  The nonlocalized clustering approach is generalized to 8-11Be isotopes with
isospin dependent spin-orbit potential. A new form of the
Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function is introduced to provide a
correct description for the {\sigma}-binding neutron in 11Be. Systematic
calculations for 8-11Be isotopes are performed and results fit well with
experimental values. The low energy spectrum of 11Be is also obtained,
especially the correct spin-parity 1/2+ is reproduced for the intruder ground
state. The exotic neutron halo structure of 11Be is studied by calculations of
root-mean-square radii and density distribution. We obtain a large spatial
distribution for the last valence neutron of 11Be, which fits the
phenomenological extracted value from experimental data. The spectroscopic
factor is also calculated and discussed for the 1/2+ ground state of 11Be.
