Surface Of 3D Topological Insulator Research Articles

Light-Induced Quantum Anomalous Hall Effect on the 2D Surfaces of 3D Topological Insulators.

Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and time‐reversal symmetry (TRS) breaking. In most cases, one can break the TRS of time‐reversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. However, conventional topological phase transition induced by external field/stimulus usually needs a route along which the bandgap closes and reopens. Hence, the transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work the authors propose that using gapless systems, the transition can happen at an arbitrarily weak (but finite) external field strength. For such an unconventional topological phase transition, the bandgap closing is guaranteed by bulk‐edge correspondence and symmetries, while the bandgap reopening is induced by external fields. This concept is demonstrated on the 2D surface states of 3D topological insulators like Bi2Se3, which become 2D QAH insulators once a circularly polarized light is turned on, according to the Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamic approach to trigger topological phase transitions and create QAH insulators.

Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition.

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig etal. [Phys. Rev. B 50, 7526 (1994)PRBMDO0163-182910.1103/PhysRevB.50.7526] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics, and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D DDF in the unitary class. We find a critical line at m=0, with an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_{IQH}=2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν_{0}=2.30-2.36 incompatible with ν_{IQH}. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.

Magnetoresistance from time-reversal symmetry breaking in topological materials

Magnetotransport measurements are a popular way of characterizing the electronic structure of topological materials and often the resulting datasets cannot be described by the well-known Drude model due to large, non-parabolic contributions. In this work, we focus on the effects of magnetic fields on topological materials through a Zeeman term included in the model Hamiltonian. To this end, we re-evaluate the simplifications made in the derivations of the Drude model and pinpoint the scattering time and Fermi velocity as Zeeman-term dependent factors in the conductivity tensor. The driving mechanisms here are the aligment of spins along the magnetic field direction, which allows for backscattering, and a significant change to the Fermi velocity by the opening of a hybridization gap. After considering 2D and 3D Dirac states, as well as 2D Rashba surface states and the quasi-2D bulk states of 3D topological insulators, we find that the 2D Dirac states on the surfaces of 3D topological insulators produce magnetoresistance, that is significant enough to be noticable in experiments. As this magnetoresistance effect is strongly dependent on the spin-orbit energy, it can be used as a telltale sign of a Fermi energy located close to the Dirac point.

Landau level quantization of Dirac electrons on the sphere

Interactions in Landau levels can stabilize new phases of matter, such as fractionally quantized Hall states. Numerical studies of these systems mostly require compact manifolds like the sphere or a torus. For massive dispersions, a formalism for the lowest Landau level on the sphere was introduced by Haldane (1983). Graphene and surfaces of 3D topological insulators, however, display massless (Dirac) dispersions, and hence require a different description. We generalize a formalism previously developed for Dirac electrons on the sphere in zero field to include the effect of an external, uniform magnetic field.

Retardation effects on plasma waves in graphene, topological insulators, and quantum wires

Retardation effects (REs) are known to cause a crossover from linear to sublinear behaviors in the dispersion relation of two-dimensional (2D) plasma waves at long wavelengths. In the present work, we systematically analyze REs on plasma waves in both 2D and 1D electron gases, and we clarify the experimental conditions for observing the crossover. We show that graphene is the only material that might gratify the conditions with current technology. Although it closely imitates graphene, the surface of 3D topological insulators is found to be unsuitable for this purpose due to strong electronic scattering by intrinsic disorder. We also show that the crossover, though theoretically possible, virtually never occurs in 1D plasma. In addition, the relevance of our results to terahertz plasmonics is discussed.

Dynamical gate-tunable supercurrents in topological Josephson junctions

Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.

Collective excitonic and plasmonic excitations on a surface of 3D topological insulator

Properties of collective excitonic and plasmonic excitations on the surface of three-dimensional topological insulator are reviewed. Due to spin-momentum locking for electrons populating the surface states plasmonic excitation manifests itself as coupled spin- and density-wave and can be called "spin-plasmon". Its excitation induces spin polarization of topological insulator surface that is perpendicular to the spin-plasmon momentum. Excitons appear on the surface when the gap in the surface spectrum is magnetically induced. Excitons correspond to the set of subgap levels with unusual dependence of the energy on orbital angular momentum quantum number and can be called "chiral". Contrary to conventional excitons chiral ones resonantly contribute to Hall component of optical conductivity tensor and play significant role in magneto-optical Faraday and Kerr effects. They resonantly enhance Faraday effect and reduce Kerr effect.

Metal-insulator transition in two-dimensional random fermion systems of chiral symmetry classes

Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vortex-like excitations of the sigma models. We derive renormalization group equations including these non-perturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the Wess-Zumino and Z_2 theta terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.