Lifshitz transition enabling superconducting dome around the quantum critical point in TiSe$_2$

TL;DR

This study demonstrates that in TiSe₂, a superconducting dome forms around the charge-density-wave quantum critical point, driven by a Lifshitz transition that enables interband unconventional superconductivity.

Contribution

It reveals the role of Lifshitz transitions in enabling superconductivity around a charge order quantum critical point in TiSe₂, linking electronic structure changes to superconducting behavior.

Findings

Superconductivity forms a dome around the CDW QCP in TiSe₂.

A Lifshitz transition in the electronic band structure triggers superconductivity.

Unconventional s₊₋ superconductivity is likely due to interband interactions.

Abstract

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature. So far, this has been mostly studied in magnetically ordered materials. By contrast, the interplay between charge order and superconductivity at a QCP is not fully understood. Here, we present resistance measurements proving that a dome of superconductivity surrounds the charge-density-wave (CDW) QCP in pristine samples of 1$T$-TiSe$_2$ tuned with hydrostatic pressure. Furthermore, we use quantum oscillation measurements to show that the superconductivity sets in at a Lifshitz transition in the electronic band structure. We use density functional theory to identify the Fermi pockets enabling superconductivity: large electron and hole pockets connected by the CDW wave vector $\vec{Q}$ which emerge upon partial suppression of the zero-pressure CDW gap. Hence, we conclude that superconductivity is of interband type enabled by the presence of hole and electron bands connected by the CDW $\vec{Q}$ vector. Earlier calculations show that interband interactions are repulsive, which suggests that unconventional s$_{\pm}$ superconductivity is realised in TiSe$_2$ - similar to the iron pnictides. These results highlight the importance of Lifshitz transitions in realising unconventional superconductivity and help understand its interaction with CDW order in numerous materials.