[Paper Review] Exceptional Heavy-Fermion Semimetals in Three Dimensions

Yu-Liang Tao, Tao Qin+1 more|arXiv (Cornell University)|Nov 5, 2021

Advanced Materials Characterization Techniques4 citations

TL;DR

This paper proposes a novel three-dimensional exceptional heavy-fermion semimetal phase in a periodic Anderson model with broken inversion symmetry, where finite-temperature effects transform Weyl points into Weyl exceptional rings and eventually into two exceptional rings hosting bounded bulk Fermi tubes. Using dynamical mean-field theory and perturbation theory, the study demonstrates experimentally accessible spectral signatures of these topological Fermi tubes via angle-resolved photoemission spectroscopy.

ABSTRACT

Topological heavy-fermion systems in three dimensions are usually classified as topological insulators or semimetals. Here, we theoretically predict a different type of heavy-fermion system (dubbed exceptional heavy-fermion semimetal) by studying a three-dimensional periodic Anderson model consisting of strongly correlated localized $f$ electrons and itinerant conduction $c$ electrons in a zincblende lattice. Due to the breaking of inversion symmetry, the quasiparticle lifetimes at different sublattices are distinct, leading to the emergence of Weyl exceptional rings in the complex pole of the Green's function at finite temperatures; such rings lead to the appearance of bounded Fermi surfaces (bulk Fermi disks). As temperatures rise, two pairs of Weyl exceptional rings merge into two exceptional rings with one bounded bulk Fermi surface (bulk Fermi tube), which are experimentally measurable by angle-resolved photoemission spectroscopy. Finally, we use the dynamical mean field theory to calculate the spectral functions which illustrate the emergence of bulk Fermi tubes. Our work thus opens the door for studying exceptional heavy-fermion semimetal phases in three dimensions.

Motivation & Objective

• To explore the emergence of topological Fermi surfaces with boundaries in three-dimensional strongly correlated systems beyond Hermitian noninteracting models.
• To investigate whether bulk Fermi surfaces with finite boundaries can arise in realistic 3D heavy-fermion materials due to non-Hermitian effects from quasiparticle decay.
• To identify a new class of topological phase—exceptional heavy-fermion semimetals—characterized by exceptional rings and bounded Fermi surfaces in the complex pole of the Green’s function.
• To provide a theoretical framework and numerical evidence for experimentally observable signatures of these phases using spectral functions and DMFT calculations.

Proposed method

• Formulates a 3D periodic Anderson model on a zincblende lattice with A and B sublattices, incorporating localized f-electrons, itinerant c-electrons, and hybridization.
• Applies second-order perturbation theory to derive the effective non-Hermitian Hamiltonian, showing that broken inversion symmetry leads to sublattice-dependent quasiparticle lifetimes.
• Identifies the emergence of Weyl exceptional rings in the complex energy plane at finite temperature, evolving from Weyl points.
• Uses dynamical mean-field theory (DMFT) to compute the spectral functions, revealing the formation of bulk Fermi tubes in momentum space.
• Analyzes the real and imaginary parts of the energy spectrum and spectral functions to identify the evolution of exceptional rings and Fermi surface topology.
• Validates the Mott transition and site-selective behavior via Matsubara Green’s functions and quasiparticle weights, confirming distinct insulating/metallic responses on A and B sublattices.

Experimental results

Research questions

• RQ1 Can topological Fermi surfaces with finite boundaries emerge in three-dimensional strongly correlated systems beyond conventional Hermitian topological semimetals?
• RQ2 How do finite-temperature effects and broken inversion symmetry lead to the formation of exceptional rings in the Green’s function's complex pole?
• RQ3 What is the evolution of the Fermi surface topology as temperature increases, and can it transition from Fermi disks to Fermi tubes?
• RQ4 Can the spectral functions computed via DMFT reveal experimentally observable signatures of these exceptional semimetal phases?
• RQ5 How does the site-selective Mott transition on A and B sublattices relate to the emergence of non-Hermitian topological features?

Key findings

• At finite temperature, Weyl points in the effective Hamiltonian evolve into Weyl exceptional rings with bounded Fermi disks due to sublattice-dependent quasiparticle lifetimes.
• As temperature increases further, two pairs of Weyl exceptional rings merge into two exceptional rings hosting a single bounded Fermi surface in the form of a bulk Fermi tube.
• The spectral functions computed via DMFT clearly show the emergence of bright, extended regions around zero energy along the Fermi tube, confirming its existence in momentum space.
• The spectral function exhibits two distinct branches: a sharp, narrow peak (blue) with small imaginary part and a broad, weak peak (red) with large imaginary part, explaining the visibility of only one branch.
• The Mott transition is site-selective: sublattice A undergoes a metal-to-insulator transition with increasing U, while sublattice B remains metallic, consistent with broken inversion symmetry.
• The imaginary parts of the Matsubara Green’s function and quasiparticle weights confirm the Mott transition and the non-equivalent behavior of f-electrons on A and B sublattices.