“…In his seminal paper [ 1 , 2 ], Landau first studied an electron dressed by phonons. Since then, such impurity problem has appeared in different incarnations, such as the Kondo [ 3 ] and Cherenkov [ 4 , 5 , 6 ] effects, the polaron physics [ 7 ], and the Landau criterion [ 8 , 9 , 10 , 11 , 12 ] for the sound speed of a superfluid. At present, there are great efforts and interest in studying a mobile impurity in a quantum medium in diverse areas [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ].…”