# Hidden Weyl Fermions in Paramagnetic Electride Y$_2$C

## TL;DR

This paper predicts the existence of Weyl fermions in the layered electride Y$_2$C through first-principles calculations, revealing topologically nontrivial surface states and magnetic properties relevant for condensed matter physics.

## Contribution

It introduces the discovery of Weyl fermions in a paramagnetic electride material Y$_2$C, highlighting their topological features and magnetic characteristics.

## Key findings

- Weyl fermions are predicted in Y$_2$C from first-principles calculations.
- Y$_2$C exhibits a topologically nontrivial drumhead surface state.
- The material has a very small magnetic anisotropy energy, consistent with experimental observations.

## Abstract

Recent experimental observations of Weyl fermions in materials opens a new frontier of condensed matter physics. Based on first-principles calculations, we here discover Weyl fermions in a two-dimensional layered electride material Y$_2$C. We find that the Y 4$d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between [Y$_2$C]$^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{\rm F}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the rotation-symmetry protected Weyl nodal lines near $E_{\rm F}$, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling (SOC). However, we reveal that, due to its small SOC effects, Y$_2$C has a topologically nontrivial drumhead-like surface state near $E_{\rm F}$ as well as a very small magnetic anisotropy energy with several ${\mu}$eV per unit cell, consistent with the observed surface state and paramagnetism at low temperatures below ${\sim}$2 K. Our findings propose that the Brillouin zone coordinates of Weyl fermions hidden in paramagnetic electride materials would fluctuate in momentum space with random orientations of the magnetization direction.