Marginal Metals and Kosterlitz-Thouless Type Phase Transition in Disordered Altermagnets

Abstract

Altermagnetism, a recently discovered magnetic phase characterized by spin-split bands without net magnetization, has emerged as promising platform for novel physics and potential applications. However, its stability against disorder-ubiquitous in real materials-remains poorly understood. Here, we study the electron localization properties of two-dimensional $d$-wave altermagnets subject to disorder. Remarkably, we discover a disorder-driven phase transition from a marginal metallic phase to an insulator, which falls into the Kosterlitz-Thouless class. We demonstrate this by strong numerical evidence and propose an interpretation in terms of vortex-antivortex pairs in the disorder-induced local in-plane spin magnetization. Moreover, we show that the characteristic spin anisotropy of altermagnets persists but gradually fades away across the transition. These changes directly affect the spin splitting features that are detectable in angle-resolved photoemission spectroscopy and tunneling magnetoconductance. Our findings provide a new perspective on recent experimental observations of altermagnetism in candidate materials.

Figures (12)

• Figure 1: (a) Momentum-resolved local density of states (LDOS) of the $d$-wave AM at disorder strength $W=2t$. (b) Normalized localization length $\text{$\lambda/L$}$ as a function of $W$ for increasing system width $L$. $\lambda$ is calculated on a long ribbon with width $L$ and length of $3\times10^{6}a$. (c) Single-parameter fitting of the correlation length $\xi$ near the KT-type phase transition, extracted from the data in (b). On the insulating side, $\xi$ scales as $\ln\xi\propto|W-W_{c}|^{-1/2}$, where $W_{c}$ denotes the critical disorder strength. Inset: Collapse of the data from (b) into a single curve under finite-size scaling. (d) Phase diagram in the $W$-$t_{J}$ plane. Other parameters are $t_{J}=0.3t$ and $\mu=-2t$.
• Figure 2: (a) Disorder-averaged logarithmic conductance $\langle\ln g\rangle$ as a function of $W$, with each point averaged over 3000 disorder configurations. (b) Scaling function $\beta\equiv\frac{d\langle\ln g\rangle}{d\ln L}$ extracted from (a). Other parameters are as the same as Fig. \ref{['fig1:main-result']}.
• Figure 3: (a) Averaged LSR $\langle r\rangle$ as a function of $W$. (b) Distribution of LSR in the metallic and insulating limits. We take $2\times10^{3}$ disorder configurations. Other parameters are as the same as Fig. \ref{['fig1:main-result']}.
• Figure 4: (a) Spin-resolved LDOS $A_{\sigma}({\bf k})$ (left and middle) and total LDOS $A({\bf k})=A_{\uparrow}({\bf k})+A_{\downarrow}({\bf k})$ (right) in momentum space for disorder strength $W=t$. (b) The same as (a) but for $W=6t$. We take $5\times10^{4}$ disorder configurations. Other parameters are $t_{J}=0.3t,$$\mu=-2t$, and $\eta=10^{-3}t$.
• Figure 5: (a) Schematic of the tunneling junction composed of two AM layers of length $L_{x}$ separated by an insulating barrier. The Néel vectors of two AM layers are configured to be either parallel (P) or antiparallel (AP). The system size is $L_{x}=10a$ and $L_{y}=40a$. (b) Tunneling conductances $G_{P}$ and $G_{AP}$ as functions of energy $E$ for the parallel and antiparallel configurations at $W=0$. (c) $G_{P}$ and $G_{AP}$ as functions of $W$ at different $E$. (d) TMC as a function of $W$. Inset: Energy spectrum of an AM ribbon of width $L_{y}=40a$ along $x$ direction. We take $2\times10^{4}$ disorder configurations. Other parameters are as the same as Fig. \ref{['fig1:main-result']}.