Systems and methods for operating a turbocharged engine are described. In one example, a turbocharger system, comprising: a bearing housing including a turbine and at least one compressor coupled to the turbine via a shaft; and wherein the turbine comprises a stator stage and a rotor stage mounted to the cylinder head by the bearing housing and positioned in an exhaust passage of a cylinder head. In this way, a more compact design is achieved which eliminates the cost and complexity of a turbine housing and improves turbine efficiency by positioning the turbine closer to the exhaust pulses.