Professor, estou tentando colocar a data do showDatePicker no TextField e não estou conseguindo. Tem alguma dica?

import 'package:flutter/material.dart';
import 'package:intl/intl.dart';

void main() {
  runApp(MaterialApp(
    debugShowCheckedModeBanner: false,
    home: Home(),
  ));
}
class Home extends StatefulWidget {
  @override
  _MyHomePageState createState() => new _MyHomePageState();
}

class _MyHomePageState extends State<Home> {
  DateTime _dateTime;
  @override
  Widget build(BuildContext context) {
   return  Scaffold(
        appBar:  AppBar(
          title:  Text("Teste de Data", ), 
        ),

      body: Column(
        children: <Widget>[
          Padding(
            padding: EdgeInsets.all(20.0),
            child: TextField(
              keyboardType: TextInputType.datetime,
              decoration: InputDecoration(
                icon: IconButton(
                  icon: Icon(Icons.date_range, color: Colors.purple,),
                  onPressed: () async {
                    final _dateTime = await showDatePicker(
                        context: context,
                        initialDate: DateTime.now(),
                        firstDate: DateTime(1930),
                        lastDate: DateTime(2030)
                    );
                    setState(() {});

                    var dataformato;
                    Text (dataformato = DateFormat('dd/MM/yyyy').format(_dateTime));
                    print(dataformato);
                    },
                ),
              ),
            ),
          ),
        ],
      ),
   );
  }
}