# Quantum critical behaviour and Lifshitz transition in intermediate valence $\alpha$-YbAlB$_4$

## TL;DR

This paper reports the discovery of quantum critical behavior and a Lifshitz transition in the intermediate valence compound $ ext{YbAlB}_4$, driven by anisotropic hybridization, challenging previous notions about valence fluctuations and quantum criticality.

## Contribution

It demonstrates that $ ext{YbAlB}_4$ exhibits quantum criticality and a Lifshitz transition at low magnetic fields due to anisotropic hybridization, offering a new pathway to achieve quantum criticality.

## Key findings

- Quantum critical behavior observed in $ ext{YbAlB}_4$ at low magnetic fields.
- Lifshitz transition identified in $ ext{YbAlB}_4$ linked to hybridization anisotropy.
- Valence fluctuations can lead to quantum criticality despite intermediate valence state.

## Abstract

Intermetallic compounds containing $f$-electron elements have been prototypical materials for investigating strong electron correlations and quantum criticality (QC). Their heavy fermion ground state evoked by the magnetic $f$-electrons is susceptible to the onset of quantum phases, such as magnetism or superconductivity, due to the enhanced effective mass ($m^{*}$) and a corresponding decrease of the Fermi temperature. However, the presence of $f$-electron valence fluctuations to a non-magnetic state is regarded an anathema to QC, as it usually generates a paramagnetic Fermi-liquid state with quasiparticles of moderate $m^{*}$. Such systems are typically isotropic, with a characteristic energy scale $T_0$ of the order of hundreds of kelvins that require large magnetic fields or pressures to promote a valence or magnetic instability. Here we show that the intermediate valence compound $\alpha$-YbAlB$_4$ surprisingly exhibits both quantum critical behaviour and a Lifshitz transition under low magnetic field, which is attributed to the anisotropy of the hybridization between the conduction and localized $f$-electrons. These findings suggest a new route to bypass the large valence energy scale in developing the QC.