Subset based on a date range

Hello, 

Can someone help me on how to make a subset of my dataframe using two dates.
This is what I have tried, but no data is being excluded in the new frame.

six_months<-subset(Two_years, vdate>2011-01-01|vdate<2011-07-01)

or all data is excluded

six_months<-subset(Two_years, vdate>2011-01-01&vdate<2011-07-01)
 

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