Robust　neuromorphic　computing　in　the　Big　Data　era　calls　for　long-term　stable　crossbar-array　memory　cells;　however,　the　elemental　segregation　in　the　switch　unit　and　memory　unit　that　inevitably　occurs　upon　cycling　breaks　the　compositional　and　structural　stability,　making　the　whole　memory　cell　a　failure.　Searching　for　a　novel　material　without　segregation　that　can　be　used　for　both　switch　and　memory　units　is　the　major　concern　to　fabricate　robust　and　reliable　nonvolatile　cross-array　memory　cells.　Tellurium　(Te)　is　found　recently　to　be　the　only　peculiar　material　without　segregation　for　switching,　but　the　memory　function　has　not　been　demonstrated　yet.　Herein,　apparent　piezoelectricity　is　experimentally　confirmed　with　spontaneous　polarization　behaviors　in　elementary　2D　Te,　even　in　monolayer　tellurene　(0.4　nm),　due　to　the　highly　oriented　polarization　of　the　molecular　structure　and　the　non-centrosymmetric　lattice　structure.　A　large　memory　window　of　7000,　a　low　working　voltage　of　2　V,　and　high　on　switching　current　up　to　36.6　mu　A　mu　m(-1)　are　achieved　in　the　as-fabricated　Te-based　memory　device,　revealing　the　great　promise　of　Te　for　both　switching　and　memory　units　in　one　cell　without　segregation.　The　piezoelectric　Te　with　spontaneous　polarization　provides　a　platform　to　build　robust,　reliable,　and　high-density　logic-in-memory　chips　in　neuromorphic　computing.