We explore a new mechanism of slowing down the rotation of neutron stars via accretion of millicharged dark matter. We find that this mechanism yields pulsar braking indices that can be substantially smaller than the standard n ∼ 3 of the magnetic dipole radiation model for millicharged dark matter particles that are not excluded by existing experimental constraints thus accommodating existing observations. Preprint: CP 3 -Origins-2014-002 DNRF90 & DIAS-2014 Pulsar spin down has been studied since its discovery but yet to date, there is not a definite clear understanding for the handful of existing data values for rotationpowered pulsars [1]. The braking index n as defined from a spin down lawΩ ∼ Ω n , where Ω is the rotational angular velocity, is consistently smaller than the n = 3 value predicted for energy loss via pure dipole radiation. In order to explain this discrepancy other mechanisms have been invoked including relativistic particle flow, and inclination angles or reconnection in the magnetosphere (see e.g. the discussion in [2] and [3]). Apart from short lived glitches or eventual transitions to a more exotic quark star [4], the rate of rotation of a neutron star (NS) drops steadily as a function of time. The deceleration of the rotation is due to torques that are applied on the star impeding its motion. There are basically two components for the torque: an "orthogonal" one, that maximizes when the magnetic moment of the NS is perpendicular to the rotation axis of the star, and an "aligned" component, maximized when the rotation and the magnetic axis of the star are aligned. In the "orthogonal" case, angular momentum is lost through emission of magnetic dipole radiation. In the "aligned" case, the torque is produced by the electric current created by escaping charged particles (mainly electrons and protons) that follow the open field lines of the NS magnetosphere. The rotational kinetic energy loss rate for both mechanisms present is [5]where θ is the angle between the magnetic and the rotational axis. If we take M and R as the mass and radius of the NS respectively, the two components can be written aswhere B 0 is the magnetic field strength on the polar caps of the star, and Ω F = Ω − Ω death (Ω death being the angular velocity below which the pulsar emission dies). The current I is approximately equal to I GJ [6], whereC ρ GJ c is the current quoted in the pioneering work of Goldreich and Julian [7], representing the emission of relativistic charged particles with charge density ρ GJ , due to a large difference in the electrostatic potential, from the NS cap regions of a surface ∼ πR 2 C . ρ GJ is the electron density which shields the electric field and yields the only stable static solution for a pulsar magnetosphere (excluding centrifugal and gravitational forces). At the poles of the NS, it was estimated to be [7] ρ GJ ≃ 7 × 10 −2 e B 0 10 12 Gwhere P is the period of the pulsar. The field lines that do not close within the so-called light cylinder of the NS (defined as a cylinder of radius R ...