Special Issue Editorial: Quantum Anomalies in Condensed Matter

Abstract

A symmetry that exists in the classical regime but is broken in the quantum realm may create what field theorists refer to as a quantum anomaly. Three of these symmetries in classical field theory that are broken in the quantum regime offer significant potential for enabling new technologies in the condensed matter context: the scale (conformal) anomaly, axial (chiral) anomaly, and parity anomaly. For example, the chiral anomaly in Weyl semimetals manifests as unusual magneto-transport phenomena, such as negative longitudinal magnetoresistance. Similarly, the parity anomaly can induce a half-quantized Hall effect, and the scale anomaly is predicted to generate anomalous thermoelectric currents. Observing these effects in topological materials not only tests quantum field theory in a laboratory setting but also advances our understanding of symmetry breaking in novel quantum phases. This paradigm is gaining ground in both theory and experiments on new topological materials which are allowing the research community to begin to realize their signatures in condensed matter as depicted in the Venn diagram of Figure 1. Although we emphasize that experimental evidence in solids remains scarce, this interdisciplinary field is opening a new frontier in physics research with promise for a unique set of new potential device applications. Technologies enabled by quantum anomalies include ultra-sensitive micro-bolometric detectors, dark matter detectors, far infrared optical modulators, low-dissipation ballistic transporters, terahertz-based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions (i.e., topological quantum computing), and qubits topologically protected against decoherence among possibly others. This has been expressed in a simple language accessible to materials scientists and physicists alike in a perspective article (202400189, https://doi.org/10.1002/apxr.202400189), which describes how each anomaly's measurable non-conserved current offers a window into quantum symmetry breaking in condensed matter, particularly topological quantum materials.

This special issue brings together an additional five technical articles that illustrate these concepts in various condensed matter systems. First, the theoretical basis is described in two articles. Maxim Chernodub et al. (202300058, https://doi.org/10.1002/apxr.202300058) report on how the scale (conformal) anomaly can produce electric currents at the boundaries of materials exposed to static magnetic fields, using scalar quantum electrodynamics simulations. The authors reveal significant differences between quantum anomaly-driven currents and classical Meissner currents, suggesting measurable effects in Dirac semimetals, and providing insights into anomaly-induced phenomena with potential applications in quantum electronics and anomaly-based sensors. The paper by Claudio Coriano et al. (202400043, https://doi.org/10.1002/apxr.202400043) connects chiral anomaly-driven interactions within 4D spacetime conformal field theories (CFTs). The authors investigate how gravitational chiral anomalies, driven by thermal gradients, are described within a CFT framework, highlighting the role of anomaly poles and their associated nonlocal actions, further emphasizing the potential for detecting axion-like quasiparticles through sum rules derived from anomaly amplitudes and measurable Faraday effects, thereby bridging fundamental quantum field theory with experimental condensed matter physics.

Next, the role of lattice electronic structure calculations on defects in topological materials including Dirac semimetals and topological Kondo insulators (TKIs) is described in two articles. Elizabeth Peterson et al. (202300111, https://doi.org/10.1002/apxr.202300111) report in their journal front cover article how tellurium vacancies influence the electronic structure and anomalous transport properties of the Dirac materials HfTe₅ and ZrTe₅ using first-principles density functional theory (DFT). The authors show that Te vacancies significantly affect electronic behavior by shifting conduction bands below the Fermi energy, introducing electron- and hole-like carriers, and thus rationalizing conflicting experimental observations of negative longitudinal magnetoresistance (NLMR). The authors demonstrate that Te vacancies substantially impact the observed transport phenomena but importantly do not rule out the potential manifestation of genuine quantum anomalies such as the chiral anomaly in materials containing such defects. Jian-Xin Zhu et al. (202500003, https://doi.org/10.1002/apxr.202500003) describe the local electronic structure of TKIs and how a single impurity will affect surface states in different topological regimes. The authors reveal that strong TKIs, which host a single Dirac cone, suppress impurity-induced resonance states under unitary scattering demonstrating topological protection. In contrast, weak TKIs with two Dirac cones support robust impurity-bound states even in the unitary limit. Importantly, the authors propose a novel route to experimentally distinguish TKI phases via scanning tunneling microscopy, offering deeper insight into topological protection in strongly correlated systems.

The last article illustrates an initial foray into experimental signatures that may be enabled by anomalies expressing themselves in new topological materials. Jin Hu et al. (202300145, https://doi.org/10.1002/apxr.202300145) report their observation of the topological Hall effect (THE) in the centrosymmetric layered compound Mn_2-xZn_xSb, revealing a striking composition-dependent behavior. Using Hall effect and magneto-optic Kerr effect measurements, the authors demonstrate that high-Zn samples (x > 0.6) show THE that strengthens at low temperatures, while low-Zn samples exhibit an opposing trend, with THE increasing at higher temperatures. This dichotomy is attributed to differing spin textures and magnetic domain structures between the two regimes, suggesting chiral magnetic order despite the centrosymmetric lattice. The findings establish Mn₂₋_xZn_xSb as a platform where distinct magnetic mechanisms potentially tied to topological anomalies can be tuned via chemical substitution.

Any one of the potential technologies enabled by realizing quantum anomalies in condensed matter would be a breakthrough for next-generation applications such as precision quantum sensing and detection. At the same time, realizing this technological potential will require overcoming substantial hurdles, both theoretical and experimental. Researchers must disentangle true topological signals from trivial band contributions, stabilize delicate chiral spin textures that give rise to phenomena like the quantum anomalous Hall effect, and devise techniques to measure often minuscule anomalous currents reliably amid background noise. This balanced optimism underscores a forward-looking vision for the field, that with continued innovation in materials design and measurement, quantum anomalies may move forward from intriguing laboratory curiosities to the foundation of transformative devices in materials science.

The authors declare no conflict of interest.