Title: Suppression of Hall number due to charge density wave order in high-$T_c$ cuprates,
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.