Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

We perform a numerical simulation of the effects of an orthogonal magnetic field on charge transport and shot noise in an armchair graphene ribbon with a lattice of antidots. This study relies on our envelope-function based code, in which the presence of antidots is simulated through a nonzero mass term and the magnetic field is introduced with a proper choice of gauge for the vector potential. We observe that by increasing the magnetic field, the energy gap present with no magnetic field progressively disappears, together with features related to commensurability and quantum effects. In particular, we focus on the behavior for high values of the magnetic field: we notice that when it is sufficiently large, the effect of the antidots vanishes and shot noise disappears, as a consequence of the formation of edge states crawling along the boundaries of the structure without experiencing any interaction with the antidots.

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Zero modes and edge states of the honeycomb lattice

Physical Review B ◽

10.1103/physrevb.76.205402 ◽

2007 ◽

Vol 76 (20) ◽

Cited By ~ 72

Author(s):

Mahito Kohmoto ◽

Yasumasa Hasegawa

Keyword(s):

Honeycomb Lattice ◽

Edge States ◽

Zero Modes

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Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices

Light Science & Applications ◽

10.1038/s41377-020-00377-6 ◽

2020 ◽

Vol 9 (1) ◽

Cited By ~ 2

Author(s):

Omar Jamadi ◽

Elena Rozas ◽

Grazia Salerno ◽

Marijana Milićević ◽

Tomoki Ozawa ◽

...

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Symmetry Breaking ◽

Distinctive Feature ◽

Direct Evidence ◽

Landau Levels ◽

Honeycomb Lattice ◽

Edge States ◽

Photonic Lattices ◽

Synthetic Magnetic Field

Abstract We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n = 0 and n = ±1 Landau levels, experimentally demonstrating a novel way of engineering propagating edge states in photonic lattices. In light of recent advances in the enhancement of polariton–polariton nonlinearities, the Landau levels reported here are promising for the study of the interplay between pseudomagnetism and interactions in a photonic system.

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Electronic structure and transport properties of graphene/h-BN controlled by boundary potential and magnetic field

Modern Physics Letters B ◽

10.1142/s0217984920501808 ◽

2020 ◽

Vol 34 (16) ◽

pp. 2050180

Author(s):

Jian Sun ◽

Lei Xu ◽

Jun Zhang

Keyword(s):

Magnetic Field ◽

Electronic Structure ◽

Band Structure ◽

Transport Properties ◽

Energy Gap ◽

Edge State ◽

Stable Configuration ◽

Edge States ◽

Boundary Potential ◽

Lattice Matched

We study the band structure of the lattice-matched graphene/[Formula: see text]-BN bilayer system in the most stable configuration. An effective way to individually manipulate the edge state by the boundary potentials is proposed. It is shown that the boundary potential can not only shift and deform the edge bands, but also modify the energy gap. We also explore the transport properties of graphene/[Formula: see text]-BN under a magnetic field. The boundary potential can change the distribution of the edge states, resulting in an interesting evolution of the quantized conductance.

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Simulating graphene dynamics in synthetic space with photonic rings

Communications Physics ◽

10.1038/s42005-021-00719-9 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Danying Yu ◽

Guangzhen Li ◽

Meng Xiao ◽

Da-Wei Wang ◽

Yong Wan ◽

...

Keyword(s):

Magnetic Field ◽

Signal Processing ◽

Lorentz Force ◽

Optical Signal Processing ◽

Optical Signal ◽

Honeycomb Lattice ◽

Edge States ◽

One Dimensional ◽

Klein Tunneling ◽

Physical Phenomena

AbstractPhotonic honeycomb lattices have attracted broad interests for their fruitful ways in manipulating light, which yet hold difficulties in achieving arbitrary reconfigurability and hence flexible functionality due to fixed geometry configurations. Here we theoretically propose to construct the honeycomb lattice in a one-dimensional ring array under dynamic modulations, with an additional synthetic dimension created by connecting the frequency degree of freedom of light. Such a system is highly re-configurable with parameters flexibly controlled by external modulations. Therefore, various physical phenomena associated with graphene including Klein tunneling, valley-dependent edge states, effective magnetic field, as well as valley-dependent Lorentz force can be simulated in this lattice, which exhibits important potentials for manipulating photons in different ways. Our work unveils an alternative platform for constructing the honeycomb lattice in a synthetic space, which holds complex functionalities and could be important for optical signal processing as well as quantum simulation.

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Topological gaps by twisting

Communications Physics ◽

10.1038/s42005-021-00630-3 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Matheus I. N. Rosa ◽

Massimo Ruzzene ◽

Emil Prodan

Keyword(s):

Magnetic Field ◽

Quantum Hall Effect ◽

Twist Angle ◽

Quantum Hall ◽

Topological Phases ◽

Edge States ◽

Layered Systems ◽

Virtual Laboratories ◽

Higher Dimensional ◽

Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

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