[Paper Review] Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory

Michał Papaj, Hiroki Isobe+1 more|arXiv (Cornell University)|Feb 1, 2018

Quantum Mechanics and Non-Hermitian Physics3 citations

TL;DR

This paper demonstrates that in two-dimensional Dirac fermions composed of two symmetry-unrelated orbitals, disorder with different scattering rates for each orbital induces a nodal arc in the electronic spectrum via non-Hermitian self-energy effects. Using renormalization group analysis and numerical simulations, the authors show that such disorder drives the system into a new strongly disordered phase with a tilted Dirac cone and a topologically robust nodal arc, replacing the clean Dirac point, due to momentum-independent but energy-dependent imaginary parts in the self-energy.

ABSTRACT

We show that Dirac fermion systems in two dimensions generally exhibit disorder-induced nodal arc replacing the nodal point and tilted Dirac cone, provided that the two components of the Dirac fermion correspond to two distinct orbitals unrelated by symmetry. This result is explicitly demonstrated using renormalization group analysis in a disordered Dirac model that we introduce, where the disorder potential acts differently on the two orbitals. As we show by numerical simulations and self-consistent Born approximation calculation, this drives the system into a new strongly disordered phase.

Motivation & Objective

• To investigate the effect of asymmetric disorder on two-dimensional Dirac fermions where the two components are not symmetry-related orbitals.
• To identify whether such disorder can lead to new quantum phases beyond the clean Dirac semimetal.
• To establish a connection between disorder-induced non-Hermitian effects and topological nodal arcs in 2D systems.
• To demonstrate the emergence of a new universality class in disordered Dirac fermions through renormalization group and numerical methods.

Proposed method

• A 2D Dirac Hamiltonian is introduced with distinct velocities along x and y directions, including a tilt parameter w to model a non-isotropic Dirac cone.
• Disorder is modeled via a spatially uncorrelated random potential acting differently on the two orbitals, parametrized by a Hermitian matrix η with asymmetric coupling.
• Renormalization group analysis is applied to show that the asymmetric disorder is marginally relevant, driving the system into a strongly disordered phase.
• Numerical simulations of a tight-binding model are performed with 2000 disorder realizations to compute the disorder-averaged retarded Green's function and spectral function A(k,ω).
• Self-consistent Born approximation is used to solve for the self-energy Σ(ω), enabling comparison with numerical results and confirming momentum-independent self-energy effects.
• The spectral function and density of states are computed from the averaged Green's function to visualize nodal arcs and band tilting.

Experimental results

Research questions

• RQ1 Can disorder with different scattering rates for two symmetry-unrelated orbitals in 2D Dirac fermions lead to a topological nodal arc?
• RQ2 What is the role of non-Hermitian self-energy effects in modifying the band structure of disordered Dirac systems?
• RQ3 Does asymmetric disorder drive the system into a new universality class distinct from conventional disordered Dirac phases?
• RQ4 How does the quasiparticle weight and lifetime differ between orbitals in the presence of such disorder?
• RQ5 Can the nodal arc and cone tilting be observed numerically and confirmed via self-consistent Born approximation?

Key findings

• The disorder-induced self-energy acquires an energy-dependent imaginary part that is orbital-specific, leading to different quasiparticle lifetimes.
• The renormalization group analysis shows that asymmetric disorder is marginally relevant, driving the system into a strongly disordered phase.
• Numerical simulations reveal a clear nodal arc in the spectral function A(k,ω), extending along the y-direction, with increasing length under stronger disorder.
• The nodal arc is confirmed by energy cuts at specific k-points, showing a single peak on the arc and two peaks off it, indicating a gapless line of degeneracy.
• The self-energy Σ(ω) exhibits a linear real part near the band touching point, which increases with disorder strength and induces cone tilting.
• The density of states shows a minimum that shifts to lower energies with increasing disorder, consistent with the self-energy shift and nodal arc formation.