SliverAppBar with TabBar

How can I add TabBar to SliverAppBar in Flutter? So far when I add a bottom to SliverAppBar, title gets pinned to those tabs, while I want it to be above those tabs.
Any ideas?

My code:

class _MyHomePageState extends State<MyHomePage> with SingleTickerProviderStateMixin{
  TabController controller;


  @override
  void initState() {
    super.initState();
    controller = new TabController(length: 3, vsync: this);
  }

  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      body: new CustomScrollView(
        slivers: <Widget>[
          new SliverAppBar(
            pinned: true,
            flexibleSpace: new FlexibleSpaceBar(
              title: new Text("Some title"),
            ),
            expandedHeight: 160.0,
            bottom: new TabBar(tabs: [
              new Tab(text: 'Tab 1'),
              new Tab(text: 'Tab 2'),
              new Tab(text: 'Tab 3'),
            ],
            controller: controller,
            ),
          ),
          new SliverList(
            delegate: new SliverChildBuilderDelegate(
              (context, idx) {
                return new ListTile(
                  title: new Text("$idx"),
                );
              },
              childCount: 20,
            ),
          ),
        ],
      ),
    );
  }
}

I had the same problem weeks ago and I could solve using SliverAppBar , FlexibleSpaceBar and SliverPersistentHeader.

Check my code

  @override
    Widget build(BuildContext context) {
      return Scaffold(
        body: DefaultTabController(
          length: 2,
          child: NestedScrollView(
            headerSliverBuilder: (BuildContext context, bool innerBoxIsScrolled) {
              return <Widget>[
                SliverAppBar(
                  expandedHeight: 200.0,
                  floating: false,
                  pinned: true,
                  flexibleSpace: FlexibleSpaceBar(
                      centerTitle: true,
                      title: Text("Collapsing Toolbar",
                          style: TextStyle(
                            color: Colors.white,
                            fontSize: 16.0,
                          )),
                      background: Image.network(
                        "https://images.pexels.com/photos/396547/pexels-photo-396547.jpeg?auto=compress&cs=tinysrgb&h=350",
                        fit: BoxFit.cover,
                      )),
                ),
                SliverPersistentHeader(
                  delegate: _SliverAppBarDelegate(
                    TabBar(
                      labelColor: Colors.black87,
                      unselectedLabelColor: Colors.grey,
                      tabs: [
                        Tab(icon: Icon(Icons.info), text: "Tab 1"),
                        Tab(icon: Icon(Icons.lightbulb_outline), text: "Tab 2"),
                      ],
                    ),
                  ),
                  pinned: true,
                ),
              ];
            },
            body: Center(
              child: Text("Sample text"),
            ),
          ),
        ),
      );
    }

And this is the implementation of SliverPersistentHeader

  class _SliverAppBarDelegate extends SliverPersistentHeaderDelegate {
    _SliverAppBarDelegate(this._tabBar);

    final TabBar _tabBar;

    @override
    double get minExtent => _tabBar.preferredSize.height;
    @override
    double get maxExtent => _tabBar.preferredSize.height;

    @override
    Widget build(
        BuildContext context, double shrinkOffset, bool overlapsContent) {
      return new Container(
        child: _tabBar,
      );
    }

    @override
    bool shouldRebuild(_SliverAppBarDelegate oldDelegate) {
      return false;
    }
  }

I wrote a post about it if you want to check :

https://medium.com/@diegoveloper/flutter-collapsing-toolbar-sliver-app-bar-14b858e87abe