检查电子邮件是否已存在于flutter应用程序的firebase中，并在屏幕上显示错误文本

dependencies:
  flutter:
    sdk: flutter
  firebase_core: ^1.0.0
  firebase_auth: ^1.0.0
  cloud_firestore: ^2.0.0

import 'package:firebase_core/firebase_core.dart';

void main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp();
  runApp(MyApp());
}

import 'package:firebase_auth/firebase_auth.dart';

class AuthService {
  final FirebaseAuth _auth = FirebaseAuth.instance;

  Future<bool> checkEmailExists(String email) async {
    try {
      UserCredential userCredential = await _auth.createUserWithEmailAndPassword(
        email: email,
        password: 'password', // 这里使用一个临时密码进行注册
      );
      await userCredential.user.delete(); // 注册成功后立即删除用户
      return false; // 如果没有抛出异常，则表示电子邮件不存在
    } catch (e) {
      return true; // 如果抛出异常，则表示电子邮件已存在
    }
  }
}

import 'package:flutter/material.dart';

class MyScreen extends StatefulWidget {
  @override
  _MyScreenState createState() => _MyScreenState();
}

class _MyScreenState extends State<MyScreen> {
  AuthService _authService = AuthService();
  String _errorText = '';

  void checkEmail(String email) async {
    bool emailExists = await _authService.checkEmailExists(email);
    setState(() {
      _errorText = emailExists ? '电子邮件已存在' : '';
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('My Screen'),
      ),
      body: Column(
        children: [
          TextField(
            onChanged: (value) => checkEmail(value),
            decoration: InputDecoration(
              hintText: '请输入电子邮件',
            ),
          ),
          Text(
            _errorText,
            style: TextStyle(color: Colors.red),
          ),
        ],
      ),
    );
  }
}