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We theoretically study superconducting proximity effect between a topologicalinsulator (TI) and a high-temperature d-wave superconductor (dSC). When theTI-dSC heterostructure violates 90 degree-rotation and certain reflectionsymmetries, we show that a sizable s-wave pairing, coexisting with a d-waveone, emerges in the proximity-induced superconductivity in the TI's top surfacestates. Weak disorder further suppresses d-wave pairing but not s-wave one inthe TI's surface states. More importantly, the pairing gap in surface states isfound to be nodeless and nearly-isotropic when the Fermi pocket of surfacestates is relatively small. Our theoretical results qualitatively explainrecent experimental evidences of a nearly-isotropic pairing gap on surfacestates of Bi_2Se_3 induced by proximity with high-T_c cuprateBi_2Ca_2Cu_2O_{8+\delta}. We also demonstrate convincing evidences of Majoranazero modes in a magnetic hc/2e vortex core, which may be detectable in futureexperiments.

Realizing Majorana Zero Modes by Proximity Effect between Topological Insulators and d-wave High-Temperature Superconductors