The phase diagram of the underdoped cuprates at high magnetic field

TL;DR

This paper explores the phase diagram of underdoped cuprates under high magnetic fields, proposing a unified SU(2) symmetry framework to explain the transition from superconductivity to charge order and their coexistence.

Contribution

It introduces a composite SU(2) order parameter to describe the transition and coexistence of charge and superconducting orders in cuprates, extending beyond competing orders models.

Findings

Charge order transition is temperature-insensitive and occurs near zero-field Tc.

A unified SU(2) symmetry describes the interplay between charge and superconducting orders.

Coexistence of orders depends on weak symmetry breaking due to biquadratic terms.

Abstract

The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives way to a long-range charge order with increasing magnetic field; both the orders coexist in a small intermediate region. The charge order transition is strikingly insensitive to temperature, and quickly reaches a transition temperature close to the zero-field superconducting $T_c$. We argue that such a transition along with the presence of the coexisting phase cannot be described simply by a competing orders formalism. We demonstrate that for some range of parameters there is an enlarged symmetry of the strongly coupled charge and superconducting orders in the system depending on their relative masses and the coupling strength of the two orders. We establish that this sharp switch from the superconducting phase to the charge order phase can be understood in the framework of a composite SU(2) order parameter comprising the charge and superconducting orders. Finally, we illustrate that there is a possibility of the coexisting phase of the competing charge and superconducting orders only when the SU(2) symmetry between them is weakly broken due to biquadratic terms in the free energy. The relation of this sharp transition to the proximity to the pseudogap quantum critical doping is also discussed.