{"id":"70f0b065-30d1-45f6-9a2d-3f01eaa8ab82","arxiv_id":"1908.03345","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Disorder alone, without tilted bands or magnetism, can create exceptional rings and flat bands in the quasiparticle spectrum of Weyl and Dirac semimetals.","lead":"This paper predicts that random impurities in Weyl semimetals make the effective electron Hamiltonian non-Hermitian, turning each Weyl point into a ring of exceptional degeneracies and creating flat bands inside the ring. The effect works with ordinary, non-magnetic disorder and should be visible in photoemission or quasiparticle interference experiments on known semimetals.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The WER is defined from exceptional points of H0+Sigma(epsilon) at epsilon=ReSigma0, which are not poles of the retarded Green's function; the paper never checks that the actual coalescing poles lie on the physical sheet.","rationale":"I take the strongest claim to be that generic disorder in WSMs produces WERs and flat bands that are observable in ARPES/QPI. For that claim, the object that must contain the WER is the retarded spectral function, not merely the eigenvalues of a non-Hermitian model built from the self-energy. The paper's own pole definition in Sec. II is the right starting point; the self-consistent T-matrix calculation is a legitimate and internally consistent way to obtain the self-energy, and the unitarity-limit and Born-approximation checks in Sec. III C and Appendices B-C give the argument some independent support. The soft spot is the step from self-energy to exceptional ring: the WER condition is imposed at epsilon = ReSigma0(epsilon), but a fixed-frequency exceptional point of H0+Sigma(epsilon) is not a pole of G^R at that real frequency. One needs to solve the pole equation at complex epsilon and check that the coalescing poles are on the retarded sheet. This is a numerical check that can be done with the authors' own equations, and it would settle whether the ring is a physical spectral feature or an artifact of evaluating the self-energy on the real axis. I therefore partially agree with the reader's weakest assumption: the reader focuses on whether the averaged momentum-diagonal Green's function is the right physical object (vertex corrections, rare regions), whereas I focus on whether the paper's WER is actually a degeneracy of that object's poles. Both are conditions on the same central claim; neither is addressed by the manuscript beyond citing Ref. 12. The conditional verdict stands, with the pole-side consistency check as the explicit condition.","tokens_in":14455,"tokens_out":21716,"duration_ms":233119,"concrete_test":"Using the converged T-matrix self-energy from Eqs. (17)-(18), solve the full pole equation on a p mesh: for each p, find all complex epsilon with Im epsilon < 0 satisfying det[epsilon - H0(p) - Sigma(epsilon)] = 0, with Sigma evaluated at the root, and compute the discriminant. Check whether two retarded poles coalesce on a closed ring and whether the ring radius and p_z match the Sec. III B formulas. Also plot the retarded spectral function A(p,omega) = -2 Im G^R(p,omega) on the real axis near the ring and look for two-peak coalescence; if coalescence occurs only for Im epsilon > 0, the WER is an artifact of the real-energy approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is observable: WERs and flat bands should appear in ARPES/QPI, i.e., in the retarded spectral function. The paper's own definition in Sec. II is that quasiparticle poles are the complex solutions of det[epsilon - H0(p) - Sigma(epsilon)] = 0, approximated by the eigenvalues of H_eff in Eq. (2). The WER condition in Sec. III B, however, is not the pole condition. It states that for epsilon = ReSigma0(epsilon), p_z = +/- cos^{-1}(m - ReSigma_z(epsilon)), and sin^2 p_x + sin^2 p_y = |ImSigma_z(epsilon)/v|, the matrix H0(p)+Sigma(epsilon) is non-diagonalizable. At that point the single eigenvalue of that matrix is Sigma0(epsilon), so det[epsilon - H0 - Sigma] = (epsilon - Sigma0)^2 = -(ImSigma0)^2, which is generically nonzero. Thus the exceptional point of the fixed-frequency matrix is not a pole of G^R at that energy. The poles that actually coalesce are the complex roots of the full pole equation, evaluated self-consistently at the pole energy, and the paper neither solves that equation nor checks the sign of Im epsilon of the coalescing pole. If the common pole has Im epsilon > 0, it is an advanced pole and invisible in ARPES; if the two poles split into one retarded and one advanced inside the ring, the flat band is not a degeneracy of two quasiparticle peaks. A related gap is that the Sec. III A ring condition, Re[R'_z] = 0 and R'_x^2 + R'_y^2 = Im[R'_z]^2, assumes the transverse sum is real and non-negative; with the complex coefficients Sigma1_0, Sigma1_z in Eqs. (8)-(9) this is not shown, so the exceptional locus may not be the circle claimed. The spectral functions in Figs. 6 and 7 are plotted at epsilon = ReSigma0(epsilon) rather than at the self-consistent pole positions, so they do not settle the question.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies disorder-induced non-Hermitian effects in Weyl and Dirac semimetals. Using a two-band lattice model of a Weyl semimetal with randomly distributed impurities, the authors compute the disorder self-energy in the self-consistent T-matrix approximation and construct an energy-independent effective quasiparticle Hamiltonian. They argue that when the Weyl points deviate from symmetric points of the Brillouin zone and the impurity scattering is not in the unitarity limit, Weyl exceptional rings (WERs) and flat bands inside them are generically realized, independent of the details of the scattering potential. They further claim that at the transition to a topological Dirac semimetal the two WERs merge into a hybrid point ring, and they illustrate the scenario for a Cd3As2 model. The paper explicitly claims these features are observable in ARPES or quasiparticle interference experiments.","tokens_in":14924,"tokens_out":10898,"duration_ms":114330,"significance":"If the central claim is correct, the paper would substantially generalize earlier work that required tilted Weyl cones or magnetic impurities, establishing that generic disorder in almost any Weyl semimetal produces ring-shaped degeneracies of the effective quasiparticle Hamiltonian. The identification of the two conditions (deviation from the unitarity limit and deviation of the Weyl points from symmetric BZ points) is concrete and potentially testable in known materials such as Co3Sn2S2 and Cd3As2. The paper also provides a useful clarification that intra-valley multiple scattering, rather than inter-valley scattering or orbital-dependent potentials, is the origin of the effect. The analytical derivation of the self-energy structure is coherent, and the connection to non-Hermitian band topology is timely. However, the observability claim rests on a mapping between the defective fixed-frequency Hamiltonian and the actual poles of the retarded Green's function, which is not established in the manuscript.","major_comments":[{"comment":"The WER condition is defined for the fixed-frequency matrix H0(p)+Σ(ε) at ε = ReΣ0(ε), but at this point the retarded Green's function does not have a pole. Evaluating det[ε−H0−Σ] at ε = ReΣ0(ε) gives (ε−Σ0)^2 = −(ImΣ0)^2, which is generically nonzero because of the finite quasiparticle lifetime. The actual quasiparticle poles are complex solutions of det[ε−H0(p)−Σ(ε)] = 0, and the paper neither solves this equation nor checks whether the coalescing poles lie on the physical sheet (Im ε < 0). Without this check, the claimed flat bands and exceptional rings may not appear in the retarded spectral function measured by ARPES, and the central observable claim is unsupported. The appeal to Ref. [12] for real-space validation is not a substitute for a direct check of the pole condition in the present model.","section":"Sec. III B, Eq. (16)"},{"comment":"The exceptional-ring condition Re[R'_z] = 0 and R'_x^2 + R'_y^2 = Im[R'_z]^2 implicitly assumes that the transverse combination R'_x^2 + R'_y^2 is real and non-negative. From Eqs. (8) and (9), R'_x^2 + R'_y^2 = [(1−Σ1_0)^2 − (Σ1_z)^2] v^2(sin^2 px + sin^2 py), which is complex for generally complex coefficients Σ1_0 and Σ1_z. The actual condition for the radical in Eq. (11) to vanish is the complex equation R'_x^2 + R'_y^2 + R'_z^2 = 0, which may have different solutions or none. The paper does not justify neglecting the imaginary part of the transverse sum, so the existence of the WER is not rigorously established.","section":"Sec. III A, Eqs. (7)-(11)"},{"comment":"The effective Hamiltonian Heff is derived by truncating the frequency expansion of the self-energy at first order, Σ(ε) = Σ0 + Σ1ε + O(ε^2), and the self-consistent T-matrix equations are solved for real ε, with the WER evaluated at ε = ReΣ0(ε). The validity range of this linear expansion is not established; the values of |ImΣ_z/v| shown in Figs. 2 and 4 are not obviously small compared with the bandwidth, and the O(ε^2) terms could modify the ring condition. The paper should provide an estimate of the truncation error or, preferably, solve the pole equation at the complex pole energy to justify the approximation.","section":"Sec. II, Eq. (2), and Sec. III B"},{"comment":"The numerical solutions of the self-consistent T-matrix equations (17)-(18) are performed on a 35^3 momentum mesh with no convergence analysis, no specification of the i0+ broadening used to treat the Green's function singularities, and no error estimates. The WER radius and DOS results in Figs. 2-4 and the spectral functions in Figs. 5 and 7 are quantitative claims, and the reliability of these numbers is not demonstrated. Convergence tests with different mesh sizes and broadening parameters are needed to support the quantitative predictions.","section":"Sec. III B and Sec. V"}],"minor_comments":[{"comment":"The manuscript contains several typos: 'Fourior' in Sec. II, 'featrure' in Sec. III C, 'We, now, consider' in Sec. III A, and the inconsistent use of 'Weyl exceptional ring' versus 'hybrid point rings' in the title and abstract.","section":"Throughout"},{"comment":"The condition 'sin^2 px + sin 2 py = |ImΣ z(ǫ)/v|' is dimensionally inconsistent; it should be sin^2 px + sin^2 py = (ImΣ_z(ǫ)/v)^2 (up to model-dependent prefactors) to match the condition R'_x^2 + R'_y^2 = Im[R'_z]^2 in Sec. III A.","section":"Sec. III B"},{"comment":"The red solid curve is described as the unitarity limit (V0→∞, nimp→0), but the parameters used are V0=300, nimp=0.01; the text should clarify that this is an approximation to the limit and state the convergence check used.","section":"Fig. 3 caption"},{"comment":"References [3] and [5] share the same arXiv number 1902.08479; please verify the correct identifiers, as the titles and author lists differ.","section":"References"},{"comment":"The Hamiltonian uses 'mp' in h(p) but defines 'm_k' in the following line; the notation should be made consistent.","section":"Sec. V, Eq. (23)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely and important question, and the qualitative mechanism is plausible. The main risk is the mapping from the defective fixed-frequency Hamiltonian to actual poles of the retarded Green's function; if the authors can show that the coincident poles are on the physical sheet, the paper would be strong. The generality claim ('regardless of the details of scattering potentials') should be softened to reflect the delta-function-potential assumption in the T-matrix calculation. The numerical mesh and broadening issues are fixable but need to be documented."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know: the object this paper calls a Weyl exceptional ring is not shown to be a degeneracy of quasiparticle poles. The authors define the quasiparticle spectrum by det[ε − H0 − Σ(ε)] = 0, but the WER condition they actually use is non-diagonalizability of H0+Σ(ε) at ε = ReΣ0. At that point the determinant equals −(ImΣ0)^2, generically nonzero, so it is not a pole of the retarded Green's function. The spectral functions in Figs. 6 and 7 are evaluated at ε = ReΣ0, so they show a merging of broadened Lorentzians, not a flat band of zero-width quasiparticles. The paper never solves for the actual complex poles, so the ARPES/QPI claim rests on an unverified approximation.\n\nThere is real substance. The self-consistent T-matrix calculation is coherent, and the demonstration that scalar disorder (β=0) can produce a finite Σz when the Weyl points sit away from the symmetric BZ points is a genuine extension of Papaj, Isobe, and Fu. The unitarity-limit and Born-limit extinction checks are useful, and the Dirac semimetal hybrid-ring discussion is a reasonable extrapolation. The appendices are honest and informative.\n\nThe soft spots are concentrated. The pole-versus-fixed-frequency gap is load-bearing; it needs to be closed by redoing the analysis with H_eff or by explicitly solving the pole equation and checking that the coalescing pole lies on the physical sheet. There is also an unproven step in the ring condition: R'_x^2+R'_y^2 is assumed real and non-negative, but the coefficients in Eqs. (8)-(9) are complex, so the exceptional locus may not be the circle they claim. The numerical self-consistency on a 35^3 mesh has no convergence tests, which is minor but real. And the novelty relative to Ref. 12 is incremental—the scalar-disorder result is new, but the phenomenon itself is already in the literature.\n\nWho gets value? Someone working on non-Hermitian topology in disordered semimetals will find the appendices and the model useful, but the main claim needs substantial revision. I would send it to peer review with a clear request that the authors address the pole condition; the idea is plausible and the fix may be straightforward.\n\nBest,\n[Your name]","headline":"The paper's WERs are exceptional points of the fixed-frequency Hamiltonian, not coalescing poles of the Green's function, so the central observable claim is not supported.","tokens_in":15500,"tokens_out":12959,"would_cite":true,"duration_ms":124543,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Generic disorder in Weyl semimetals creates Weyl exceptional rings whenever impurity scattering is not in the unitarity limit and Weyl points are off the Brillouin zone's symmetric points.","keywords":["Weyl exceptional ring","non-Hermitian quasiparticle Hamiltonian","disordered Weyl semimetal","self-consistent T-matrix approximation","flat band","topological Dirac semimetal","hybrid point ring","quasiparticle interference"],"falsifier":"Compute the spectral function of the same two-band lattice model with random scalar impurities ($\\beta=0$, $m\\neq 0$, moderate $V_0$) on finite real-space systems by exact diagonalization, average over impurity configurations, and look for the predicted ring of coalescing quasiparticle poles with a flat interior in $G(p,p)$; if no such ring appears, the T-matrix averaging invented it. In a candidate material such as Co$_3$Sn$_2$S$_2$ or Cd$_3$As$_2$, angle-resolved photoemission showing no ring-shaped anisotropic broadening around the Weyl points at the predicted radius would likewise falsify the claim.","tokens_in":2221,"feed_emoji":"🌀","tokens_out":3079,"duration_ms":144163,"temperature":0.7,"pith_summary":"This paper argues that generic disorder turns the quasiparticle Hamiltonian of a Weyl semimetal non-Hermitian in a way that creates Weyl exceptional rings: closed loops in momentum space where two complex energy eigenvalues and their eigenvectors coalesce, with a flat band inside each loop. The proposed mechanism needs only two conditions: impurity scattering must depart from the unitarity limit, and the Weyl points must sit away from the symmetric points of the Brillouin zone. No magnetic impurities, orbital-dependent scattering, or tilted Weyl cones are required, so the effect should appear in most real Weyl semimetals. At the transition to a topological Dirac semimetal, the two rings merge into a hybrid point ring whose flat band has no vorticity in the phase of the complex eigenvalues. Because the signatures sit in the spectral function, the authors conclude they are observable in photoemission and quasiparticle interference experiments.","feed_headline":"Ordinary disorder forms rings in Weyl semimetals","feed_subtitle":"Two generic conditions suffice; no magnetic impurities or tilted cones needed, and ARPES can see it.","key_machinery":"The load-bearing object is the effective quasiparticle Hamiltonian $H_{\\rm eff}(p)=[1-\\Sigma_1]^{-1}(H_0(p)+\\Sigma_0)$ obtained from the poles of the dressed retarded Green's function; its non-Hermiticity encodes quasiparticle lifetime. The decisive quantity is the $\\sigma_z$ component of the self-energy, $\\Sigma_z(\\epsilon)$. In the two-band Weyl model the integrated Green's function decomposes as $G_0(\\epsilon)+G_z(\\epsilon)\\sigma_z$, and $G_z$ is nonzero exactly when the Weyl points are displaced from the symmetric points of the Brillouin zone. The self-consistent $T$-matrix equations then produce a finite $\\mathrm{Im}\\,\\Sigma_z$ for scalar disorder, and the condition for non-diagonalizability of $H_{\\rm eff}$---$\\mathrm{Re}\\,R'_z=0$ together with $R'_x{}^2+R'_y{}^2=\\mathrm{Im}\\,R'_z{}^2$---defines the Weyl exceptional ring. Repeating the same structure with two opposite-chirality copies gives the hybrid point ring at the topological Dirac semimetal transition.","core_discovery":"The paper's central claim is that a disordered Weyl semimetal generically exhibits Weyl exceptional rings, controlled by two conditions: (i) deviation of the Weyl points from the symmetric points of the Brillouin zone and (ii) deviation of the impurity scattering from the unitarity limit. The argument uses a minimal two-band model $H_0(p)=R(p)\\cdot\\sigma$, with $R(p)=(v\\sin p_x,v\\sin p_y,\\gamma(\\cos p_z-m))$, where $m$ moves the Weyl points away from the symmetric points $p_{\\rm sym}=(0,0,\\pm\\pi/2)$. The disorder-averaged self-energy, computed self-consistently in the $T$-matrix approximation, has the form $\\Sigma(\\epsilon)=\\Sigma_0(\\epsilon)\\sigma_0+\\Sigma_z(\\epsilon)\\sigma_z$; even for purely scalar scattering the $\\sigma_z$ component is nonzero whenever $m\\neq 0$. Its imaginary part sets the radius of the exceptional ring through $R'_x{}^2+R'_y{}^2=\\mathrm{Im}\\,R'_z{}^2$ at $\\mathrm{Re}\\,R'_z=0$, and inside the ring the real part of the complex eigenvalue vanishes, giving a flat band. The paper shows that $\\mathrm{Im}\\,\\Sigma_z$ vanishes in the unitarity limit and in the Born approximation, so intra-valley multiple scattering by moderate-strength impurities is the operative origin of the rings; at the Weyl-to-Dirac transition two rings of opposite vorticity merge into a hybrid point ring with a vorticity-free flat band.","pith_inferences":["The paper leaves implicit that the absence of ring-shaped spectral broadening in a candidate Weyl semimetal would itself be diagnostic: it would mean the disorder is effectively in the unitarity limit or the Weyl points sit at symmetric points, rather than that the mechanism fails.","A natural next test, suggested by the paper's own appeal to real-space comparisons, is exact diagonalization of finite disordered lattices; if the momentum-diagonal spectral function does not show the ring, the T-matrix averaging invented it.","The hybrid-point-ring mechanism should be generic for any non-Hermitian topological transition at which two exceptional rings of opposite vorticity annihilate, so engineered photonic or cold-atom analogs may realize the same vorticity-free flat bands outside solids.","Because the ring radius grows with the displacement of the Weyl points from symmetric points and with orbital or magnetic scattering asymmetry, strain or doping that moves the Weyl points should produce a measurable migration of the ring in ARPES."],"forward_implications":["Most real Weyl semimetals have Weyl points away from the symmetric points, so ordinary scalar disorder should create Weyl exceptional rings; neither magnetic impurities, orbital-dependent potentials, nor tilted cones are needed.","The effect requires moderate-strength impurities: it disappears in the unitarity limit and in the Born approximation, so intra-valley multiple scattering is the operative process.","In a valley-separated model, intervalley scattering opens gaps at the Weyl points, so the intra-valley channel must dominate for the rings to survive.","At the Weyl-to-Dirac transition, two Weyl exceptional rings with opposite vorticity annihilate into a hybrid point ring whose flat band has no vorticity; this is demonstrated in the Cd$_3$As$_2$ effective model.","The resulting anisotropic broadening of quasiparticle peaks and the slightly asymmetric density of states are directly measurable by ARPES, quasiparticle interference, and STM."],"supporting_citations":[{"why":"Shows Weyl exceptional rings in Weyl semimetals with tilted cones; the prior scenario that this paper generalizes and frees from the tilt requirement.","marker":"[13]"},{"why":"Establishes exceptional rings in disordered two-dimensional Dirac systems and their need for orbital-dependent or magnetic scattering, the contrast highlighting the new result here.","marker":"[11]"},{"why":"Provides the real-space comparison and disorder-induced tilt analysis that justify identifying physical quasiparticle spectra with complex poles of the averaged Green's function.","marker":"[12]"},{"why":"Identifies Weyl exceptional rings in dissipative Weyl systems with spin-dependent gain or loss, supplying the non-Hermitian physics being transplanted to disordered solids.","marker":"[21]"},{"why":"Supplies the two-band effective model for Co$_3$Sn$_2$S$_2$ that the paper uses as its concrete Weyl-semimetal platform.","marker":"[27]"},{"why":"Provides the Cd$_3$As$_2$ effective Hamiltonian used to demonstrate the hybrid point ring and vorticity-free flat band in a topological Dirac semimetal.","marker":"[41]"},{"why":"Demonstrates nonperturbative disorder contributions to the Weyl-semimetal density of states, which the paper invokes to argue that Weyl exceptional rings can survive even where the semimetal is unstable.","marker":"[36]"},{"why":"Supports the same disorder-driven instability picture used to argue that Weyl exceptional rings are not restricted to the perturbatively stable semimetal region.","marker":"[37]"}],"fun_headline_variants":["Ordinary disorder spawns Weyl exceptional rings","Disorder alone generates Weyl rings in semimetals","No magic needed: disorder makes Weyl exceptional rings","Two generic conditions produce Weyl exceptional rings"],"cache_read_input_tokens":17408,"weakest_assumption_plain":"The whole construction identifies the physical quasiparticle spectrum with the complex poles of the disorder-averaged, momentum-diagonal Green's function built from a momentum-independent self-energy; if effects that averaging leaves out—rare spatial regions, momentum-dependent broadening, or interference between scattering events—shift or destroy those poles, the exceptional rings are an artifact of the averaging scheme.","fun_headline_variants_meta":{"raw":{"variants":["Ordinary disorder spawns Weyl exceptional rings","Disorder alone generates Weyl rings in semimetals","No magic needed: disorder makes Weyl exceptional rings","Two generic conditions produce Weyl exceptional rings"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000379,"raw_usage":{"total_tokens":2038,"prompt_tokens":996,"completion_tokens":1042,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":981}},"tokens_in":612,"tokens_out":1042,"duration_ms":8726,"temperature":1.0,"reasoning_tokens":981,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:17:35.074750+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the spectral function of the same two-band lattice model with random scalar impurities ($\\beta=0$, $m\\neq 0$, moderate $V_0$) on finite real-space systems by exact diagonalization, average over impurity configurations, and look for the predicted ring of coalescing quasiparticle poles with a flat interior in $G(p,p)$; if no such ring appears, the T-matrix averaging invented it. In a candidate material such as Co$_3$Sn$_2$S$_2$ or Cd$_3$As$_2$, angle-resolved photoemission showing no ring-shaped anisotropic broadening around the Weyl points at the predicted radius would likewise falsify the claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows Weyl exceptional rings in Weyl semimetals with tilted cones; the prior scenario that this paper generalizes and frees from the tilt requirement."},{"cited_title":"Papaj , author H","cited_arxiv_id":null,"evidence_quote":"Provides the real-space comparison and disorder-induced tilt analysis that justify identifying physical quasiparticle spectra with complex poles of the averaged Green's function."},{"cited_title":"Xu , author S.-T","cited_arxiv_id":null,"evidence_quote":"Identifies Weyl exceptional rings in dissipative Weyl systems with spin-dependent gain or loss, supplying the non-Hermitian physics being transplanted to disordered solids."},{"cited_title":"Two-orbital effective model for magnetic Weyl semimetal in Kagome-lattice shandite","cited_arxiv_id":"1904.08148","evidence_quote":"Supplies the two-band effective model for Co$_3$Sn$_2$S$_2$ that the paper uses as its concrete Weyl-semimetal platform."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates nonperturbative disorder contributions to the Weyl-semimetal density of states, which the paper invokes to argue that Weyl exceptional rings can survive even where the semimetal is unstable."},{"cited_title":"[33], non-perturbative contributions to the DOS have weak frequency dependence","cited_arxiv_id":null,"evidence_quote":"Supports the same disorder-driven instability picture used to argue that Weyl exceptional rings are not restricted to the perturbatively stable semimetal region."}],"review_version":1}