Related papers: Zero modes and index theorems for non-Hermitian Di…
In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this work, we develop a theoretical framework for…
Dirac points (DP) in Hermitian systems play a key role in topological phenomena. Their existence in non-Hermitian systems is then desirable, but the addition of loss or gain transforms DPs into pairs of Exceptional Points (EPs) joined by a…
We numerically demonstrate that the topological corner states residing in the corners of higher-order topological insulator possess non-Abelian braiding properties. Such topological corner states are Dirac fermionic modes other than…
Lorentz spacetime symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum…
Exotic quantum phases and phase transition in the strongly interacting Dirac systems has attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment,…
Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising example of non-Abelian anyons. On the…
The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous…
The fixed point Dirac operator on the lattice has exact chiral zero modes on topologically non-trivial gauge field configurations independently whether these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$, where $n_L$…
Due to their iconic linearly vanishing density of states near the zero-energy, half-filled two-dimensional Dirac materials in flat Euclidean and negatively-curved hyperbolic spaces exhibit dynamic mass generation only once a critical…
We present the electronic properties of massless Dirac fermions characterized by geometry and topology on a graphene sheet in this chapter. Topological effects can be elegantly illuminated by the Atiyah-Singer index theorem. It leads to a…
Non-Hermitian (NH) Dirac semimetals describe open gain--loss systems. Yet at charge neutrality, models featuring real spectrum often look Hermitian-like, with NH effects absorbed into renormalized band parameters. Here, we show that a…
We propose a family of free fermion lattice models that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal…
We propose a lattice action including unphysical Wilson fermions with a negative mass m_0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0) cannot appear and…
We consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…
Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic…
When a Dirac fermion system acquires an energy-gap, it is said to have either trivial (positive energy-gap) or non-trivial (negative energy-gap) topology, depending on the parity ordering of its conduction and valence bands. The non-trivial…
Dirac materials, hosting linearly dispersing quasiparticles at low energies, exhibit an emergent Lorentz symmetry close to a quantum critical point (QCP) separating semimetallic state from a strongly-coupled gapped insulator or…
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…
In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a $(1+1)$-dimension flat spacetime.…
We study zero modes of Laplacians on compact and non-compact metric graphs with general self-adjoint vertex conditions. In the first part of the paper the number of zero modes is expressed in terms of the trace of a unitary matrix…