Symmetry, Disorder and Transport Through Altermagnetic Quantum Dots and Their Antiferromagnetic Twins

TL;DR

This work analyzes transport through nanoscale altermagnetic quantum dots and their antiferromagnetic twins using tight-binding models and the Büttiker-Landauer framework. It finds that $C_4\mathcal{T}$ symmetry in altermagnetic dots forbids the anomalous Hall effect, while the $\mathcal{IT}$-symmetric antiferromagnetic twins show giant anomalous Hall responses; spin-Hall effects emerge when mirror symmetry is broken, and two-terminal spin filtering occurs only for altermagnetic dots. Disorder or lead configurations that break the relevant symmetries reintroduce all three effects in both classes, highlighting symmetry as a key design principle for nanoscale spin transport. Overall, the paper provides a symmetry-based map of when and how AHE, SH, and spin filtering appear in altermagnetic versus antiferromagnetic quantum dots, with implications for spintronic device engineering.

Abstract

Altermagnetic crystals resemble antiferromagnets in that they have no macroscopic magnetization, but unlike antiferromagnets they exhibit spin-split band structures. Here the transport properties of altermagnetic quantum dots and their antiferromagnetic twins are explored theoretically with the help of Landauer-Buttiker theory, symmetry considerations and tight-binding models. The influence of the symmetries of the quantum dots, their parent crystal lattices, their shapes and edges, lead arrangements and disorder on the anomalous Hall effect, the spin-Hall effect and spin filtering by the quantum dots are investigated.

Figures (11)

• Figure 1: (Color online). (a) An altermagnetic model quantum dot and leads with C$_4$$\mathcal{T}$ symmetry and (b) its antiferromagnetic twin and leads with $\mathcal{IT}$ symmetry. Red (blue) disks are sites with up (down) out of plane local spins. Wavy lines represent one dimensional ideal conductors (modeled as tight binding chains) each carrying a spin up and a spin down conducting channel. Four such conductors constitute each electrical lead contacting the quantum dot. In a Hall measurement leads 1 and 2 carry the electric current, leads 3 and 4 carry no current, and the Hall voltage drop is measured between leads 3 and 4. The quantum dots (a) and (b) are fragments of the altermagnetic and antiferromagnetic 1/5-depleted square lattice bulk crystals discussed in Ref. Zhu2025, respectively. The dot edges are of the armchair type. Images prepared using Macmolplt software.MacMolPlt
• Figure 2: (Color online). Absolute values of the Hall resistance vs. electron Fermi energy of the antiferromagnetic nanostructure in Fig.\ref{['start']} (b). Positive (negative) values of $R_\text{H}$ are shown in red (blue).
• Figure 3: (Color online). Spin-Hall conductance vs. electron Fermi energy of the altermagnetic (antiferromagnetic) nanostructure in Fig.\ref{['start']} (a) (Fig.\ref{['start']} (b)) shown in red (blue).
• Figure 4: (Color online). Spin filtering efficiencies $F_{\uparrow}$ (red) and $F_{\downarrow}$ (blue) vs. electron Fermi energy for the altermagnetic quantum dot in Fig.\ref{['start']}(a). $F_{\uparrow}$ and $F_{\downarrow}$ for the antiferromagnetic dot in Fig.\ref{['start']} (b)are shown in mauve.
• Figure 5: (Color online). Quantum dots (a) and (b) are fragments of the altermagnetic and antiferromagnetic 1/5-depleted square lattice bulk crystals respectively, as in Fig.\ref{['start']} but with leads attached to the corners of the dots, while preserving the overall C$_4$$\mathcal{T}$ symmetry and $\mathcal{IT}$ symmetry, respectively. Notation as in Fig.\ref{['start']}.