# Type-II nodal loops: theory and material realization

## TL;DR

This paper introduces a new type of nodal loop, called type-II, characterized by strongly tilted linear spectra, and demonstrates its realization in the compound K4P3, highlighting unique magnetic and optical properties.

## Contribution

The paper proposes the concept of type-II nodal loops, distinguishes them from conventional loops, and provides a material realization in K4P3 with analysis of their symmetry and topological protections.

## Key findings

- Type-II nodal loops exhibit strongly tilted spectra.
- K4P3 hosts a pair of type-II nodal loops near the Fermi level.
- Type-II loops are protected by symmetry and topological considerations.

## Abstract

Nodal loop appears when two bands, typically one electron-like and one hole-like, are crossing each other linearly along a one-dimensional manifold in the reciprocal space. Here we propose a new type of nodal loop which emerges from crossing between two bands which are both electron-like (or hole-like) along certain direction. Close to any point on such loop (dubbed as a type-II nodal loop), the linear spectrum is strongly tilted and tipped over along one transverse direction, leading to marked differences in magnetic, optical, and transport responses compared with the conventional (type-I) nodal loops. We show that the compound K4P3 is an example that hosts a pair of type-II nodal loops close to the Fermi level. Each loop traverses the whole Brillouin zone, hence can only be annihilated in pair when symmetry is preserved. The symmetry and topological protections of the loops as well as the associated surface states are discussed.