# Suppression of Hall number due to charge density wave order in high-$T_c$ cuprates

## TL;DR

This paper investigates how charge density wave order affects the Hall number in high-$T_c$ cuprates, revealing that CDW-induced Fermi surface reconstruction explains the observed Hall effect anomalies across the pseudogap phase.

## Contribution

It proposes that unidirectional and bidirectional charge density wave orders, coexisting or separately present, account for the Hall coefficient behavior in high-$T_c$ cuprates.

## Key findings

- Charge density wave order causes Fermi surface reconstruction.
- Hall coefficient sign change linked to CDW order.
- Suppression of Hall number explained by CDW-induced Fermi surface changes.

## Abstract

Understanding the pseudogap phase in hole-doped high temperature cuprate superconductors remains a central challenge in condensed matter physics. From a host of recent experiments there is now compelling evidence of translational symmetry breaking charge density wave (CDW) order in a wide range of doping inside this phase. Two distinct types of incommensurate charge order -- bidirectional at zero or low magnetic fields and unidirectional at high magnetic fields close to the upper critical field $H_{c2}$ -- have been reported so far in approximately the same doping range between $p\simeq 0.08$ and $p\simeq 0.16$. In concurrent developments, recent high field Hall experiments have also revealed two indirect but striking signatures of Fermi surface reconstruction in the pseudogap phase, namely, a sign change of the Hall coefficient to negative values at low temperatures at intermediate range of hole doping and a rapid suppression of the positive Hall number without change in sign near optimal doping $p \sim 0.19$. We show that the assumption of a unidirectional incommensurate CDW (with or without a coexisting weak bidirectional order) at high magnetic fields near optimal doping and a coexistence of both types of orders of approximately equal magnitude at high magnetic fields at intermediate range of doping may help explain the striking behavior of low temperature Hall effect in the entire pseudogap phase.