# Effective interaction for vanadium oxyhydrides Sr$_{n+1}$V$_n$O$_{2n+1}$H$_n$ ($n=1$ and $n\to\infty$): A constrained-RPA study

## TL;DR

This study evaluates the effective Coulomb interactions in vanadium oxyhydrides using constrained-RPA, revealing strong screening effects in the $t_{2g}$ model and significant interactions in the $d$ model due to band separation, indicating potential for unique correlation phenomena.

## Contribution

First comprehensive cRPA analysis of vanadium oxyhydrides, highlighting how hydrogen influences screening and interaction strength in low-energy models.

## Key findings

- Effective interactions strongly screened in the $t_{2g}$ model.
- Large interaction strength in the $d$ model due to band separation.
- Hydrogen stabilizes O-$p$ states, affecting correlation effects.

## Abstract

Transition metal oxides have been one of the central objects in the studies of electron correlation effects because of their rich variety of physical properties mainly depending on the transition metal element. On the other hand, exploiting the anion degrees of freedom is less popular but can be another promising way to control properties of strongly correlated materials. In particular, oxyhydrides offer a unique playground of strongly correlated low-dimensional electronic structure, where the $s$ orbitals of hydrogen breaks a chemical bond between the cation $t_{2g}$ orbitals. In this study, we evaluate the effective interaction, i.e., the screened Coulomb interaction parameters in low-energy effective models, for vanadium oxyhydrides Sr$_{n+1}$V$_n$O$_{2n+1}$H$_n$ ($n=1,\infty$) using the constrained random-phase approximation (cRPA). We find that the effective interaction in the $t_{2g}$ model, where only the $t_{2g}$ orbitals are explicitly considered, is strongly screened by the $e_g$ bands compared with that for oxides, because the $e_g$ bands are much entangled with the $t_{2g}$ bands in the oxyhydrides. On the other hand, the effective interaction is rather strong in the $d$ model, where all the vanadium $d$ orbitals are explicitly considered, owing to a large energy separation between the V-$d$ bands and the anion bands (O-$p$ and H-$s$), because the O-$p$ states are stabilized by the existence of the hydrogen atoms. These findings suggest that non-trivial and unique correlation effects can take place in vanadium oxyhydrides.