We consider a doped quantum antiferromagnet in a phase of alternating hole-rich/hole-poor domains and we study tunneling of multi-hole clusters between neighboring hole-rich domains through the intervening antiferromagnetically ordered regions. We find that bound hole-pairs are much more effective in crossing the intervening antiferromagnetic domains as compared to single-hole of multi-hole clusters. This implies that the presence of the antiferromagnetic domains acts as a filter which allows only bound hole-pairs to exist throughout the entire system. We also find that at temperature of around 100 K bound hole-pairs can tunnel between neighboring hole-rich domains at high rates.
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