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We investigate the finite size effects of a three-dimensional second-order topological insulator with fourfold rotational symmetry and time-reversal symmetry. Starting from the effective Hamiltonian of the three-dimensional second-order topological insulator, we derive the effective Hamiltonian of four two-dimensional gapped surface states by perturbative methods. Then, the sign alternation of the mass term of the effective Hamiltonian on the adjacent surface leads to the hinge state. In addition, we obtain the effective Hamiltonian and its wave function of one-dimensional gapless hinge states with semi-infinite boundary conditions based on the effective Hamiltonian of two-dimensional surface states. In particular, we find that the hinge states on the two sides of the same surface can couple to produce a finite energy gap. [ABSTRACT FROM AUTHOR]

The Seebeck effect in graphene with uniform Kekulé lattice distortion has been studied using the tight-binding model combined with the nonequilibrium Green's function method. The numerical results of this work show that the Seebeck coefficient of the O-shaped Kekulé graphene can be enhanced by modulating the gate voltage. At room temperature (T ≈ 300 K), the Seebeck coefficient for the armchair nanoribbon is S c ≈ 1370 μV/K and for the zigzag nanoribbon is S c ≈ 1260 μV/K. At low temperature (T ≈ 128 K), the Seebeck coefficient for the armchair nanoribbon is S c ≈ 2500 μV/K. In addition, the nano-structuration of the O-shaped Kekulé graphene layer induces an anisotropic behavior in the Seebeck effect. Our work provides an idea for the fabrication of efficient and controllable thermoelectric effect devices. [ABSTRACT FROM AUTHOR]

The Nernst and Seebeck effects in graphene with uniform Kekulé lattice distortion have been studied using the tight-binding model combined with the nonequilibrium Green's function method. Numerical results of this work showed that due to the electron–hole symmetry, the Nernst coefficient is an even function of the Fermi energy, while the Seebeck coefficient is an odd function regardless of the magnetic field. The Nernst and Seebeck coefficients show peaks when the Fermi energy crosses the Landau levels at high magnetic fields or crosses the transverse subbands at the zero magnetic fields. The peak height can be very large when the Fermi energy approaches the Dirac point, the Seebeck coefficient can reach about 0.78 mV/K, and the Nernst coefficient can reach about 0.95 mV/K at the corresponding hopping energy modification parameter δ = 0.03 and T = 0.009 t / k B ≈ 288 K. When δ = 0.08 and T = 0.024 t / k B ≈ 766 K, the Seebeck coefficient (or Nernst coefficient) is still up to about 0.78 mV/K (or 0.95 mV/K). This suggests that tunable Seebeck and Nernst coefficients can be achieved because the bandgap is a function of the corresponding hopping energy modification parameter δ. Experimentally, δ can be modulated by changing the type and amount of atoms adsorbed on graphene. In strong magnetic fields, the Nernst coefficient does not depend on the chirality of the nanoribbon. [ABSTRACT FROM AUTHOR]

Performing the non-equilibrium Green's function method, we calculate the Seebeck coefficient (S) and the thermoelectrical figure of merit (Z T) in the quantum anomalous Hall insulator-topological superconductor-quantum anomalous Hall insulator hybrid structure with temperature gradient. It is found that a high thermoelectrical figure of merit can be achieved with the helical topological superconductor phase. The S and the Z T are mainly affected by the temperature and the device size. At a certain temperature and the right device size, the Seebeck coefficient and the figure of merit can reach very high values. [ABSTRACT FROM AUTHOR]

We have studied in detail the influence of same-orbit and different-orbit hopping disorders in HgTe/CdTe quantum wells. Intriguingly, similar to the behavior of the on-site Anderson disorder, a phase transition from a topologically trivial phase to a topological phase is induced at a proper strength of the same-orbit hopping disorder. For different-orbit hopping disorder, however, the phase transition does not occur. The results have been analytically verified by using effective medium theory. A consistent conclusion can be obtained by comparing phase diagrams, conductance, and conductance fluctuations. In addition, the influence of Rashba spin-orbit interaction (RSOI) on the system has been studied for different types of disorder, and the RSOI shows different influence on topological phase at different disorders. The topological phase induced by same-orbit hopping disorder is more robust against the RSOI than that induced by on-site Anderson disorder. For different-orbit hopping disorder, no matter whether the RSOI is included or not, the phase transition does not occur. The results indicate, whether or not the topological Anderson insulator can be observed depends on a competition between the different types of the disorder as well as the strength of the RSOI in a system. [ABSTRACT FROM AUTHOR]