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Register a new userEdge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes
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Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of quantum Hall phases, and time-reversal invariant topological insulators. Here we study the edge of a 2D, topologically trivial insulating phase, as a function of the strength of the electronic interactions and the steepness of the confining potential. For sufficiently smooth confining potentials, alternating compressible and incompressible stripes appear at the edge. Our findings signal the emergence of gapless edge modes which may give rise to finite conductance at the edge. This would suggest a novel scenario of a non-topological metal-insulator transition in clean 2D systems. The incompressible stripes appear at commensurate fillings and may exhibit broken translational invariance along the edge in the form of charge density wave ordering. These are separated by structureless compressible stripes.
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We consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term $t$, a chemical potential $mu$, an extended $s$-wave pairing $Delta$ and spin-orbit coupling $lambda$. We show that for $|Delta|=|lambda|$, $mu=t=0$, the model can be solved exactly defining new fermion operators involving nearest-neighbor sites. The many-body ground state is four-fold degenerate due to the existence of two zero-energy modes localized exactly at the first and the last site of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results we correct some statements related with the so called time-reversal anomaly. Addition of a small hopping term for a chain with an even number of sites breaks the degeneracy and the ground state becomes unique with an even number of particles. We also consider a small magnetic field applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains with numerical results %for a small chain obtaining good agreement.
We study the scattering of the Dirac electrons by a point-like nonmagnetic impurity on the surface of a topological insulator, driven by a time-periodic gate voltage. It is found that, due to the doublet degenerate crossing points of different Floquet sidebands, resonant backscattering can happen for the surface electrons, even without breaking the time-reversal (TR) symmetry of the topological surface states (TSSs). The energy spectrum is reshuffled in a way quite different from that for the circularly polarized light, so that new features are exhibited in the Friedel oscillations of the local charge and spin density of states. Although the electron scattering is dramatically modified by the driving voltage, the $1/rho$ scale law of the spin precession persists for the TSSs. The TR invariant backscattering provides a possible way to engineer the Dirac electronic spectrum of the TSSs, without destroying the unique property of spin-momentum interlocking of the TSSs.
Here we describe how certain classes of two dimensional topological insulators, including the CdTe$/$HgTe quantum wells, display a new type of optical activity in two dimensions similar to the magneto-optical Kerr effect in the quantum Hall effect. This optical activity is characterized by a genuine Kerr angle and it is compatible with time reversal symmetry, being thus fundamentally different to other known types of time reversal invariant optical activity. The term responsible of such optical activity, having the form of $(mathbf{E}cdotpartialmathbf{B}/partial t-mathbf{B}cdotpartialmathbf{E}/partial t)$, can be considered a time reversal invariant counterpart of the magneto-electric term $mathbf{E}cdotmathbf{B}$. The microscopical origin of this response is a chiral non-minimal coupling between electrons and the external electromagnetic field. This optical activity constitutes a proof of principle that there is possible to find systems that are time reversal invariant displaying a genuine Kerr effect.
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.
The relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model is studied numerically by solving the full set of equations of motion. A Lindblad coupling of a few sites at the opposite edge to an absorbing bath ensures that convergence with respect to the system size is achieved with only a moderate number of core sites. This allows us to numerically exactly study the long-time limit and to determine the parameter regimes where spin relaxation takes place. Corresponding dynamical phase diagrams for the topologically trivial and the nontrivial cases are constructed. The dynamical phase boundaries, the role of the topological edge state and its internal Zeeman splitting for the spin-relaxation process, as well as incomplete spin relaxation on long time scales can be explained within the framework of a renormalized linear-response approach when explicitly taking retardation effects and nonequilibrium spin-exchange processes into account.
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