Fermion Doubling Theorems in Two-Dimensional Non-Hermitian Systems for Fermi Points and Exceptional Points

Area of Science:

• Condensed matter physics
• Topological materials science

Background:

• The fermion doubling theorem is crucial for Hermitian topological materials, mandating pairs of Weyl points in 3D semimetals.
• Understanding topological invariants in non-Hermitian systems is an active area of research.

Purpose of the Study:

• To extend the fermion doubling theorem to non-Hermitian lattice Hamiltonians.
• To investigate topological point nodes in 2D non-Hermitian systems without symmetry constraints.

Main Methods:

• Focus on two-dimensional non-Hermitian systems.
• Introduction of a generalized winding number invariant, the "discriminant number," for exceptional points.
• Analysis of Fermi points and exceptional points.

Main Results:

• Demonstration that Fermi points and exceptional points in 2D non-Hermitian systems obey doubling theorems, appearing in pairs.
• The "discriminant number" is shown to be applicable to arbitrary order exceptional points and nondefective degeneracy points.
• Observation that 3D system surfaces can violate non-Hermitian doubling theorems, suggesting novel bulk phenomena.

Conclusions:

• The fermion doubling theorem is successfully extended to non-Hermitian systems, unifying the understanding of topological point nodes.
• The "discriminant number" provides a powerful tool for characterizing degeneracies in non-Hermitian Hamiltonians.
• Violations of non-Hermitian doubling theorems on surfaces hint at exotic bulk properties in three-dimensional non-Hermitian topological materials.