Emergence in quantum materials: from relativistic quantum criticality to non-Fermi liquids and unconventional superconductivity

Understanding and controlling novel states of matter is at the heart of condensed matter research.

In modern quantum materials we find a rich resource of extraordinary states which emerge from the complex interplay of quantum effects and many-body physics.

They pose the fundamental challenge of describing an interacting system with many constituents in the quantum realm and hold the key for future quantum technology.A major common trait behind the complex phase diagrams of many correlated quantum materials evades a description with conventional many-body approaches: a strange metal phase that exhibits non Fermi liquid behaviour nearby quantum phase transitions and superconductivity.

QuantEmerge opens a new way to comprehend such non Fermi liquids and their intertwined phases by establishing a connection to relativistic quantum criticality and moiré materials.

Relativistic quantum criticality arises at quantum phase transitions with emergent Lorentz symmetry and can be viewed as a minimal model for non Fermi liquid behaviour, while moiré materials constitute a new materials platform with unprecedented experimental control over such transitions.

Their connection allows us to tune into the strongly correlated quantum regime from a controlled starting point in both experiment and theory.Exploiting different tuning parameters such as interaction, symmetry, temperature, and density, we develop a comprehensive picture of emergent phases in a quantum critical regime with cutting-edge renormalisation group methods.

We characterise novel types of quantum phase transitions in this setup and determine the corresponding quantum (critical) behaviour.

We calculate thermodynamic and transport properties and study the competition of non Fermi liquid and superconductivity.

Our theoretical insights will provide an improved understanding of the remarkable quantum-dominated phase structure that emerges in correlated quantum materials and pave the way for future materials design.