Refine
Document Type
- Doctoral Thesis (2)
Language
- English (2) (remove)
Has Fulltext
- yes (2)
Is part of the Bibliography
- no (2)
Keywords
- Floquet (2) (remove)
Institute
This thesis contains studies on a special class of topological insulators, so called anomalous Floquet topological insulators, which exclusively occur in periodically driven systems. At the boundary of an anomalous Floquet topological insulator, topologically protected transport occurs even though all of the Floquet bands are topologically trivial. This is in stark contrast to ordinary topological insulators of both static and Floquet type, where the topological invariants of the bulk bands completely determine the chiral boundary states via the bulk-boundary correspondence. In anomalous Floquet topological insulators, the boundary states are instead characterized by bulk invariants that account for the full dynamical evolution of the Floquet system.
Here, we explore the interplay between topology, symmetry, and non-Hermiticity in two-dimensional anomalous Floquet topological insulators. The central results of this exploration are (i) new expressions for the topological invariants of symmetry-protected anomalous Floquet topological phases which can be efficiently computed numerically, (ii) the construction of a universal driving protocol for symmetry-protected anomalous Floquet topological phases and its experimental implementation in photonic waveguide lattices, (iii) the discovery of non-Hermitian boundary state engineering which provides unprecedented possibilities to control and manipulate the topological transport of anomalous Floquet topological insulators.
Graphene is a strictly two-dimensional honeycomb lattice of carbon atoms whose low-energy charge-carrier dynamics obey the massless pseudospin-1/2 Dirac-Weyl equation (or chiral Weyl equation) where the chiral centers (or valleys) are the corners K and K‘ of the Brillouin zone. The linear spectrum near the Dirac nodal points lends graphene its exotic and ultra-relativistic properties.
However, condensed matter systems can possess fermionic excitations with linear dispersions that have no analog in high-energy physics since the crystal space group - instead of the Poincare group - constrains the energy dispersions. Perhaps the first example in this regard is the T_3 lattice (Dice Gitter), a honeycomb-like lattice with an extra atom placed at the center of each hexagon and coupled to only one of the sublattices. The spectrum features a strictly flat band that crosses the two conical intersections of the Dirac cones at K and K' inherited from graphene. The enlarged pseudospin-1 Dirac-Weyl equation describes the low-energy dynamics. By rescaling the transfer amplitude of the additional atoms in the T_3 lattice with a parameter 0<α<1, the resulting α-T_3 lattice continously interpolates between graphene and the T_3 lattice.
In this work, we explore the behavior of generalized Dirac-Weyl quasiparticles in external magnetic and valley-dependent pseudoelectromagnetic fields induced by out-of-plane strain. First, we studied Dirac-Weyl quasiparticles in external fields confined to circular quantum dots by generalizing the infinite-mass boundary condition to the α-T_3 lattices. We verified the analytically derived valley-anisotropic eigenstates of the quantum dot by numerically solving the tight-binding lattice-model in closed (isolated) and open (contacted) systems.
Second, we considered strain fields in the α-T_3 lattices to modify the low-energy transport properties by an effective pseudo-gauge field with opposite signs at the K and K‘ valley. In particular, we showed that the inhomogeneous pseudomagnetic field generated by Gaussian out-of-plane strain at the center of a four-terminal Hall bar setup acts as a valley filter. Most interestingly, the valley polarization is most dominant when incoming electrons are excited to pseudo-Landau level subbands. These bands are linked to different iso-field orbits encircling the lobes of the pseudomagnetic field. Addittionaly, any intermediate α breaks the inversion symmetry of the α-T_3 lattice and thus splits the pseudo-Landau levels into sublattice-polarized bands.
Third, we equipped the out-of-plane strain with a time-periodic drive to induce a valley-dependent pseudoelectric field perpendicular to the pseudomagnetic field. We assessed the steady-state transport properties and found – besides the static regime for small energies – two α-dependent valley-filtering regimes due to the periodic drive. Firstly, we found an additional valley-polarization plateau at the Floquet-zone boundary between the central and first Floquet copy that also displayed a “flower”-like pattern in the local density of states. Secondly, we detected a series of transmission gaps at the center of every Floquet sideband 2mΩ related to the Floquet coupling of the flat band with the central Floquet copy. Under certain strain parameters, a novel valley-filtering regime appears near the transmission gaps where the incoming K electrons are focused through the bump by the pseudoelectric field, instead of encircling the lobes of the pseudomagnetic field. A stability analysis demonstrated that the polarization regimes are tunable by the driving frequency.
Lastly, we demonstrated that the flat band in the Haldane-dice lattice modified by a uniaxial strain along the zigzag orientation remains singular at all band crossings where the model undergoes a topological phase transition between C=+-2 and C=0. To show this, we computed the compact localized eigenstates and the quantum distance of the Bloch wave function around the band-touching points. We derived the resulting non-contractible loop states and an extended state whose components are tunabe by the system parameters.