Research Poster

Confined states and topological phases in two-dimensional quasicrystalline $\ensuremath{\pi}$-flux modelMotivated by topological equivalence between an extended Haldane model and a chiral-$\ensuremath{\pi}$-flux model on a square lattice, we apply $\ensuremath{\pi}$-flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial $\ensuremath{\pi}$-flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the $\ensuremath{\pi}$-flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain $\ensuremath{\pi}$-flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the $\ensuremath{\pi}$-flux models. This finding suggests a direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.

Quantum valley and subvalley Hall effect in large-angle twisted bilayer grapheneWe study the quantum valley Hall effect and related domain wall modes in twisted bilayer graphene at a large commensurate angle. Due to the quantum valley and subvalley Hall effect, a small deviation from the commensurate angle generates two-dimensional conducting network patterns composed of one-dimensional domain walls, which can host non-Fermi-liquid behavior within an accessible temperature range. The domain wall modes can be manipulated using an external electric field and layer shifting, manifesting the physics of the celebrated Haldane and Semenoff models for the subvalley Dirac cones, living on the domain walls. These findings open up an alternative direction towards realizing the emergence and manipulation of topological quantum valley and subvalley Hall states and possible applications in valleytronics. Our theory can be generalized to many twisted bilayer systems, including twisted graphene, twisted $\ensuremath{\alpha}$-graphene, and twisted kagome bilayers at large-angle rotation.

Boundary-obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric fieldIn this work, we show that a buckled honeycomb lattice can host a boundary-obstructed topological superconductor (BOTS) in the presence of $f$-wave spin-triplet pairing (fSTP). The underlying buckled structure allows for the manipulation of both chemical potential and sublattice potential using a double gate setup. Although a finite sublattice potential can stabilize the fSTP with a possible higher-order band topology, because it also breaks the relevant symmetry, the stability of the corner modes is not guaranteed. Here we show that the fSTP on the honeycomb lattice gives a BOTS under nonzero sublattice potential, thus the corner modes can survive as long as the boundary is gapped. Also, by examining the large sublattice potential limit where the honeycomb lattice can be decomposed into two triangular lattices, we show that the boundary modes in the normal state are the quintessential ingredient leading to the BOTS. Thus the effective boundary Hamiltonian becomes nothing but the Hamiltonian for Kitaev chains, which eventually gives the corner modes of the BOTS.

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.224511

f-wave.pptx

Topological superconductivity in quasicrystalsWe propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrystals with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional $s$-wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confirmed by the existence of a zero-energy surface bound state and the chiral propagation of a wave packet projected onto the midgap bound state along the surfaces. Furthermore, we confirm the existence of a single Majorana zero mode each in a vortex at the center of the system and along the surfaces, signifying the non-Abelian character of the system when the Bott index is unity.

poster.pptx

Majorana Zero-Energy Mode and Fractal Structure in Fibonacci–Kitaev Chain

Rasoul Ghadimi1,2, Takanori Sugimoto2, and Takami Tohyama2

Received July 25, 2017; Accepted September 11, 2017; Published October 10, 2017

We theoretically study a Kitaev chain with a quasiperiodic potential, where the quasiperiodicity is introduced by a Fibonacci sequence. Based on an analysis of the Majorana zero-energy mode, we find the critical p-wave superconducting pairing potential separating a topological phase and a non-topological phase. The topological phase diagram with respect to Fibonacci potentials follow a self-similar fractal structure characterized by the box-counting dimension, which is an example of the interplay of fractal and topology like the Hofstadter’s butterfly in quantum Hall insulators.

https://doi.org/10.7566/JPSJ.86.114707

Fibonacci Kitaev model.pptx

Mean-field study of the Bose-Hubbard model in the Penrose latticeWe examine the Bose-Hubbard model in the Penrose lattice based on inhomogeneous mean-field theory. Since the averaged coordination number in the Penrose lattice is four, the mean-field phase diagram consisting of the Mott insulator (MI) and superfluid (SF) phase is similar to that of the square lattice. However, the spatial distribution of the Bose condensate in the SF phase is significantly different from uniform distribution in the square lattice. We find a fractal structure in its distribution near the MI-SF phase boundary. The emergence of the fractal structure is a consequence of the cooperative effect between quasiperiodicity in the Penrose lattice and criticality at the phase transition.

new scaling bose hubbard.pptx

Higher-dimensional Hofstadter butterfly on the Penrose latticeIt is now possible to use quasicrystals to search for novel topological phenomena enhanced by their peculiar structure characterized by an irrational number and high-dimensional primitive vectors. Here, we extend the concept of a topological insulator with an emerging staggered local magnetic flux (i.e., without external fields), similar to Haldane's honeycomb model, to the Penrose lattice as a quasicrystal. The Penrose lattice consists of two different tiles, where the ratio of the numbers of tiles corresponds to an irrational number. Contrary to periodic lattices, the periodicity of the energy spectrum with respect to the magnetic flux no longer exists, reflecting the irrational number in the Penrose lattice. Calculating the Bott index as a topological invariant, we find topological phases appearing in a fractal energy spectrum similar to the Hofstadter butterfly. More intriguingly, by folding the one-dimensional aperiodic magnetic flux into a two-dimensional periodic flux space, the fractal structure of the energy spectrum is extended to a higher dimension, whose section corresponds to the Hofstadter butterfly.

Higher dimensional Hofsdater.pptx

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