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We study a three-dimensional chiral second order topological insulator (SOTI) subject to a magnetic field. Via its gauge field, the applied magnetic field influences the electronic motion on the lattice, and via the Zeeman effect, the field influences the electronic spin. We compare two approaches to the problem: an effective surface theory, and a full lattice calculation. The surface theory predicts a massive Dirac spectrum on each of the gapped surfaces, giving rise to Landau levels once the surfaces are pierced by magnetic flux. The surface theory qualitatively agrees with our lattice calculations, accurately predicting the surface gap as well as the spin and orbital components of the states at the edges of the surface Dirac bands. In the context of the lattice theory, we calculate the spectrum with and without magnetic field and find a deviation from the surface theory when a gauge field is applied. The energy of the lowest-lying Landau level is found closer to zero than is predicted by the surface theory, which leads to an observable magnetotransport signature: inside the surface gap, there exist different energy regions where either one or two chiral hinge modes propagate in either direction, quantizing the differential conductance to either one or two conductance quanta.
We study the topological phase in dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and $mathbb{Z}_{4}$ Berry phase, we obtain the phase diagram and identify that the second-order
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern insulators with op
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related
A second-order topological insulator (SOTI) in $d$ spatial dimensions features topologically protected gapless states at its $(d-2)$-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state,
Two recent experiments successfully observed Landau levels in the tunneling spectra of the topological insulator Bi2Se3. To mimic the influence of a scanning tunneling microscope tip on the Landau levels we solve the two-dimensional Dirac equation in