Floquet-driven thermal transport in topological Haldane lattice systems

Abstract

In this paper, we employ a modified Haldane lattice model to investigate the light-driven, spin- and valley-dependent anomalous Nernst effect in two-dimensional hexagonal topological systems. We demonstrate that two-dimensional buckled materials exhibit a hierarchy of electrically and optically tunable topological phases when subjected to off-resonant circularly polarized light in the presence of intrinsic spin-orbit coupling and a staggered sublattice potential. Within a Berry-curvature-driven transport framework, we systematically analyze charge-, spin-, and valley-resolved anomalous Nernst responses and identify their correspondence with distinct topological regimes. A finite charge Nernst conductivity arises under optical driving combined with spin-orbit coupling, whereas the generation of a pure valley Nernst current requires the simultaneous presence of sublattice asymmetry and off-resonant light. Substrate-induced inversion asymmetry further enables thermally driven valley currents with tunable magnitude and sign. We find that single-spin and single-valley Nernst responses occur in selected insulating and metallic phases, while the valley Nernst signal is suppressed in spin-polarized and anomalous quantum Hall phases. Extending our analysis to monolayer MoS$_2$, we show that strong spin-orbit coupling and broken inversion symmetry allow fully spin- and valley-polarized Nernst currents over a broad energy window. The temperature dependence of the Nernst response exhibits characteristic signatures of topological phase transitions, establishing the anomalous Nernst effect as a sensitive probe of field-engineered band topology in two-dimensional Dirac materials.

Figures (9)

• Figure 1: The phase diagram of a monolayer crystal as a function of $M/\lambda_{\textit{so}}$ and $\lambda_{\omega}/\lambda_{\textit{so}}$ in the left panel (a). The distinct electronic phases are labeled by different colors and are indexed by the total, spin, and valley Chern numbers ($\mathcal{C}$, $\mathcal{C}_{s}$ and $\mathcal{C}_{v}$). Band structure of the buckled Xene materials at the $K$ valley for different topological regimes is shown in the right panel. (b) QSHI ($M=0.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (c) VSPM ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (d) BI ($M=1.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (e) SPM ($M=0$, $\lambda_{\omega}=\lambda_{\text{so}}$), (f) AQHI ($M=0$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) and (g) PS-QHI ($M=\lambda_{so}$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) respectively. The corresponding phases of the band structures are indicated in the phase diagram. The blue (magenta) curves are for spin-up (down).
• Figure 2: The Barry curvature of the modified-Haldane model material along high-symmetry points in distinct topological phases at K and $K^{'}$ valleys including spin, valley, and Floquet-engineered (time-periodic) symmetry-breaking term. (a) Topological, (b) Trivial, (c) QSHI ($M=0.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (d) VSPM ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (e) BI ($M=1.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (f) SPM ($M=0$, $\lambda_{\omega}=\lambda_{\text{so}}$), (g) AQHI ($M=0$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) and (h) PS-QHI ($M=\lambda_{so}$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) respectively. The blue, orange, and green colors are for the $N_c$, $N_s$, and $N_v$, respectively.
• Figure 3: The charge, spin, and valley Nernst conductivities in distinct topological phases at the $K$ and $K^{'}$ valleys. (a) QSHI ($M=0.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (b) VSPM ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (c) BI ($M=1.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (d) SPM ($M=0$, $\lambda_{\omega}=\lambda_{\text{so}}$), (e) AQHI ($M=0$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) and (f) PS-QHI ($M=\lambda_{so}$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) respectively The blue and red colors show the corresponding changes in the value $N_c$, $N_s$, and $N_v$ in different topological states shown in [Fig.\ref{['Energy']}].
• Figure 4: The charge, spin, and valley Nernst conductivities in distinct topological phases at the $K$ and $K^{'}$ valleys. (a) QSHI ($M=0.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (b) VSPM ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (c) BI ($M=1.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (d) SPM ($M=0$, $\lambda_{\omega}=\lambda_{\text{so}}$), (e) AQHI ($M=0$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) and (f) PS-QHI ($M=\lambda_{so}$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) respectively. The blue, orange, and green colors are for the $N_c$, $N_s$, and $N_v$, respectively.
• Figure 5: The anomalous Nernst conductivity of the modified-Haldane Model material including spin, valley, and Floquet-engineered (time-periodic) symmetry-breaking terms in distinct topological phases at the $K$ and $K^{'}$ valleys. (a) Topological, (b) Trivial, (c) QSHI ($M=0.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (d) VSPM ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (e) BI ($M=1.5\lambda_{\text{so}}$, $\lambda_{\omega}=0$), (f) SPM ($M=0$, $\lambda_{\omega}=\lambda_{\text{so}}$), (g) AQHI ($M=0$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) and (h) PS-QHI ($M=\lambda_{\text{so}}$, $\lambda_{\omega}=1.5\lambda_{\text{so}}$) respectively.