Topological magnetotransport in modified-Haldane systems

Abstract

We present a theoretical study of quantum magneto-transport and magneto-optical (M-O) properties in modified-Haldane model; which is applicable to diverse classes of two-dimensional (2D) quantum materials such as buckled Xene monolayers and transition metal dichalcogenide (TMDC) monolayers. By varying the staggered sublattice potential and intrinsic spin-orbit coupling, we identify distinct topological regimes and analyze their manifestations in the emergence of Landau levels, the evolution of the density of states, and the characteristics of M-O absorption spectra. Using the Kubo formalism, we compute the longitudinal and Hall M-O conductivities and show that inter-Landau-level (inter-LL) transitions produce characteristic resonance features that provide optical signatures of the underlying topological phases. Within this framework, we demonstrate electrically tunable topological phase transitions in buckled silicene. Extending our study to monolayer TMDCs, we show that inspite of large band gap, the spin-valley coupling provides a powerful tool for tailoring M-O absorption features across wide range of 2D materials. Collectively, these results underscore modified-Haldane-model materials as an ideal testbed for engineering quantum transport, with promising applications in topological photonics, valleytronic devices, and next-generation optoelectronics.

Figures (12)

• Figure 1: (a) Schematic of the modified-Haldane model on the 2D hexagonal lattice consisting of $A$ and $B$ sublattices with lattice constant $a_0$. The nearest neighbor(NN) hopping amplitude is denoted by $t_1$ while the complex next-nearest neighbor (NNN) hopping is given by $t_2 e^{+i \phi}\left(t_2 e^{-i \phi}\right)$ for the clockwise (anticlockwise) hopping paths. The on-site sublattice potential is $+M(-M)$ for $A(B)$ sublattice. (b) The first Brillouin zone of the 2D hexagonal lattice indicating high-symmetry points. (c) Phase diagram of the modified-Haldane model, where regions (i) and (ii) correspond to the TI phases, while regions (iii) and (iv) represent trivial BI phase.
• Figure 2: First column shows band structure of trivial BI and TI phases of modified-Haldane model i.e. LL spectrum (in units of eV) as function of magnetic field B (in units of Tesla). Second column plots the DOS $(D(E)/D_0)$ for both phases. The upper(down) row shows trivial(topological) phase. The dotted blue (dashed red) curves show $K$ and $K'$ valleys. We have taken $B=10$ T and $\Gamma=0.5$ meV and $t_2=0.05$ eV. For trivial (topological) case, $M=0.05(0)$ eV.
• Figure 3: (a) M-O conductivities for trivial phase. Both valleys show same M-O behavior. The blue and red curves represent $\mathrm{Re[\sigma_{xx}/\sigma_0]}$ and $\mathrm{Im[\sigma_{xy}/\sigma_0]}$ respectively. The first peak corresponds to $\Delta_{0\rightarrow1}$ (b) and (c) show M-O conductivities for TI phase in $K$ and $K'$ valley respectively. Dotted blue (dashed red) represent $\mathrm{Re[\sigma_{xx}/\sigma_0]}$ and $\mathrm{Im[\sigma_{xy}/\sigma_0]}$ in $K$ valley and and black (green) in $K'$ valley. The first peak corresponds to $\Delta_{-1\rightarrow0}$. We have taken $B=5$ T and $\Gamma=1$ meV. (d) Effect of $B$ on M-O response. We have plotted conductivities for TI in $K'$ valley at 3 different values of $B$ i.e. 5 T, 10 T and 15 T).
• Figure 4: Allowed transitions for trivial BI and TI phases. (a) In trivial regime, LLL is located at VB (CB) in $K(K')$ valley. So $\Delta_{0\rightarrow1}$ and $\Delta_{-1\rightarrow0}$ both occur at energy . (b) In TI, LLL is at CB so only $\Delta_{-1\rightarrow0}$ is allowed in both valleys and $\Delta_{0\rightarrow1}$ is Pauli-blocked.
• Figure 5: (a) LL spectrum of silicene in QSHI phase (in units of eV) as function of magnetic field B (in units of Tesla) parametrized by $M = 0.5\Delta_{so}$ at the $K$ and $K'$ valleys with up and down spin energy bands shown simultaneously. (b) The DOS $(D(E)/D_0)$ at two in-equivalent valleys $K$ and $K'$ shows negligible spin-splitting within each valley. The blue(red) curves represent up(down) spins in $K$ valley and black(green) curves represent up(down) spins in $K'$ valley. We have taken $B=0.5$ T and $\Gamma=0.5$ meV.