Weyl-Transition-Driven Giant Reversible Orbital Hall Conductivity

Abstract

Orbital Hall conductivity (OHC) is a central ingredient of orbitronics, yet how to control it microscopically remains largely unexplored. Here we identify a general mechanism in which tilted Weyl crossings formed by orbitally distinct bands generate a strongly asymmetric orbital Berry curvature (OBC) distribution, whose imbalance survives Brillouin-zone integration and yields a sizable OHC already at zeroth order. Using first-principles calculations, we show that monolayer PtBi2 realizes this mechanism and hosts a giant OHC dominated by a type-II Weyl point. A small biaxial tensile strain drives a type-II $\rightarrow$ type-I $\rightarrow$ type-II Weyl transition, leading to a reversible sign change of the OHC through the evolution of the OBC imbalance. This process is governed by the chiral orbital texture of the crossing bands and is further assisted by a strain-induced first-order structural phase transition through bonding reconstruction and polarization change. Our results establish Weyl engineering of orbital quantum geometry as a powerful route to generating and reversibly controlling OHC in polar multi-orbital materials.

Figures (4)

• Figure 1: Weyl-point tilting–driven orbital Hall switching in the orbital Rashba model. (a) Schematic illustration of the strain-induced transition between different types of Weyl points. (b) Illustration of the OHC switching direction after the change in Weyl-point type. (c) Schematic orbital texture showing opposite chiral states: clockwise blue arrows and counterclockwise red arrows represent the $p_x - i p_y$ and $p_x + i p_y$ states, respectively. (d) Band structure of the orbital Rashba model with tilted Weyl points. Red and blue colors denote projections onto states with opposite chirality. The parameter $w$ controls the degree of Weyl-point tilting. (e) Distribution of OBC in the tight-binding (TB) model as a function of $w$. (f) Evolution of OHC in the orbital Rashba TB model as a function of Weyl-point tilting, where the color changes from blue to red correspond to $w$ varying from $-2$ to $2$.
• Figure 2: Crystal and electronic structure of monolayer PtBi$_2$. (a) Top view of the monolayer PtBi$_2$ crystal structure. The inset shows the Brillouin zone. (b) Side view of the monolayer structure. The central silver atoms correspond to Pt. The buckled structure consists of Bi atoms occupying Wyckoff 1a (top layer), 2b (second layer), and 3c (bottom layer) sites. The overall out-of-plane polarization points from the 1a layer toward the 3c layer. (c) Calculated exfoliation energy of monolayer PtBi$_2$. The inset illustrates the five-layer structure used in the calculation. (d) Phonon spectrum of monolayer PtBi$_2$. (e),(f) Orbital-resolved band structures of monolayer PtBi$_2$ without and with SOC, respectively. For clarity, only Bi orbital components are shown. Purple, orange, blue, red, and green dots represent Bi 1a $p_y$, 1a $p_z$, 2b $p_z$, 3c $p_x$, and 3c $p_y$ orbitals, respectively. The red dashed line indicates the Fermi level.
• Figure 3: Strain-driven evolution of OBC and OHC. (a) $k$-resolved OBC projected onto the band structure. Red and blue colors represent positive and negative OBC, respectively. The dashed circles highlight the dominant OBC contributions near the Fermi level. (b) OHC as a function of biaxial tensile strain. (c) Strain-dependent band structure with $k$-resolved OBC along the K--$\Gamma$ path, focusing on the region highlighted by the red box. (d) Distribution of BC near the Weyl points corresponding to (c) under different strain values.
• Figure 4: Structural phase transition and its electronic origin. (a) Strain dependence of the out-of-plane thickness between Bi 1a and Bi 2b atoms, showing an abrupt jump between 0.7% and 0.8%. (b) Evolution of the ferroelectric polarization under biaxial strain. (c) Schematic side view of the buckled Bi structure before and after the transition. The deformation is exaggerated for clarity; the dashed box marks the original configuration. (d) Strain-dependent $-$ICOHP for representative bonds: Bi 2b $p_x$--Bi 2b $p_x$, Bi 1a $p_z$--Bi 2b $p_z$, Bi 2b $p_z$--Bi 1a $p_x$, and Bi 2b $p_x$--Bi 1a $p_x$. (e) Orbital projections of Bi 1a (orange) and Bi 2b $p_z$ (blue) states. A degeneracy emerges near the type-I Weyl point at $+0.6\%$ strain due to overlapping DOS peaks. (f) Schematic illustration showing that splitting of DOS peaks lowers the total energy and drives the structural transition.