The emergence of net chirality in two-dimensional Dirac fermions system with altermagnetic mass

Abstract

In two-dimensional lattice systems, massless Dirac fermions undergo doubling, leading to the cancellation of net chirality. We demonstrate that the recently discovered altermagnetism can induce a unique mass term, the altermagnetic mass term, which gaps out Dirac cones with one chirality while maintaining the other gapless, leading to the emergence of net chirality. The surviving gapless Dirac cones retain identical winding numbers and exhibit the quantum anomalous Hall effect in the presence of the trivial constant mass term. When subjected to an external magnetic field, the altermagnetic mass induces Landau level asymmetry in Dirac fermions, resulting in fully valley-polarized quantum Hall edge states. Our findings reveal that Dirac fermions with the altermagnetic mass harbor rich physical phenomena warranting further exploration.

Figures (4)

• Figure 1: DFs without [(a) and (b)] and with [(c) and (d)] the altermagnetic mass in a 2D lattice. (a) and (c) show the band structures of $H_{\rm{DF}}$ and $H_{\rm{DFA}}$, respectively, with the color reflecting the absolute value of energy. (b) and (d) are the corresponding spin textures $\bm{S}$ of the negative-energy state, with the color reflecting the $S_z$ component. The unit of energy is ${v_F}$ and $m_{\rm Am}=0.4{v_F}$ is maintained throughout the paper.
• Figure 2: The band structure of gapless (a-c) and gapped (d-f, $m=-0.2{v_F}$) DFAs nanoribbons in the $x$-direction, with the width in the $y$-direction $L_y=100a$. (a) and (d) are complete energy bands. (b) and (e) are enlarged views of the Dirac cone near $\Gamma$ point, with the color reflecting the center of wavefunctions in the $y$-direction $\langle y \rangle$. (c) and (f) are the modular squares of the wavefunctions of the outermost states at $k_x=\pm0.05$.
• Figure 3: The quantum anomalous Hall effect of DFAs. (a) Schematic of a Hall bar with six leads (shown in gold), where the blue region is composed of Dirac materials with altermagnetic mass and Zeeman term, described by $H_{\rm{DFA}}+m\sigma_z$. The width of lead-L and R is $L_y=100a$, the width of lead-(1-4) is $L_x=50a$, and the spacing between the leads is $L_0=50a$. (b,c) The Hall resistances (b) and longitudinal resistances (c) versus $m$ with four different $E_F$. (d) The phase diagram ($R_H$ in the unit of $h/e^2$) with $E_F$ and $m$. (e) The comparison of the Chern number under a Zeeman term $m\sigma_z$ of $H_{\rm DFA}$, $H_{\rm DF}$, and graphene. The energy unit of $m$ of DFA and DF is ${v_F}$, and that of graphene is the nearest-neighbor hopping.
• Figure 4: The behavior of DFAs under magnetic fields. (a) The band structure of a DFA nanoribbon, with a width $L_y=100a$ and the magnetic flux $\phi=0.01$ (in the unit of $h/e$). (b) and (c) are the longitudinal and Hall resistances of the DFA Hall bar device versus $E_F$, which corresponds to the energy $E$ in (a). (d) The longitudinal (blue) and Hall (red) resistances versus $\phi$ with $E_F=0.2v_F$. (e,f) are the local density of states of two $100a\times 100a$ coupling DFA samples, with parallel [in (e)] and antiparallel [in (f)] Néel vectors. $E=0.2$, $\phi=0.03$, and the valley Chern numbers are shown in the insets.