Topological quantum properties of chiral crystals (1611.07925v3)

Abstract: Chiral crystals are materials whose lattice structure has a well-defined handedness due to the lack of inversion, mirror, or other roto-inversion symmetries. These crystals represent a broad, important class of quantum materials; their structural chirality has been found to allow for a wide range of phenomena in condensed matter physics, including skyrmions in chiral magnets, unconventional pairing in chiral superconductors, nonlocal transport and unique magnetoelectric effects in chiral metals, as well as enantioselective photoresponse. Nevertheless, while these phenomena have been intensely investigated, the topological electronic properties of chiral crystals have still remained largely uncharacterized. While recent theoretical advances have shown that the presence of crystalline symmetries can protect novel band crossings in 2D and 3D systems, we present a new class of Weyl fermions enforced by the absence of particular crystal symmetries. These "Kramers-Weyl" fermions are a universal topological electronic property of all nonmagnetic chiral crystals with spin-orbit coupling (SOC); they are guaranteed by lattice translation, structural chirality, and time-reversal symmetry, and unlike conventional Weyl fermions, appear at time-reversal-invariant momenta (TRIMs). We cement this finding by identifying representative chiral materials in the majority of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to low-energy physics. By combining our analysis with the results of previous works, we determine that all point-like nodal degeneracies in nonmagnetic chiral crystals with relevant SOC carry nontrivial Chern numbers. We further show that, beyond the previous phenomena allowed by structural chirality, Kramers-Weyl fermions enable unusual phenomena, such as a novel electron spin texture, chiral bulk Fermi surfaces over large energy windows.

• The paper reveals new topological quasiparticles (Kramers-Weyl fermions) that emerge in nonmagnetic chiral crystals with strong spin-orbit coupling.
• It employs a tight-binding model to demonstrate how crystal handedness and symmetry constraints produce linear dispersion and quantized chiral charges at time-reversal invariant momenta.
• Numerical band structure calculations on 65 chiral space groups identify candidate materials like Ag3BO3, underscoring promising experimental prospects in quantum material research.

Topological Quantum Properties of Chiral Crystals: An Analysis of Kramers-Weyl Fermions

The exploration of topological properties within chiral crystals, particularly in the context of electronic structures, has yielded significant insights into condensed matter physics. This paper rigorously investigates the emergence of Kramers-Weyl fermions—a novel class of topological quasiparticles—within nonmagnetic chiral crystals that incorporate spin-orbit coupling (SOC). The research primarily centers around the implications of handedness in crystal lattices and its absence of mirror, inversion, or roto-inversion symmetries, which facilitates the existence of these fermions.

The Significance of Chiral Crystals

Chiral crystals, devoid of chirality-inverting symmetries, embrace a unique structure that contributes to numerous phenomena, such as nonlocal transport and magnetoelectric effects. Their topology becomes even more pronounced when considering band crossings at time-reversal invariant momenta (TRIMs), which are pivotal in the manifestation of Kramers-Weyl fermions. These findings expand the catalog of known topological entities in materials and emphasize their distinct divergence from conventional Weyl semimetals.

Kramers-Weyl Fermions: Theoretical Framework and Numerical Results

The theoretical foundation laid out in this paper elaborates on a tight-binding model to exemplify Kramers-Weyl nodes at TRIMs, using an exemplary analysis within space group 16 ($P222$). This approach elucidates how combinations of lattice translation, SOC, structural chirality, and time-reversal symmetry enforce the existence of Kramers-Weyl fermions. These nodes are characterized by linear dispersion and quantized chiral charges, leading to significant topological consequences.

Numerically, the paper asserts that Kramers-Weyl fermions are intrinsic to the majority of the 65 known chiral space groups and inherently contribute to nontrivial Chern numbers. This deduction rests on systematic band structure calculations, proving that no point-like nodal degeneracies exist without accompanying quantized Chern numbers in these systems. Notably, the identification of multiple representative chiral materials underlines the broad applicability and relevance of these theoretical predictions.

Implications and Future Directions

Practically, the research identifies candidate materials, such as Ag$_3$BO$_3$ and AgBi(Cr$_2$O$_7$)$_2$, which exhibit these exotic fermions near their Fermi surfaces. Such compounds emerge as promising candidates for experimental exploration using tools like ARPES and neutron scattering to explore the behavior and effects of Kramers-Weyl fermions in real systems.

Theoretically, the implications span beyond conventional frameworks. The Kramers-Weyl fermions enable unusual phenomena including chiral bulk Fermi surfaces and potentially quantized photogalvanic responses, dependent on the chirality of incident light. These properties suggest applications in designing materials with tunable optical and transport characteristics.

Conclusion

This paper significantly contributes to the corpus of knowledge surrounding topological phases in chiral systems. The identification and characterization of Kramers-Weyl fermions not only enhance theoretical constructs but also pose intriguing possibilities for experimental material science and future quantum technology applications. The findings invite further research into exploiting these fermions' unique properties for novel electronic devices, shedding light on unexplored dimensions of solid-state physics.