Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4

Abstract: In three dimensional (3D) momentum space of solid crystal, a topological phase boundary separating the Chern insulating layers from normal insulating layers may exist, where the gap must be closed, resulting in a "Chern semi-metal" state with topologically unavoidable band-crossings at fermi level. This state, if found to exist, is a condensed-matter realization of chiral fermions (or called Weyl fermions) in (3+1)D, and should exhibit remarkable features, like magnetic monopoles in the bulk and fermi arcs on the surface. Here we predict, based on first-principles calculations, that such novel quantum state can be realized in a known ferromagnetic compound HgCr2Se4, with a single pair of Weyl fermions separated in momentum space. The characteristic feature of this state in HgCr2Se4 is the presence of quantum Hall effect without external magnetic field in its quantum-well structure.

• The paper demonstrates through first-principles calculations that HgCr2Se4 hosts a Chern semimetal state with emergent Weyl nodes and fermi arcs.
• The analysis reveals that the inverted band structure driven by spin-orbit coupling and exchange splitting underlies the novel topological phase in HgCr2Se4.
• The study predicts that a quantum well structure of HgCr2Se4 can exhibit the quantized anomalous Hall effect with Hall conductance quantized at 2e²/h.

Chern Semimetal and Quantized Anomalous Hall Effect in HgCr$_2$Se$_4$

The study presents a theoretical investigation into the realization of a Chern semimetal state within the ferromagnetic compound HgCr$_2$Se$_4$. Using first-principles calculations, the authors predict that HgCr$_2$Se$_4$ features a novel topological phase characterized by Weyl fermions in a three-dimensional momentum space, offering potential applications in quantum computing and spintronics due to its unique electronic properties.

The research addresses the concept of a Chern semimetal, a state emerging at the phase boundary in a 3D momentum space where the gap closes between Chern insulating layers and normal insulating layers, leading to topologically unavoidable band crossings. This condition culminates in the presence of Weyl nodes that serve as sources and sinks of Berry curvature, behaving like magnetic monopoles in momentum space. Notably, the semimetallic state manifests without the need for an external magnetic field and exhibits surface states known as "fermi arcs" on the side surfaces, distinguishing it from conventional metals where fermi surfaces are fully closed or tied to the Brillouin zone boundaries.

HgCr$_2$Se$_4$ is identified as a promising candidate for such a state. It exhibits ferromagnetic behavior with a high Curie temperature (106-120 K) and shows unique transport characteristics, shifting from semiconducting to metallic behavior across different phases. The ferromagnetic ordering and the interplay between spin-orbit coupling and exchange splitting lead to an inverted band structure, a fundamental requirement for realizing the Chern semimetal state.

The authors explore the implications of this state further by investigating the quantized anomalous Hall effect (QAHE) within HgCr$_2$Se$_4$. The study indicates that a quantum well structure of the material can achieve QAHE, with quantized Hall conductance in units of $2e^2/h$, ascribed to the non-trivial Chern number arising from the inversion of subbands. This finding highlights the potential for achieving the quantum Hall effect without an external magnetic field, a highly pursued goal in condensed matter physics for its prospective technological impacts.

The calculations predict the existence of a single pair of Weyl nodes, a peculiarity that may be experimentally tested using techniques such as angle-resolved photoemission spectroscopy (ARPES) to observe their associated fermi arcs. These findings advance our understanding of topological phases in three dimensions and provide a platform for exploring novel quantum phenomena.

The theoretical insights into the properties of HgCr$_2$Se$_4$ enrich the broader field of topological materials, offering fertile ground for future studies that can experimentally validate these predictions. Potential developments include tailoring the electronic properties of related materials to harness the Chern semimetal state and exploring its implications for next-generation electronic devices. Further research could focus on the influence of electron correlation and other intrinsic factors that may refine or challenge the current predictions, offering a clearer understanding of this promising quantum state.