2008)

Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations
Christoph Freysoldt, Jörg Neugebauer, and Chris G. Van de Walle
Phys. Rev. Lett. 102, 016402 (2009)

Shallow versus Deep Nature of Mg Acceptors in Nitride Semiconductors
John L. Lyons, Anderson Janotti, and Chris G. Van de Walle
Phys. Rev. Lett. 108, 156403 (2012)

Finite-size supercell correction schemes for charged defect calculations
Hannu-Pekka Komsa, Tapio T. Rantala, and Alfredo Pasquarello
Phys. Rev. B 86, 045112 (2012)

Electrostatics-based finite-size corrections for first-principles point defect calculations
Yu Kumagai and Fumiyasu Oba
Phys. Rev. B 89, 195205 (2014)

Methodological consolidation

A 2014 Reviews of Modern Physics article consolidated much of the methodological development of the preceding two decades and remains a widely used reference for first-principles defect calculations, providing the fourth major review in the field following those of Seitz, Pantelides, and Fahey.

First-principles calculations for point defects in solids
Christoph Freysoldt, Blazej Grabowski, Tilmann Hickel, Jörg Neugebauer, Georg Kresse, Anderson Janotti, and Chris G. Van de Walle
Rev. Mod. Phys. 86, 253 (2014)

Beyond static thermodynamics

Developments over the past decade have extended defect calculations beyond static formation energies and electronic transition levels toward direct prediction of functional properties. The first-principles treatment of nonradiative carrier capture developed during this period provided a route toward calculating Shockley-Read-Hall recombination rates from electronic-structure theory, complementing the earlier phenomenological treatment of carrier capture developed during the spectroscopic era.

First-principles theory of nonradiative carrier capture via multiphonon emission
Audrius Alkauskas, Qimin Yan, and Chris G. Van de Walle
Phys. Rev. B 90, 075202 (2014)

Modern perspectives

Building on the landmark results described above, the study of point defects remains an important topic across a range of functional materials and applications. This research particularly impacts the control of semiconductor performance for tailored applications in quantum information, renewable energy systems, and electronic devices. Here, our editors highlight a selection of recent point defect research published across the portfolio between 2023 and 2026. The sections below are organized by application area rather than chronology, with brief introductions to each for readers coming to point defects from adjacent fields.

Quantum spin/optical defects

Wide-band-gap semiconductors can host point defects with optically addressable spin states. These spin defects interact with the environment to sense other spins and magnetic fields, enabling quantum sensing and quantum spin control. Visible and ultraviolet light can probe and manipulate these spin defects; this optical response has been used to create solid-state optical qubits for quantum computing. Ongoing research explores the creation and control of these spin defects, their interactions, and their viability for emerging quantum technologies.

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Diamond hosts

Diamond is an ultrastable host for vacancy-related spin defects, including the widely studied nitrogen-vacancy (NV⁻) center and group-IV split-vacancy centers. Spin defects in diamond can exhibit long coherence times, on the order of milliseconds at room temperature. Active research seeks to precisely control their generation and interactions and looks toward their integration into advanced technologies.

Optically Coherent Nitrogen-Vacancy Defect Centers in Diamond Nanostructures
Laura Orphal-Kobin, Kilian Unterguggenberger, Tommaso Pregnolato, Natalia Kemf, Mathias Matalla, Ralph-Stephan Unger, Ina Ostermay, Gregor Pieplow, and Tim Schröder
Phys. Rev. X 13, 011042 (2023)

Calculation of the energies of the multideterminant states of the nitrogen vacancy center in diamond with quantum Monte Carlo
K. A. Simula and I. Makkonen
Phys. Rev. B 108, 094108 (2023)

Efficient creation of shallow NV− ensembles by high-angle ion implantation
Kento Sasaki, Hideyuki Watanabe, Tokuyuki Teraji, Takashi Taniguchi, Kenji Watanabe, and Kensuke Kobayashi
Phys. Rev. Materials 10, 086202 (2026)

Germanium Vacancy in Diamond Quantum Memory Exceeding 20 ms
Katharina Senkalla, Genko Genov, Mathias H. Metsch, Petr Siyushev, and Fedor Jelezko
Phys. Rev. Lett. 132, 026901 (2024)

Defect in diamond with millisecond-scale spin relaxation time at room temperature
Sounak Mukherjee, Anran Li, Johannes Eberle, Sean Karg, Zi-Huai Zhang, Mayer M. Feldman, Yilin Chen, Mark E. Turiansky, Mengen Wang, Yogendra Limbu, Tharnier O. Puel, Yueguang Shi, Matthew L. Markham, Rajesh L. Patel, Patryk Gumann, Michael E. Flatté, Chris G. Van de Walle, Stephen A. Lyon, and Nathalie P. de Leon
Phys. Rev. B 114, 074105 (2026)

Optical probing of phononic properties of a tin-vacancy color center in diamond
Cem Güney Torun, Joseph H. D. Munns, Franziska Marie Herrmann, Viviana Villafane, Kai Müller, Ulrich Kentsch, Shavkat Akhmadaliev, Anthony C. Withers, Andreas Thies, Wentao Zhang, Aleksei Tsarapkin, Katja Höflich, Tommaso Pregnolato, Gregor Pieplow, and Tim Schröder
Phys. Rev. Research 8, 023230 (2026)

Carbide and nitride hosts

Beyond diamond, other wide-band-gap semiconductors in the carbide and nitride families can host spin defects. These materials offer advantages in designed semiconductor fabrication for defect control and photonic manipulation but may suffer from shorter coherence times. New research on carbide- and nitride-based defects explores a wider family of materials and introduces two-dimensional materials as spin-defect hosts.

Two-Emitter Multimode Cavity Quantum Electrodynamics in Thin-Film Silicon Carbide Photonics
Daniil M. Lukin, Melissa A. Guidry, Joshua Yang, Misagh Ghezellou, Sattwik Deb Mishra, Hiroshi Abe, Takeshi Ohshima, Jawad Ul-Hassan, and Jelena Vučković
Phys. Rev. X 13, 011005 (2023)

Theory of optical spin-polarization of axial divacancy and nitrogen-vacancy defects in 4H-SiC
Guodong Bian, Gergő Thiering, and Ádám Gali
Phys. Rev. Research 7, 013320 (2025)

Isotope Substitution and Polytype Control for Point Defects Identification: The Case of the Ultraviolet Color Center in Hexagonal Boron Nitride
J. Plo, A. Pershin, S. Li, T. Poirier, E. Janzen, H. Schutte, M. Tian, M. Wynn, S. Bernard, A. Rousseau, A. Ibanez, P. Valvin, W. Desrat, T. Michel, V. Jacques, B. Gil, A. Kaminska, N. Wan, J. H. Edgar, A. Gali, and G. Cassabois
Phys. Rev. X 15, 021045 (2025)

Optically Active Spin Defects in Few-Layer Thick Hexagonal Boron Nitride
A. Durand, T. Clua-Provost, F. Fabre, P. Kumar, J. Li, J. H. Edgar, P. Udvarhelyi, A. Gali, X. Marie, C. Robert, J. M. Gérard, B. Gil, G. Cassabois, and V. Jacques
Phys. Rev. Lett. 131, 116902 (2023)

Quantifying the creation of negatively charged boron vacancies in He-ion irradiated hexagonal boron nitride
Amedeo Carbone, Ilia D. Breev, Johannes Figueiredo, Silvan Kretschmer, Leonard Geilen, Amine Ben Mhenni, Johannes Arceri, Arkady V. Krasheninnikov, Martijn Wubs, Alexander W. Holleitner, Alexander Huck, Christoph Kastl, and Nicolas Stenger
Phys. Rev. Materials 9, 056203 (2025)

Scandium-based point defect in AlN for quantum information processing
Kamil Czelej, Mark E. Turiansky, Sai Mu, and Chris G. Van de Walle
Phys. Rev. B 110, 125116 (2024)

Other hosts

Emerging research explores spin and optical defects in a wide range of material families. These studies highlight new theoretical frameworks and experimental approaches that enable the creation and understanding of the next generation of quantum defects.

First-principles investigation of near-field energy transfer between localized quantum emitters in solids
Swarnabha Chattaraj, Supratik Guha, and Giulia Galli
Phys. Rev. Research 6, 033170 (2024)

Defect Complexes in CrSBr Revealed Through Electron Microscopy and Deep Learning
Mads Weile, Sergii Grytsiuk, Aubrey Penn, Daniel G. Chica, Xavier Roy, Kseniia Mosina, Zdenek Sofer, Jakob Schiøtz, Stig Helveg, Malte Rösner, Frances M. Ross, and Julian Klein
Phys. Rev. X 15, 021080 (2025)

Electron paramagnetic resonance spectroscopy of a scheelite crystal using microwave-photon counting
E. Billaud, L. Balembois, J. Travesedo, M. Le Dantec, M. Rančić, E. Albertinale, R. Truong, S. Bertaina, T. Chanelière, P. Goldner, D. Estève, D. Vion, E. Flurin, and P. Bertet
Phys. Rev. Research 7, 013011 (2025)

Defect-enabled sensing applications

The optical emission of the NV⁻ center in diamond varies with the local magnetic or electric field, and the defect’s sensitivity, long lifetime, and optical addressability have made it a practical quantum sensor. These capabilities have been applied to provide a frequency reference, to map the properties of superconducting materials, and to sense magnetic fields in a living animal for medical imaging.

Toward a temperature-insensitive composite diamond clock
Sean Lourette, Andrey Jarmola, Jabir Chathanathil, Victor M. Acosta, A. Glen Birdwell, Peter Blümler, Dmitry Budker, Sebastián C. Carrasco, Tony G. Ivanov, Shimon Kolkowitz, and Vladimir S. Malinovsky
Phys. Rev. Applied 25, 064046 (2026)

Imaging the Meissner effect and flux trapping of superconductors under high pressure using N-V centers
Cassandra Dailledouze, Antoine Hilberer, Martin Schmidt, Marie-Pierre Adam, Loïc Toraille, Kin On Ho, Anne Forget, Dorothée Colson, Paul Loubeyre, and Jean-François Roch
Phys. Rev. Applied 23, 064067 (2025)

Noninvasive magnetocardiography of a living rat based on a diamond quantum sensor
Ziyun Yu, Yijin Xie, Guodong Jin, Yunbin Zhu, Qi Zhang, Fazhan Shi, Fang-yan Wan, Hongmei Luo, Ai-hui Tang, and Xing Rong
Phys. Rev. Applied 21, 064028 (2024)

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Defects in energy materials

Charge generation and transport are central to the performance of semiconductor materials for renewable energy applications. Across energy generation, transformation, and storage technologies, point defects influence the flow of charge carriers. These highlighted studies use a combination of experimental and computational approaches to understand why some defects harm the performance of energy materials, why others have no apparent effect, and why still others enable the desired performance.

Dynamic Vacancy Levels in CsPbCl3 Obey Equilibrium Defect Thermodynamics
Irea Mosquera-Lois and Aron Walsh
PRX Energy 4, 043008 (2025)

Challenges in predicting positron annihilation lifetimes in lead halide perovskites: Correlation functionals and polymorphism
Kajal Madaan, Guido Roma, Jasurbek Gulomov, Pascal Pochet, Catherine Corbel, and Ilja Makkonen
Phys. Rev. B 113, 184118 (2026)

Modulation of point defect properties near surfaces in metal halide perovskites
Bilal Ahmad, Md Salman Rabbi Limon, and Zeeshan Ahmad
Phys. Rev. Materials 8, 125402 (2024)

Charge Transport and Defects in Sulfur-Deficient Chalcogenide Perovskite BaZrS3
Garima Aggarwal, Adeem Saeed Mirza, Stefania Riva, Corrado Comparotto, Robert J. W. Frost, Soham Mukherjee, Monica Morales-Masis, Håkan Rensmo, and Jonathan Staaf Scragg
PRX Energy 4, 033001 (2025)

Predicting Thermochemical Equilibria with Interacting Defects: Sr1−xCexMnO3−δ Alloys for Water Splitting
Anuj Goyal, Michael D. Sanders, Ryan P. O’Hayre, and Stephan Lany
PRX Energy 3, 013008 (2024)

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Defects in electronic materials

As device requirements move beyond the performance limits of silicon, alternative electronic materials have become increasingly important. III-V semiconductors like (In,Ga)As offer a tunable band gap and high mobility, while wide-band-gap semiconductors like Ga2O3 are suited for high-performance power electronics. Control of point defects in these materials underpins the design of these devices.

Shockley-Read-Hall recombination and trap levels in In0.53Ga0.47As point defects from first principles
Christian Dam Vedel, Tue Gunst, Søren Smidstrup, and Vihar P. Georgiev
Phys. Rev. B 108, 094113 (2023)

Investigation of Ga interstitial and vacancy diffusion in β−Ga2O3 via split defects: A direct approach via master diffusion equations
Channyung Lee, Michael A. Scarpulla, and Elif Ertekin
Phys. Rev. Materials 8, 054603 (2024)

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Widening participation

The growing interdisciplinary interest noted above brings researchers to point defects from adjacent fields, where the conventions of defect and defect level diagrams are not always familiar. A shared language and pedagogical framing such as those presented in this Tutorial will support that expansion.

Beginner’s Guide to Interpreting Defect and Defect Level Diagrams
Prashun Gorai
PRX Energy 4, 032001 (2025)

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