# Phase Separation in the Vicinity of Fermi Surface Hot Spots

## TL;DR

This paper investigates how phase separation near Fermi surface hot spots influences charge-density-wave textures and superconductivity in 1T-TiSe2, revealing a fundamental link between Fermi surface topology and electronic inhomogeneity.

## Contribution

It uncovers the intrinsic tendency for electronic phase separation near Fermi surface hot spots in 1T-TiSe2, highlighting the role of Fermi surface topology in CDW texturing.

## Key findings

- Phase separation occurs near Fermi surface hot spots.
- Fermi surface topology influences CDW inhomogeneity.
- Textured electronic phases are linked to band crossings near the Fermi level.

## Abstract

Spatially inhomogeneous electronic states are expected to be key ingredients for the emergence of superconducting phases in quantum materials hosting charge-density-waves (CDWs). Prototypical materials are transition-metal dichalcogenides (TMDCs) and among them, 1$T$-TiSe$_2$ exhibiting intertwined CDW and superconducting states under Cu intercalation, pressure or electrical gating. Although it has been recently proposed that the emergence of superconductivity relates to CDW fluctuations and the development of spatial inhomogeneities in the CDW order, the fundamental mechanism underlying such a phase separation (PS) is still missing. Using angle-resolved photoemission spectroscopy and variable-temperature scanning tunneling microscopy, we report on the phase diagram of the CDW in 1$T$-TiSe$_2$ as a function of Ti self-doping, an overlooked degree of freedom inducing CDW texturing. We find an intrinsic tendency towards electronic PS in the vicinity of Fermi surface (FS) "hot spots", i.e. locations with band crossings close to, but not at the Fermi level. We therefore demonstrate an intimate relationship between the FS topology and the emergence of spatially textured electronic phases which is expected to be generalizable to many doped CDW compounds.