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Register a new userQuantum Hall effective action for anisotropic Dirac semi-metal
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We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.
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Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo)$_3$, we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate effects from different contributions to the Hamiltonian we study the model in various limits. First, in the limit of a very thin material where the linearly dispersive $z$-direction is frozen out at zero momentum and the dispersion in the $x$-$y$ plane is rotationally symmetric. In this limit we find a Klein tunneling reminiscent of what is observed in single layer graphene and linearly dispersive Dirac semi-metals. Second, an increase in thickness of the material leads to the possibility of a non-zero momentum eigenvalue $k_z$ that acts as an effective mass term in the Hamiltonian. We find that these lead to a suppression of Klein tunneling. Third, the inclusion of an anisotropy parameter $lambda eq 1$ leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle $theta$ and anisotropy parameter $lambda$ the Hamiltonian supports different numbers of modes propagating to infinity. We display this effect in form of a diagram that is similar to a phase diagram of a distant detector. Fourth, we consider coexistence of both anisotropy and non-zero $k_z$ but do not find any effect that is unique to the interplay between non-zero momentum $k_z$ and anisotropy parameter $lambda$. Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling $T-1propto theta^6+mathcal{O}(theta^8)$ that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where $T-1propto theta^2+mathcal{O}(theta^4)$.
Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.
We show that a class of compounds with $I$4/$mcm$ crystalline symmetry hosts three-dimensional semi-Dirac fermions. Unlike the known two-dimensional semi-Dirac points, the degeneracy of these three-dimensional semi-Dirac points is not lifted by spin-orbit coupling due to the protection by a nonsymmorphic symmetry -- screw rotation in the $a-b$ plane and a translation along the $c$ axis. This crystalline symmetry is found in tetragonal perovskite oxides, realizable in thin films by epitaxial strain that results in a$^0$a$^0$c$^-$-type octahedral rotation. Interestingly, with broken time-reversal symmetry, two pairs of Weyl points emerge from the semi-Dirac points within the Brillouin zone, and an additional lattice distortion leads to enhanced intrinsic anomalous Hall effect. We discuss possible fingerprints of this symmetry-protected band topology in electronic transport experiments.
Quantum Hall matrix models are simple, solvable quantum mechanical systems which capture the physics of certain fractional quantum Hall states. Recently, it was shown that the Hall viscosity can be extracted from the matrix model for Laughlin states. Here we extend this calculation to the matrix models for a class of non-Abelian quantum Hall states. These states, which were previously introduced by Blok and Wen, arise from the conformal blocks of Wess-Zumino-Witten conformal field theory models. We show that the Hall viscosity computed from the matrix model coincides with a result of Read, in which the Hall viscosity is determined in terms of the weights of primary operators of an associated conformal field theory.
The prospect of a Dirac half metal, a material which is characterized by a bandstructure with a gap in one spin channel but a Dirac cone in the other, is of both fundamental interest and a natural candidate for use in spin-polarized current applications. However, while the possibility of such a material has been reported based on model calculations[H. Ishizuka and Y. Motome, Phys. Rev. Lett. 109, 237207 (2012)], it remains unclear what material system might realize such an exotic state. Using first-principles calculations, we show that the experimentally accessible Mn intercalated epitaxial graphene on SiC(0001) transits to a Dirac half metal when the coverage is > 1/3 monolayer. This transition results from an orbital-selective breaking of quasi-2D inversion symmetry, leading to symmetry breaking in a single spin channel which is robust against randomness in the distribution of Mn intercalates. Furthermore, the inclusion of spin-orbit interaction naturally drives the system into the quantum anomalous Hall (QAH) state. Our results thus not only demonstrate the practicality of realizing the Dirac half metal beyond a toy model but also open up a new avenue to the realization of the QAH effect.
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