zap also seems to offer global loggers - zap.L() for the mandatory structure logger, and zap.S(), for the Sugared logger.
From what I have seen, these loggers are not meant to be used out of the box (like log.Print() in the standard library), but rather their purpose seems only to provide a shared logger throughout the code. If you really want to use it, you need to replace the core with that of a different logger. You are also provided a way to undo a replacement. Out of the box, the global loggers have no output.
$ go run src/globallogger/main.go
*** Using the global logger out of the box
*** After replacing the global logger with a development logger
2018-05-02T16:24:40.992-0700 INFO globallogger/main.go:17 An info message {"iteration": 1}
*** After replacing the global logger with a production logger
{"level":"info","ts":1525303480.993161,"caller":"globallogger/main.go:22","msg":"An info message","iteration":1}
*** After undoing the last replacement of the global logger
2018-05-02T16:24:40.993-0700 INFO globallogger/main.go:26 An info message {"iteration": 1}