Lifshitz transition with interactions in high magnetic fields: Application to CeIn$_3$

The N\'eel ordered state of CeIn$_3$ is suppressed by a magnetic field of 61 T at ambient pressure. There is a second transition at $\sim$45 T, which has been associated with a Lifshitz transition [1,2]. Skin depth measurements [2] indicate that the transition is discontinuous as $T \to 0$. Motivated by this transition we study the effects of Landau quantization and interaction among carriers on a Lifshitz transition. The Landau quantization leads to quasi-one-dimensional behavior for the direction parallel to the field. Repulsive Coulomb interactions give rise to a gas of strongly coupled carriers [3]. The density correlation function is calculated for a special long-ranged potential [4]. It is concluded that in CeIn$_3$ a pocket is being emptied as a function of field in a discontinuous fashion in the ground state. This discontinuity is gradually smeared by the temperature [4] in agreement with the skin depth experiments [2]. \vskip 0.05in \par\noindent [1] S.E. Sebastian {\it et al}, PNAS {\bf 106}, 7741 (2009). \par\noindent [2] K.M. Purcell {\it et al}, Phys. Rev. B {\bf 79}, 214428 (2009). \par\noindent [3] P. Schlottmann and R. Gerhardts, Z. Phys. B {\bf 34}, 363 (1979). \par\noindent [4] P. Schlottmann, Phys. Rev. B {\bf 83}, 115133 (2011); J. Appl. Phys., in print.