Hyper-Kamiokande consists of two identical water-Cherenkov detectors of total 520~kt with the first one in Japan at 295~km from the J-PARC neutrino beam with 2.5$^{textrm{o}}$ Off-Axis Angles (OAAs), and the second one possibly in Korea in a later stage. Having the second detector in Korea would benefit almost all areas of neutrino oscillation physics mainly due to longer baselines. There are several candidate sites in Korea with baselines of 1,000$sim$1,300~km and OAAs of 1$^{textrm{o}}$$sim$3$^{textrm{o}}$. We conducted sensitivity studies on neutrino oscillation physics for a second detector, either in Japan (JD $times$ 2) or Korea (JD + KD) and compared the results with a single detector in Japan. Leptonic CP violation sensitivity is improved especially when the CP is non-maximally violated. The larger matter effect at Korean candidate sites significantly enhances sensitivities to non-standard interactions of neutrinos and mass ordering determination. Current studies indicate the best sensitivity is obtained at Mt. Bisul (1,088~km baseline, $1.3^circ$ OAA). Thanks to a larger (1,000~m) overburden than the first detector site, clear improvements to sensitivities for solar and supernova relic neutrino searches are expected.
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