Abstract
Large density of states may have competing effects on electronic properties of metals: enhanced susceptibility towards ordering and strong screening of electron repulsion. This work investigates electron interaction effects near a high-order Van Hove singularity, where the density of states shows a power-law divergence. By combining the mean-field and renormalization-group studies, the authors reveal a supermetal, a non-Fermi liquid metal with various divergent susceptibilities but no long range order due to scale invariance.
Highlights
A Bloch electron in a crystal is described by the energy dispersion Ek that relates the energy with its wave vector k
By introducing a small parameter associated with the density of states (DOS) divergence, we present a controlled renormalization group (RG) analysis and find that short-range repulsive interaction is relevant at the noninteracting fixed point and drives the system into a nontrivial T = 0 interacting fixed point
II, we introduce a tight-binding model with a high-order Van Hove singularities (VHS) and calculate the power-law divergent DOS, whose exponent is determined from the scaling property of energy dispersion near the high-order saddle point
Summary
A Bloch electron in a crystal is described by the energy dispersion Ek that relates the energy with its wave vector k. This allows us to formulate a continuum field theory of interacting fermions by taking the leading-order energy dispersion relation Ek near the saddle point and extending the range of momentum to infinity In this field theory, when the high-order VHS is right at the Fermi level, the Fermi surface in k space becomes scale invariant. The outline of the paper is as follows: In Sec. II, we introduce a tight-binding model with a high-order VHS and calculate the power-law divergent DOS, whose exponent is determined from the scaling property of energy dispersion near the high-order saddle point. The two-loop calculation shows the finite anomalous dimension of the fermion field at a high-order saddle point This result directly establishes the non-Fermi-liquid nature of an interacting supermetal.
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