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The chiral surface states of Weyl semimetals have an open Fermi surface called a Fermi arc. At the interface between two Weyl semimetals, these Fermi arcs are predicted to hybridize and alter their connectivity. In this Letter, we numerically study a one-dimensional (1D) dielectric trilayer grating where the relative displacements between adjacent layers play the role of two synthetic momenta. The lattice emulates 3D crystals without time-reversal symmetry, including Weyl semimetal, nodal line semimetal, and Chern insulator. Besides showing the phase transition between Weyl semimetal and Chern insulator at telecom wavelength, this system allows us to observe the Fermi arc reconstruction between two Weyl semimetals, confirming the theoretical predictions.

We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.

This corrects the article DOI: 10.1103/PhysRevLett.118.206602.

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several nontrivial checks of the relations, including for the Jain states and their PH conjugates.

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions ν=N/(2N+1) at large N. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are O(N) neutral excitations, each carrying a well-defined spin that runs integer values 2,3,…. The mixing of modes at nonzero momentum q leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at qℓ_{B}=z_{i}/(2N+1), where ℓ_{B} is the magnetic length and z_{i} are the zeros of the Bessel function J_{1}, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.