We address the problem of hybridization between topological surface states and a non-topological flat bulk band. Our model, being a mixture of three-dimensional Bernevig–Hughes–Zhang and two-dimensional pseudospin-1 Hamiltonian, allows explicit treatment of the topological surface state evolution by continuously changing the hybridization between the inverted bands and an additional ‘parasitic’ flat band in the bulk. We show that the hybridization with a flat band lying below the edge of the conduction band converts the initial Dirac-like surface states into a branch below and one above the flat band. Our results univocally demonstrate that the upper branch of the topological surface states is formed by Dyakonov–Khaetskii surface states, known for HgTe since the 1980s. Additionally we explore an evolution of the surface states and the arising of Fermi arcs in Dirac semimetals when the flat band crosses the conduction band.

We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle θ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at θ 1⁄4 0, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only ten period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nanomechanical devices.

In this paper, magnetoplasmonic manipulation of near-field radiative heat transfer (NFRHT) is realized using two twisted graphene gratings. As a result of the quantum Hall regime of magneto-optical graphene and the grating effect, three types of graphene surface plasmon polaritons (SPPs) modes are observed in the system: near-zero modes, high-frequency hyperbolic modes, and elliptic modes. The elliptic SPPs modes, which are caused by the combined effect of magnetic field and grating, are observed in the graphene grating system for the first time. In addition, the near-zero modes can be greatly enhanced by the combined effect grating and magnetic field, rendering graphene devices promising for thermal communication at ultra-low frequency. In particular, the near-zero modes result in a unique enhancement region of heat transfer, no matter for any twisted angle between gratings. The combined effect of grating and magnetic field is investigated simultaneously. By changing the strength of magnetic field, the positions and intensities of the modes can be modulated, and hence the NFRHT can be tuned accordingly, no matter for parallel or twisted graphene gratings. The magnetic field endows the grating action (graphene filling factors and twisted angles) with a higher modulation ability to modulate the NFRHT compared with zero-field. Moreover, the modulation ability of twist can be tuned by the magnetic field at different twisted angles. In sum, the combined effect of magnetic field and grating provides a tunable way to realize the energy modulation or multi-frequency thermal communications related to graphene devices.