A. Sinha, P. Roy
We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.
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By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac equation can be mapped into a Schrödinger-like equation by rescaling one of the two Dirac wave functions in the case of the position dependent mass. The energy levels, and the corresponding Dirac eigenfunctions are found analytically.
We establish a connection between an arbitrary Hermitian tight-binding model with chiral (C) symmetry and its non-Hermitian counterpart with chiral-time (CT ) symmetry.We show that such a non-Hermitian Hamiltonian is pseudo-Hermitian. The eigenvalues and eigenvectors of the non-Hermitian Hamiltonian can be easily obtained from those of its parent Hermitian Hamiltonian. It provides a way to generate a class of non-Hermitian models with a tunable full real band structure by means of additional imaginary potentials.We also present an illustrative example that could achieve a cone structure from t…
A Non-Hermitian Relativistic Oscillator Exactly Mapped to a Hermitian Schrodinger Problem
通过非厄米替换得到狄拉克振子，而厄米替换导致反演狄拉克振子，其势能无下界、能谱连续且本征函数不可归一化。本文证明该哈密顿量是伪-PT对称的，并通过非酉变换与标准狄拉克振子关联，给出精确解析解。
A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-hermitian operators, which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-hermitian relativistic quantum systems are presented by establishing/employ…
A method to construct non-Dirac-hermitian supersymmetric quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving both bosonic and fermionic degrees of freedom in terms of non-Dirac-hermitian operators which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. A pseudo-hermitian realization of the Clifford algebra for a pre-determined positive-definite metric is used to construct supersymmetric systems with one or many…
A non-Hermitian P$_ϕ$T$_ϕ$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_θ$, and H$_ϕ$ play essential roles and offer some user-feriendly options as to which one (or ones) of them is (or are) non-Hermitian. Considering a P$_ϕ$T$_ϕ$-symmetrized H$_ϕ$, we have shown that the conventional relativistic energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction $V(θ)$=0 in the descendant Hamiltonian H$_θ$ w…
Gouy Phase across PT-Symmetry Breaking in Non-Hermitian Dirac Systems
该研究探究非厄米狄拉克系统中PT对称破缺时的古伊相位行为，发现其可作为对称破缺阈值的灵敏探针，并提出通过损耗波导测量其分量的实验方案，展示了其在光子学领域的应用潜力。
It has been observed that a quantum theory need not to be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and we obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac charged particle in complex static and spherically symmetric potentials. Complex Dirac-Eckart, complex Dirac-Rosen-Morse II, complex Dirac-Scarf and complex Dirac-Poschl-Teller potential are investigated.
Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the two energy levels connected at this Dirac EP remain real in its vicinity and display a linear instead of square root dispersion, forming a tilted Dirac cone in the hybrid space consisting of a momentum dimension and a synthetic dimension for the strength of non-Hermiticity. In this report, we first present simple three-band and two-band matrix models with a …
Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian interactions. Spectral singularities and PT symmetry breaking of the Dirac Hamiltonian are shown to correspond to simple observable physical quantities and related to well-known physical phenomena like resonance narrowing and laser oscillation.
We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both the cases we show that the energy spectrum is real and all the other features of non-relativistic pseudo-Hermitian formulation are present. Using the spectral method the positive defin…
Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap, the phase transition is of universal form and described by a non-Hermitian Dirac equation with Lorentz-symmetry violation. A simple photonic system displaying such a phase transition is discussed, which is based on light coupling in co-propagating gratings.
Experimental observation of Dirac exceptional point
本文利用金刚石氮-空位中心实验观测到新型狄拉克例外点，验证其本征值简并且附近保持实数，并通过量子态层析确认其非厄米简并性质，为非厄米系统动力学和量子控制提供新视角。
Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension
通过非厄米性，一维系统在周期边界条件下实现随机狄拉克费米子普适类的内在临界性，揭示了谱拓扑驱动的退局域化机制。
Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional…
We study generalized Dirac oscillators with complex interactions in $(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $η$ pseudo Hermitian with respect to certain metric operators $η$. Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.
We present a large class of non-Hermitian non-PT-symmetric two-component Dirac Hamiltoninas with real energy spectra. These Hamiltonians are invariant under the combined action of "charge" conjugation (two-component transpose) and space-parity. Examples are given from the two subclasses of these systems having localized and/or continuum states with real energies.
We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creati…
The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a metric related to the strain tensor is discussed within the Pseudo-Hermitian operator theory. Furthermore, analytical solutions are obtained for two cases, namely, constant and position-dependent Fermi velocity.
Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses
该研究建立了磁场中实谱非厄米狄拉克费米子的平衡热力学标度关系，通过相似变换实现非厄米系统到厄米模型的映射，揭示了不同条件下的热与磁响应规律，为非厄米量子物质研究提供了热力学框架。
The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schrödinger equation. Despite the non-hermiticity of the effective potential, we find real energies for the fermion.
Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems $\mathcal{PT}$ symmetry gives rise to stable and protected Dirac points. Here, we study a $\mathcal{PT}$-symmetric system which is both non-Hermitian and topological, namely a $\mathcal{PT}$-symmetric Dirac semimetal with non-Hermitian perturbations in three dimensions. We find that, in general, there are only two types of symmetry allowed non-Hermitian perturbatio…
Multiple non-hermitian phase transitions on quantum torus surface
本文研究了受限于量子环面表面的单费米子Dirac方程的非厄米相变，通过tetrad形式和自旋联络考虑几何效应，数值计算旋量分量的本征值和本征函数，揭示了相变与环面几何特征及质量虚部大小的关系。
We present a new approach to study a class of non-Hermitian (1+1)-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well known Nikiforov-Uvarov method to solve such a system. We discuss applications and explore the solvability of both $\mathcal{PT}$-symmetric and non-$\mathcal{PT}$ symmetric classes of potentials. In the former case we obtain the solution of a harmonic oscillator in the presence of a linear vector potential while in the latter case we solve the shifted harmonic oscillator problem.
We identify and investigate two classes of non-Hermitian systems, i.e., one resulting from Lorentz-symmetry violation (LSV) and the other from a complex mass (CM) with Lorentz invariance, from the perspective of quantum field theory. The mechanisms to break, and approaches to restore, the bulk-boundary correspondence in these two types of non-Hermitian systems are clarified. The non-Hermitian system with LSV shows a non-Hermitian skin effect, and its topological phase can be characterized by mapping it to the Hermitian system via a non-compact $U(1)$ gauge transformation. In contrast, there ex…
Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
本研究通过无符号问题投影量子蒙特卡洛算法，研究非厄米不对称跳跃对蜂窝Hubbard模型的影响，发现其增强反铁磁序且临界行为符合XY普适类，暗示量子临界点厄米性涌现，方法可推广至其他非厄米模型。
Thermodynamic signatures of spectral compression in weakly non-Hermitian Dirac fermions
研究通过量子电容在狄拉克材料中探测非厄米特性，揭示非厄米效应在低能态和热力学密度中的普遍行为，以及磁场所致的Landau能级塌缩。
The modified Dirac-Pauli equations, which are introduced by means of ${γ_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention to their (g-2) gyromagnetic factor. The basis of this approach is developing of methods for study of the structure of regions of unbroken $\cal PT$ symmetry of Non-Hermitian Hamiltonians which be no studied earlier. For that, without the use of perturbation theory in the external field the exact energy spectra are deduced with re…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal PT}$-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well-known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here…
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to investigate the underlying physics in a different perspective. For particles with small mass such as the neutrino, the leading order equation has a Hermitian effective Hamiltonian, implying there is no leakage between the upper and lower spinors. In the weak relativistic regime, the leading order corresponds to a non-Hermitian correction to the Pauli equation,…
Dirac monopole magnets in non-Hermitian systems
本文理论上证明非厄米微扰可将点状狄拉克单极子转化为扩展分布，揭示了微小能量差与复几何相移间的定量关系，并提出利用耗散两分量Bose-Einstein凝聚体孤子动力学直接测量该拓扑特征的方案。
It has been observed that a quantum mechanical theory need not to be Hermitian to have a real spectrum. In this paper we obtain the eigenvalues of a Dirac charged particle in a complex static and spherically symmetric potential. Furthermore, we study the Complex Morse and complex Coulomb potentials.
Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and Schrodinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H(r), H(theta), and H(phi) play essential roles and offer some "user-feriendly" options as to which one (or ones) of them is (or are) non-Hermitian. Considering a P(phi)T(phi)-symmetrized H(phi), we have shown that the conventional Dirac (relativistic) and Schrodinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, settin…
Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or surfaces. They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point. The annihilation of 2D Dirac points carrying opposite charges has been experimentally reported. It remained elusive for Weyl points and second order EPs terminating different Fermi arcs. Here, we observe the annihilation of second or…
Jia and Dutra (J. Phys. A: Math. Gen. 39 (2006) 11877) have considered the one-dimensional non-Hermitian complexified potentials with real spectra in the context of position-dependent mass in Dirac equation. In their second example, a smooth step shape mass distribution is considered and a non-Hermitian non - PT- symmetric Lorentz vector potential is obtained. They have mapped this problem into an exactly solvable Rosen-Morse Schrodinger model and claimed that the energy spectrum is real. The energy spectrum they have reported is pure imaginary or at best forms an empty set. Their claim on the…
We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, satisfying $|r| ^{2}+|t| ^{2}=1$, i.e., the Dirac probability current is conserved, when one of two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional PT-symmetric potentials, which is more feasible in experiment. Exactly solvable model is presented to illustrate the theor…
The monopole for the geometric curvature is studied for non-Hermitian systems. We find that the monopole contains not only the exceptional points but also branch cuts. As the mathematical choice of branch cut in the complex plane is rather arbitrary, the monopole changes with the branch-cut choice. Despite this branch-cut dependence, our monopole is invariant under the $GL(l,\mathbb{C})$ gauge transformation that is inherent in non-Hermitian systems. Although our results are generic, they are presented in the context of a two-mode non-Hermitian Dirac model. A corresponding two-mode Hermitian s…
Hermitian Kirkwood-Dirac real operators for discrete Fourier transformations
针对量子态在不同物理相关转移矩阵下是否为KD正态的关键问题，本工作证明当转移矩阵为任意有限维离散傅里叶变换矩阵时，任何KD正态都可表示为纯KD正态的实线性组合。
In this article we study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on $C_4$-symmetric non-Hermitian systems where we investigate inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetric models of NHHODSMs having real bulk spectra. We show that they exhibit the striking property that the bulk and surfaces are anti-PT and PT symmetric, respectively, and so belong to two different topological classes realizing a novel non-Hermitian topological phase which we call a \emph{hybrid-PT topological phases}. Interestingly, while the bulk spectrum is still fully …
Curvature-Flux Representation of Local Dirac-Node Topology from Non-Hermitian Zeeman Quantum Geometry
本文研究了非厄米特性Zeeman量子几何张量，揭示了其分解为正常与异常度曲率部分，并探讨了局部狄拉克节点拓扑与可测量输运特征的联系。
Quasiparticle states in Dirac systems with complex impurity potentials are investigated. It is shown that an impurity site with loss leads to a nontrivial distribution of the local density of states (LDOS). While the real part of defect potential induces a well-pronounced peak in the density of states (DOS), the DOS is either weakly enhanced at small frequencies or even forms a peak at the zero frequency for a lattice in the case of non-Hermitian impurity. As for the spatial distribution of the LDOS, it is enhanced in the vicinity of impurity but shows a dip at a defect itself when the potenti…
The modified Dirac-Pauli equations, which is entered by means of ${γ_5}$-mass extension of Hamiltonian operators, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention on (g-2) gyromagnetic factor of particles with spin $1/2$. Without the use of perturbation theory in the external field the exact energy spectra are deduced with regard to spin effects of fermions. We discuss the possible proposals of experimental measuring of properties of new particles which arising in this model.
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic evolution of non-Hermitian quantum systems. We find that the adiabatic evolution is possible only when the eigen-energies are real. The accompanying geometric phase is found to be generally complex and associated with not only the phase of a wavefunction but also its amplitude. The condition for the real geometric phase is laid out. Our results are illustrated …
We propose a pair of the complex Berry curvatures associated with the non-Hermitian Hamiltonian and its Hermitian adjoint to reveal new physics in non-Hermitian systems. We give the complex Berry curvature and Berry phase for the two-dimensional non-Hermitian Dirac model. The imaginary part of the complex Berry phase induces the quantum Hall susceptance such that the quantum Hall conductance is generalized to quantum Hall admittance for non-Hermitian systems, which implies that the non-Hermiticity of systems could induce an intrinsic quantum capacitance or inductance of systems depending on th…
Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
本文在非厄米量子哈密顿量框架内引入非厄米费米-狄拉克分布，导出基于复谱的持续电流解析表达式，发现电流在例外点无异常且仅在磁化率中显现，为平衡态非厄米系统多体可观测量计算提供了通用框架。
A non-Hermitian PT-symmetric system can have full real spectrum but does not ensure probability preserving time evolution, in contrast to that of a Hermitian system. We present a non-Hermitian two-band model, which is comprised of dimerized hopping terms and staggered imaginary on-site potentials, and study the dynamics in the exact PT-symmetric phase based on the exact solution. It is shown that an initial state, which does not involve two equal-momentum-vector eigenstates in different bands, obeys perfectly probability-preserving time evolution in terms of the Dirac inner product. Beyond thi…
We calculate the bound-state energy spectrum of the Dirac Equation in a Schwarzschild black hole background using a minimax variational method. Our method extends that of Talman to the case of non-Hermitian interactions, such as a black hole. The trial function is expressed in terms of a basis set that takes into account both the Hermitian limit of the interaction in the non-relativistic approximation, and the general behaviour of the solutions at the origin, the horizon and infinity. Using this trial function an approximation to the full complex energy bound-state spectrum is computed. We stu…
Non-hermitian phase transitions on a generalized Ellis-Bronnikov wormhole bridge
本文研究量子虫洞表面上单费米子的非厄米相变，通过tetrad形式和自旋联络处理几何效应，数值求解狄拉克方程，探讨虫洞几何特征与质量虚部对相变的影响。
We present a mathematical formalism of non-Hermitian quantum mechanics, following the Dirac-von Neumann formalism of quantum mechanics. In this formalism, the state postulate is the same as in the Dirac-von Neumann formalism, but the observable postulate should be changed to include para-Hermitian operators (spectral operators of scalar type with real spectrum) representing observable, as such both the measurement postulate and the evolution postulate must be modified accordingly. This is based on a Stone type theorem as proved here that the dynamics of non-Hermitian quantum systems is governe…
Heat-Kernel approach to the Atiyah--Singer Index of Non-Hermitian Dirac Operators
研究非厄米特狄拉克算子的指标是否受拓扑保护，通过热核方法证明其在满足一定条件时具有拓扑保护性。
We theoretically investigate the emergence of non-hermitian physics at the heterojunction of a type-II Dirac semi-metal (DSM) and a dirty superconductor (DSC). The non-hermiticity is introduced in the DSM through the self-energy term incorporated via the dirtiness of the superconducting material. This causes the spectra of the effective Hamiltonian to become complex, which gives rise to the appearance of the exceptional points (EPs). This complex self energy, apart from having a frequency dependence, also acquires spatial dependence as well, which is unique and can provide interesting effects …
We study the dynamical behavior of a non-Hermitian moire superlattice system, which consists of two-coupled SSH chains with staggered imaginary on-site potentials. There are two main spatial regions, in which systems are in unbroken symmetric phases with fully real spectrum, appearing periodically along the ladder. We show that the two quantum phases are dimerized and tetramerized, which determine the distinct dynamical behaviors. Dirac probability can oscillate periodically, increase quadratically and increase exponentially, which correspond to the unbroken phase, exceptional point and the br…
Relativistic Path-Integral Origin of the Dirac Equation, Quantum Collapse, Decoherence and Non-Hermitian Phenomena
本文通过构建自洽的相对论路径积分，揭示了量子测量的动态机制，并推导出退相干和非厄米特描述的原理，同时提出通过工程有色噪声加速量子态缩减的新方法。
A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra …
An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here we show that such a transformation can be performed in momentum space as well, which reveals that certain gain and loss modulated systems in their parity-time (PT) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a PT transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP i…
Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
本研究利用散射技术通过谱奇点探索狄拉克半金属的新特性，发现二向色性狄拉克半金属可产生12种独特拓扑激光类型，并揭示了θ项在拓扑性质中的明确作用。
Distinguishing between Dirac and Majorana neutrinos using temporal correlations
本文首次在两味中微子PT对称非厄米哈密顿量框架下利用Leggett-Garg不等式的时间关联区分狄拉克与马约拉纳中微子，并展示优化参数下K4和K3的差异分别可达约15%和10%。
We present the observation of diabolic points in Hermitian and non-Hermitian electronics dimers. The condition of unbreakable Parity-time symmetry is established for both PT-symmetric ZRC and RLC dimers. We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. When a non- Hermitian perturbation is added in the setup, the non-Hermitian diabolic point (NHDP) turns into a ring of exceptional points as in some Dirac and Weyl semimetals. Some experimental simulations of oscillations around these particular points in LTspice are…
In this work we consider a generalization of the symmetry classification of topological insulators to non-Hermitian Hamiltonians which satisfy a combined $PT$-symmetry (parity and time-reversal). We show via examples, and explicit bulk and boundary state proofs that the typical paradigm of forming topological insulator states from Dirac Hamiltonians is not compatible with the construction of non-Hermitian $PT$-symmetric Hamiltonians. The topological insulator states are $PT$-breaking phases and have energy spectra which are complex (not real) and thus such non-Hermitian Hamiltonians are not co…
We investigate the impact on basic quantum transport properties of disorder-induced exceptional points (EPs) that emerge in a disorder-averaged Green's function description of two-dimensional (2D) Dirac semimetals with spin- or orbital-dependent potential scattering. Remarkably, we find that EPs may promote the nearly vanishing conductance of a finite sample at the Dirac point to a sizable value that increases with disorder strength. This striking behavior exhibits a strong directional anisotropy that is closely related to the Fermi arcs connecting the EPs. We corroborate our results by numeri…
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