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Register a new userTopological obstructed atomic limit by annihilating Dirac fermions
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Added by
Santosh Kumar Radha
Publication date
2020
fields
Physics
and research's language is
English
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We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semi-metallic phase to an Obstructed Atomic Limit (OAL) insulator phase instead of a trivial insulator. This is shown to happen because of branch-cuts in the phase of the wave functions, leading to non trivial Zak phase along certain directions. To this end, we study their Z$_2$ invariant and also study the phase transition using Entanglement Entropy. We use low energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials including strained graphene and buckled honeycomb group-V (Sb/As).
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Relativistic massless Dirac fermions can be probed with high-energy physics experiments, but appear also as low-energy quasi-particle excitations in electronic band structures. In condensed matter systems, their massless nature can be protected by crystal symmetries. Classification of such symmetry-protected relativistic band degeneracies has been fruitful, although many of the predicted quasi-particles still await their experimental discovery. Here we reveal, using angle-resolved photoemission spectroscopy, the existence of two-dimensional type-II Dirac fermions in the high-temperature superconductor La$_{1.77}$Sr$_{0.23}$CuO$_4$. The Dirac point, constituting the crossing of $d_{x^2-y^2}$ and $d_{z^2}$ bands, is found approximately one electronvolt below the Fermi level ($E_mathrm{F}$) and is protected by mirror symmetry. If spin-orbit coupling is considered, the Dirac point degeneracy is lifted and the bands acquire a topologically non-trivial character. In certain nickelate systems, band structure calculations suggest that the same type-II Dirac fermions can be realised near $E_mathrm{F}$.
We examine the presence and evolution of magnetic Dirac nodes in the Heisenberg honeycomb lattice. Using linear spin theory, we evaluate the collinear phase diagram as well as the change in the spin dynamics with various exchange interactions. We show that the ferromagnetic structure produces bosonic Dirac and Weyl points due to the competition between superexchange interactions. Furthermore, it is shown that the criteria for magnetic Dirac nodes are coupled to the magnetic structure and not the overall crystal symmetry, where the breaking of inversion symmetry greatly affects the antiferromagnetic configurations. The tunability of the nodal points through variation of the exchange parameters leads to the possibility of controlling Dirac symmetries through an external manipulation of the orbital interactions.
Topological states of matter challenge the paradigm of symmetry breaking, characterized by gapless boundary modes and protected by the topological property of the ground state. Recently, angle-resolved photoemission spectroscopy (ARPES) has revealed that semiconductors of Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ belong to such a class of materials. Here, we present undisputable evidence for the existence of gapless surface Dirac fermions from transport in Bi$_{2}$Te$_{3}$. We observe Sondheimer oscillation in magnetoresistance (MR). This oscillation originates from the quantization of motion due to the confinement of electrons within the surface layer. Based on Sondheimers transport theory, we determine the thickness of the surface state from the oscillation data. In addition, we uncover the topological nature of the surface state, fitting consistently both the non-oscillatory part of MR and the Hall resistance. The side-jump contribution turns out to dominate around 1 T in Hall resistance while the Berry-curvature effect dominates in 3 T $sim$ 4 T.
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.
Magnetic topological phases of quantum matter are an emerging frontier in physics and material science. Along these lines, several kagome magnets have appeared as the most promising platforms. Here, we explore magnetic correlations in the transition-metal-based kagome magnet TbMn$_{6}$Sn$_{6}$. Our results show that the system exhibits an out-of-plane ferrimagnetic structure $P6/mmm$ (comprised by Tb and Mn moments) with slow magnetic fluctuations in a wide temperature range. These fluctuations exhibit a slowing down below $T_{rm C1}^{*}$ ${simeq}$ 120 K and a slightly modified quasi-static magnetic state is established below $T_{rm C1}$ ${simeq}$ 20 K. A canted variation of the $P6/mmm$ structure is possible, where all moments contribute to a net $c$-axis ferrimagnetic state which exhibits zero net in-plane components. Alternatively, a small incommensurate $k$-vector could arise below $T_{rm C1}$. We further show that the temperature evolution of the anomalous Hall conductivity (AHC) is strongly influenced by the low temperature magnetic crossover. More importantly, the here identified magnetic state seems to be responsible for the large quasi-linear magnetoresistance as well as for the appearance of quantum oscillations, which are related to the quantized Landau fan structure featuring a spin-polarized Dirac dispersion with a large Chern gap. Therefore the exciting perspective of a magnetic system arises in which the topological response can be controlled, and thus explored, over a wide range of parameters.
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