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Interplay of Fermi surface topology and electron correlation is thequintessential ingredient underlying spontaneous symmetry breaking in itinerantelectronic systems. In one-dimensional (1D) systems at half-filling, theinherent Fermi surface nesting makes the translationally invariant metallicstate unstable, which is known as Peierls instability. Extending the scope ofPeierls instability to two (2D) or three dimensions (3D), however, is notstraightforward, since the Fermi surface in higher dimensions is generally notnested. In this work, we show that a perfectly nested Fermi surface can berealized in a class of 2D perovskite oxides, giving rise to 2D Peierlsinstability. Here the central role is played by the zone boundary Dirac linenode (DLN) protected by two orthogonal glide mirrors induced by the rotation ofoxygen octahedra. Especially, at a critical angle of the octahedron rotation,the zone-boundary DLN flattens, leading to logarithmically divergingsusceptibility. We propose the 2D Peierls instability driven by dispersionlessDLN as a principle mechanism for spontaneous symmetry breaking in variouslayered perovskite oxides including the antiferromagnetism of Sr$_2$IrO$_4$. Asa clear signature of the 2D Peierls instability, we predict that the magneticdomain wall in Sr$_2$IrO$_4$ hosts localized soliton modes.

Two-dimensional Peierls instability via zone boundary Dirac line nodes in layered perovskite oxides