Fractional Quantum Hall Effect in Weyl Semimetals.

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Field Theory

Background:

• Weyl semimetals are gapless topological phases protected by chiral anomaly and symmetries.
• Their nontrivial topology leads to unique surface states and anomalous Hall effects.
• Weak interactions preserve the band gap, but strong interactions pose a challenge.

Purpose of the Study:

• Investigate if a magnetic Weyl semimetal can open a band gap while retaining its topological properties.
• Explore the possibility of achieving a fractional quantum Hall effect in 3D without external magnetic fields.
• Examine the role of strong interactions in modifying the topological state.

Main Methods:

• Theoretical analysis of magnetic Weyl semimetals under strong interactions.
• Investigating the preservation of chiral anomaly and crystal symmetries.
• Characterizing the emergent topological order and its excitations.

Main Results:

• Demonstrated that a gap can indeed open in magnetic Weyl semimetals while preserving topology and symmetries.
• Identified a novel topologically ordered state realizing a 3D fractional quantum Hall effect without external magnetic fields.
• Discovered loop excitations with nontrivial braiding statistics linked to lattice dislocations.

Conclusions:

• Strong interactions can lead to a gapped topological phase in Weyl semimetals.
• This provides a new platform for realizing 3D topological states and quantum phenomena.
• The findings open avenues for exploring novel topological phases and their applications.