Nonreciprocal transport in U(1) gauge theory of high- Tc cuprates

The nature of the charge carriers in high-${T}_{c}$ cuprates is an essential issue to reveal their novel physical properties and the mechanism of their superconductivity. However, the experimental probes and the theoretical analysis have been mostly restricted to the linear responses. On the other hand, recent observations of Rashba-type spin-orbit coupling on the surface of high-${T}_{c}$ cuprates imply the possible nonlinear and nonreciprocal transport phenomena under in-plane magnetic fields. In this paper, we study the nonreciprocal transport properties on the surface of cuprates by employing a $U(1)$ gauge theory framework, where the electrons are considered to be fractionalized. Our investigation highlights the intricate variations in nonreciprocal transport with respect to temperatures and dopings. First, it reveals contrasting behavior of nonreciprocity in each normal phase. Second, it discerns the tendencies between underdoped and overdoped superconducting states and their paraconductivity. The complex behaviors of nonreciprocal transport originate from the spinful and spinless nature of the charge carriers and their kinetic energy scales. These findings pave a new avenue to explore the electronic states in high-${T}_{c}$ cuprates in terms of nonreciprocal transport phenomena.