Tilted-Cone-Induced Easy-Plane Pseudo-Spin Ferromagnet and Kosterlitz–Thouless Transition in Massless Dirac Fermions

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The possible quantum Hall ferromagnet at a filling factor $\nu = 0$ is investigated for the zero-energy ($N=0$) Landau level of the two dimensional massless Dirac fermions in $\alpha$-(BEDT-TTF)2I3 under pressure with tilted cones and a twofold valley degeneracy resulting from time-reversal symmetry. In the case of the Dirac cones without tilting, the long-range Coulomb interaction in the $N=0$ Landau level exhibits the $SU(2)$ valley-pseudo-spin symmetry even to the order $O(a/l_{\text{H}})$, in contrast to $N \neq 0$ Landau levels, where $a$ and $l_{\text{H}}$ represent the lattice constant and the magnetic length, respectively. Such a characteristic comes from a fact that zero-energy states in a particular valley are restricted to only one of the spinor components, whereas the other spinor component is necessarily zero. In the case of the tilted Dirac cones as found in $\alpha$-(BEDT-TTF)2I3, one obtains a non-zero value of the second component and then the backscattering processes between valleys becomes non-zero. It is shown that this fact can lead to easy-plane pseudospin ferromagnetism (XY-type). In this case, the phase fluctuations of the order parameters can be described by the XY model leading to Kosterlitz–Thouless transition at lower temperature. In view of these theoretical results, experimental findings in resistivity of $\alpha$-(BEDT-TTF)2I3 are discussed.
2009-11-15