  In the history of condensed matter physics, reinvestigation of a well-studied
material with enhanced quality sometimes led to important scientific
discoveries. A well-known example is the discovery of fractional quantum Hall
effect in high quality GaAs/AlGaAs heterojunctions. Here we report the first
single crystal growth and magnetoresistance (MR) measurements of the silver
chalcogenide $\beta $-Ag$_2$Se (Naumannite), a compound has been known for the
unusual, linear-field-dependent MR in its polycrystalline form for over a
decade. With the quantum limit (QL) as low as 3 Tesla, a moderate field
produced by a superconductor magnet available in many laboratories can easily
drive the electrons in Ag$_2$Se to an unprecedented state. We observed
significant negative longitudinal MR beyond the QL, which was understood as a
`charge-pumping' effect between the novel fermions with opposite chiralities.
Characterization of the single-crystalline Ag$_2$Se and the fabrication of
electric devices working above the QL, will represent a new direction for the
study of these exotic electrons.
