Magnetic properties of Dirac fermions in a buckled honeycomb lattice

Abstract

We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field Ez. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field (B), a distinct signature of the transition is seen in the derivative of the magnetization with respect to chemical potential (µ) which gives the quantization of the Hall plateaus through the Streda relation. When plotted as a function of the external electric field, the magnetization has an abrupt change in slope at its minimum which signals the VSPM state. The magnetic susceptibility (χ) shows jumps as a function of µ when a band gap is crossed which provides a measure of the gaps' variation as a function of external electric field. Alternatively, at fixed µ, the susceptibility displays an increasingly large diamagnetic response as the electric field approaches the critical value of the VSPM phase. In the VSPM state, magnetic oscillations exist for any value of chemical potential while for the TI, and BI state, µ must be larger than the minimum gap in the system. When µ is larger than both gaps, there are two fundamental cyclotron frequencies (which can also be tuned by Ez) involved in the de-Haas van-Alphen oscillations which are close in magnitude. This causes a prominent beating pattern to emerge.

Emergent elemental two-dimensional materials beyond graphene

“…Band-gap engineering may mitigate this problem: band gap may be switched on and off by strain [44]; alternatively, an external electric field applied in a direction perpendicular to the buckled lattice can induce charge imbalance between the sublattices, and open a band gap [44]. In addition, a variable perpendicular electric field can induce a phase transition from a topological insulator to a trivial band insulator, passing through a valley-spin polarized metal [45], and can also induce superconducting states when doped. A tunable quantum phase transition from a singlet chiral d + id'-wave pairing phase to a triplet f-wave phase could occur, provoking an increase in the superconducting critical temperature [46].…”

Valley-polarized magnetoconductivity and particle-hole symmetry breaking in a periodically modulated α−T3 lattice

“…Moreover, graphene and the α-T 3 lattice both exhibit particlehole symmetry breaking under the influence of both modulations. Very recently, the Carbotte group has shown that a small asymmetry in the energy band can be very sensitive to magneto-optical excitation 56,57 . Therefore, we conclude that the combination of both modulations can be used as a tool to break the particle-hole symmetry for manipulation of the valley degree of freedom in optical devices.…”

Unconventional quantum Hall effect in Floquet topological insulators

“…The results of Fig. 3(a), dashed curve, can be reduced to those of single-valley gapped graphene for ∆ h = 0 [26], irrespective of a factor of 2 due to valley degeneracy, and to those of gapped TIs [31]. However, for ∆ Ω > ∆ h = 0 only one surface must be considered, see Fig.…”