Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHigher Order Topological Insulator via Periodic Driving
121
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We theoretically investigate a periodically driven semimetal based on a square lattice. The possibility of engineering both Floquet Topological Insulator featuring Floquet edge states and Floquet higher order topological insulating phase, accommodating topological corner modes has been demonstrated starting from the semimetal phase, based on Floquet Hamiltonian picture. Topological phase transition takes place in the bulk quasi-energy spectrum with the variation of the drive amplitude where Chern number changes sign from $+1$ to $-1$. This can be attributed to broken time-reversal invariance ($mathcal{T}$) due to circularly polarized light. When the discrete four-fold rotational symmetry ($mathcal{C}_4$) is also broken by adding a Wilson mass term along with broken $mathcal{T}$, higher order topological insulator (HOTI), hosting in-gap modes at all the corners, can be realized. The Floquet quadrupolar moment, calculated with the Floquet states, exhibits a quantized value of $ 0.5$ (modulo 1) identifying the HOTI phase. We also show the emergence of the {it{dressed corner modes}} at quasi-energy $omega/2$ (remnants of zero modes in the quasi-static high frequency limit), where $omega$ is the driving frequency, in the intermediate frequency regime.
rate research
Read More
We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and nontopological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a nontopological phase which has states localized on only two of the four edges of a finite-sized square. When an appropriate term is added, the edge states get gapped and gapless states appear at the four corners of a square; we have shown that these corner states can be labeled by the eigenvalues of a certain operator. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss to what extent the system can be characterized by topological invariants such as the Chern number and a diagonal winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at both the time-reversal invariant momenta and other momenta which have no special symmetries.
Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not depend on the choice of the specific angles as long as the underlying symmetries are intact. Our results show that the twisted bilayer graphene can serve as a robust candidate material of two-dimensional higher-order topological insulator.
The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics. One example is a d-dimensional quantized multipole topological insulator, which supports multipoles of order up to 2^d and a hierarchy of gapped boundary modes with topological 0-D corner modes at the top. While multipole topological insulators have been successfully realized in electromagnetic and mechanical 2D systems with quadrupole polarization, and a 3D octupole topological insulator was recently demonstrated in acoustics, going beyond the three physical dimensions of space is an intriguing and challenging task. In this work, we apply dimensional reduction to map a 4D higher-order topological insulator (HOTI) onto an equivalent aperiodic 1D array sharing the same spectrum, and emulate in this system the properties of a hexadecapole topological insulator. We observe the 1D counterpart of zero-energy states localized at 4D HOTI corners - the hallmark of multipole topological phase. Interestingly, the dimensional reduction guarantees that one of the 4D corner states remains localized to the edge of the 1D array, while all other localize in the bulk and retain their zero-energy eigenvalues. This discovery opens new directions in multi-dimensional topological physics arising in lower-dimensional aperiodic systems, and it unveils highly unusual resonances protected by topological properties inherited from higher dimensions.
High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D TI, but instead has topologically-protected zero-dimensional (0D) corner states. So far, higher-order TIs have been demonstrated only in classical mechanical and electromagnetic metamaterials exhibiting quantized quadrupole polarization. Here, we experimentally realize a second-order TI in an acoustic metamaterial. This is the first experimental realization of a new type of higher-order TI, based on a breathing Kagome lattice, that has zero quadrupole polarization but nontrivial bulk topology characterized by quantized Wannier centers (WCs). Unlike previous higher-order TI realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the Kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically-protected but reconfigurable local resonances.
Random flux is commonly believed to be incapable of driving metal-insulator transitions. Surprisingly, we show that random flux can after all induce a metal-insulator transition in the two-dimensional Su-Schrieffer-Heeger model, thus reporting the first example of such a transition. Remarkably, we find that the resulting insulating phase can even be a higher-order topological insulator with zero-energy corner modes and fractional corner charges, rather than a conventional Anderson insulator. Employing both level statistics and finite-size scaling analysis, we characterize the metal-insulator transition and numerically extract its critical exponent as $ u=2.48pm0.08$. To reveal the physical mechanism underlying the transition, we present an effective band structure picture based on the random flux averaged Greens function.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
