account.cs

public void SignIn(string authType)
{
    // Send an OpenID Connect sign-in request.
    if (!Request.IsAuthenticated)
    {
        string callbackUrl = Url.Action("SignInCallback", "Account", routeValues: new { authType = authType }, protocol: Request.Url.Scheme);

        HttpContext.GetOwinContext().Authentication.Challenge(new AuthenticationProperties { RedirectUri = callbackUrl },
            authType);
    }
}

public ActionResult SignInCallback(string authType)
{
    //NOTE: I am throwing the value into session state
    //depending on your application you will probably want to store this in something more durable (i.e. Redis Cache)
    Session["AuthType"] = authType;

    return RedirectToAction("Index", "Home");
}

public void SignOut()
{
    string callbackUrl = Url.Action("SignOutCallback", "Account", routeValues: null, protocol: Request.Url.Scheme);

    HttpContext.GetOwinContext().Authentication.SignOut(
        new AuthenticationProperties { RedirectUri = callbackUrl },
        Session["AuthType"].ToString(), CookieAuthenticationDefaults.AuthenticationType);
}

public ActionResult SignOutCallback()
{
    return RedirectToAction("Index", "Home");
}