Competing orders at higher-order Van Hove points

Abstract

Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective lowenergy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

“…However, the magnitudes of the eigenvalues can be affected by, e.g., the coupling between renormalizations in the particle-particle and particle-hole channels (this effect is captured within, e.g., parquet and functional RG). In particular, an attraction in a d-wave Pomeranchuk channel can potentially become the strongest, as it was argued to happen in other systems 67 . We argue in Sec.…”

“…Such an order has recently been studied in Ref. 67. The total spin order parameter with this configuration winds twice around the unit circle.…”

Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone

“…Such divergence can lead to significantly different phase diagram from the one at the conventional Van Hove singularity. The manifestations of high-order Van Hove singularity has been investigated in the context of cuprate materials [44,45], doped intercalated graphene [46][47][48], strontium materials [49], bilayer graphene [50], and twisted bilayer transition metal dichalcogenide [51]. General discussions of the eligible band structures and locations of high-order Van Hove singularity have been conducted with complete classifications [52,53].…”

“…This fixed point possesses divergent susceptibilities without developing long-range orders in various channels, thereby manifesting itself as a supermetal. When the high-order Van Hove singularity occurs at multiple points, the system may develop ferromagnetism as a leading weak-coupling instability of our interest [48,50]. Superconductivity may also arise as a competing order.…”

“…In this work, we analyze the weakly repulsive electrons at the high-order Van Hove singularity in twisted bilayer graphene. Our study adopts the parquet RG analysis, which has been conducted at the conventional Van Hove singularity in square lattice [38,54,55], doped graphene [56], and twisted bilayer graphene [21][22][23][24], as well as at the high-order Van Hove singularity in doped intercalated graphene [48] and bilayer graphene [50]. Unlike [48,50] we consider a setting (relevant for twisted bilayer graphene) when the high-order Van Hove points occur away from the Brillouin zone boundary, which qualitatively alters the analysis.…”