  Understanding the superconducting proximity effect on the surface of a
topological insulator is of critical importance in realizing topological
superconductivity and Majorana fermions in solid state settings. We fabricate
delicate heterostructure samples between topological insulator (TI) Bi2Se3 thin
film and high temperature superconductor Bi2Sr2CaCu2O8+ (Tc ~ 91 K). Using
angle-resolved photoemission spectroscopy, we probe the electronic structure
and the possible existence of superconducting gap on the top surface of Bi2Se3
thin films. Our systematic data show no significant proximity-induced
superconducting gap in the topological surface states with sample temperature
down to 10 K (<<91 K) and with a confidence level of sub 5 meV, much smaller
than what have been claimed previously, which indicates the near absence of the
proximity-induced superconductivity on the TI surface. Our momentum space
imaging provides evidence for the coexistence of two crystalline phases in
Bi2Se3/Bi2Sr2CaCu2O8+ samples, which we argue to be due to the strong mismatch
of lattice crystalline symmetries. Our data identify the major contributors in
reducing the proximity-induced superconducting gap below the meV range,
including the lack of momentum space overlap between the Bi2Se3 and
Bi2Sr2CaCu2O8+ Fermi surfaces, the strong mismatch of lattice crystalline
symmetries and superconducting pairing symmetries, as well as the very short
superconducting coherence length in Bi2Sr2CaCu2O8+. Our ARPES studies not only
provide critical momentum space insights into the Bi2Se3/Bi2Sr2CaCu2O8+
heterostructure, but also set an upper bound on the proximity induced gap for
realizing a Majorana fermion condition in this system, which may be further
destabilized by the d-wave nodes dominated in a cuprate superconductor.
