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Brown dwarfs are important objects because they may provide a missing link between stars and planets, two populations that have dramatically different formation history. In this paper, we present the candidate binaries with brown dwarf companions that are found by analyzing binary microlensing events discovered during 2004 - 2011 observation seasons. Based on the low mass ratio criterion of q < 0.2, we found 7 candidate events, including OGLE-2004-BLG-035, OGLE-2004-BLG-039, OGLE-2007-BLG-006, OGLE-2007-BLG-399/MOA-2007-BLG-334, MOA-2011-BLG-104/OGLE-2011-BLG-0172, MOA-2011-BLG-149, and MOA-201-BLG-278/OGLE-2011-BLG-012N. Among them, we are able to confirm that the companions of the lenses of MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149 are brown dwarfs by determining the mass of the lens based on the simultaneous measurement of the Einstein radius and the lens parallax. The measured mass of the brown dwarf companions are (0.02 +/- 0.01) M_Sun and (0.019 +/- 0.002) M_Sun for MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149, respectively, and both companions are orbiting low mass M dwarf host stars. More microlensing brown dwarfs are expected to be detected as the number of lensing events with well covered light curves increases with new generation searches.
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Short-timescale microlensing events are likely to be produced by substellar brown dwarfs (BDs), but it is difficult to securely identify BD lenses based on only event timescales $t_{rm E}$ because short-timescale events can also be produced by stellar lenses with high relative lens-source proper motions. In this paper, we report three strong candidate BD-lens events found from the search for lensing events not only with short timescales ($t_{rm E} lesssim 6~{rm days}$) but also with very small angular Einstein radii ($theta_{rm E}lesssim 0.05~{rm mas}$) among the events that have been found in the 2016--2019 observing seasons. These events include MOA-2017-BLG-147, MOA-2017-BLG-241, and MOA-2019-BLG-256, in which the first two events are produced by single lenses and the last event is produced by a binary lens. From the Bayesian analysis conducted with the combined $t_{rm E}$ and $theta_{rm E}$ constraint, it is estimated that the lens masses of the individual events are $0.051^{+0.100}_{-0.027}~M_odot$, $0.044^{+0.090}_{-0.023}~M_odot$, and $0.046^{+0.067}_{-0.023}~M_odot/0.038^{+0.056}_{-0.019}~M_odot$ and the probability of the lens mass smaller than the lower limit of stars is $sim 80%$ for all events. We point out that routine lens mass measurements of short time-scale lensing events require survey-mode space-based observations.
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