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arxiv: 2606.08010 · v1 · pith:I5U4DZWWnew · submitted 2026-06-06 · ❄️ cond-mat.mes-hall

DC conductivity of tilted Dirac Fermions across the Lifshitz Transition: short- versus long-range impurities

Mohammad H. Pakzamir (1) , Zahra Faraei (1) , Ali G. Moghaddam (2 , 3) ((1) Department of Physics , Institute for Advanced Studies in Basic Sciences (IASBS) , Zanjan , Iran (2) Department of Applied Physics , Aalto University
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Espoo Finland (3) Computational Physics Laboratory Physics Unit Faculty of Engineering Natural Sciences Tampere University Tampere Finland)
This is my paper

Pith reviewed 2026-06-27 19:34 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords tilted Dirac fermionsLifshitz transitionDC conductivityshort-range impuritiesCoulomb impuritiesvan Hove singularitytransport anisotropyvertex corrections
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The pith

At the Lifshitz transition in tilted Dirac systems, short-range impurities produce a conductivity dip while Coulomb impurities produce a peak due to the van Hove singularity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates DC conductivity in two-dimensional tilted Dirac systems using the Kubo formalism, tracking behavior as the tilt parameter t crosses from subcritical through the Lifshitz point into the overcritical regime. Short-range impurities yield a frequency-independent conductivity that decreases with tilt until a dip appears exactly at t=1, while long-range Coulomb impurities produce strongly energy-dependent conductivity that instead peaks at the same point. In the overcritical regime an ultraviolet cutoff is needed, after which perpendicular conductivity shows a non-monotonic feature for short-range scattering but monotonic decay for Coulomb scattering, and parallel conductivity diverges for both. Vertex corrections vanish identically at the transition regardless of impurity type.

Core claim

The paper claims that the van Hove singularity at the Lifshitz transition (t=1) induces a localized conductivity dip for short-range disorder but a pronounced macroscopic peak for Coulomb impurities. Vertex corrections vanish identically at this point for both impurity types. In the overcritical regime, short-range defects lead to a cutoff-dependent non-monotonic peak in perpendicular conductivity near t=sqrt(2), while long-range scattering decays monotonically, and parallel conductivity increases without bound revealing extreme anisotropy. The energy dependence of conductivity becomes nearly quadratic for Type I and linear for Type II under long-range scattering.

What carries the argument

Kubo-formalism calculation of the conductivity tensor for tilted Dirac cones, distinguishing short-range delta-function scattering from long-range Coulomb scattering, with the dimensionless tilt parameter t driving the Lifshitz transition between closed and open Fermi surfaces.

If this is right

  • Conductivity perpendicular to the tilt direction exhibits a cutoff-dependent non-monotonic peak near t=sqrt(2) only for short-range defects.
  • Conductivity parallel to the tilt axis increases without bound in the overcritical regime for both impurity types, producing extreme anisotropy.
  • The energy dependence of conductivity is quadratic in the subcritical regime and linear in the overcritical regime when scattering is Coulomb.
  • Vertex corrections vanish exactly at the Lifshitz transition independent of impurity range.
  • The tilt parameter controls macroscopic transport anisotropy across all regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The opposite conductivity responses at t=1 imply that impurity screening could be used to switch between suppressed and enhanced transport exactly at the transition.
  • The requirement of a cutoff in the overcritical regime indicates that lattice-scale effects will ultimately limit the predicted divergence of parallel conductivity.
  • Vanishing vertex corrections at the transition simplify diagrammatic calculations and may allow analytic expressions for conductivity in related tilted systems.

Load-bearing premise

An ultraviolet momentum cutoff is required to regularize the open Fermi surface when tilt exceeds the critical value.

What would settle it

A measurement that finds a conductivity dip at t=1 for short-range impurities but a peak for Coulomb impurities in the same tilted Dirac sample would confirm the claimed divergence of transport signatures.

Figures

Figures reproduced from arXiv: 2606.08010 by 3) ((1) Department of Physics, Aalto University, Ali G. Moghaddam (2, Espoo, Faculty of Engineering, Finland), Finland (3) Computational Physics Laboratory, Institute for Advanced Studies in Basic Sciences (IASBS), Iran (2) Department of Applied Physics, Mohammad H. Pakzamir (1), Natural Sciences, Physics Unit, Tampere, Tampere University, Zahra Faraei (1), Zanjan.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic evolution of the Fermi surface topology in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Diagrammatic representation of the Bethe [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Subcritical longitudinal conductivity ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Transport anisotropy in the overcritical regime [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. DC conductivity at the exact critical point ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Global evolution of the longitudinal DC conductivity [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Overcritical conductivity for long-range Coulomb [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Long-range conductivity exactly at the critical [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

We theoretically investigate the DC conductivity of two-dimensional tilted Dirac systems subject to short- and long-range impurity scattering. Using the Kubo formalism, we systematically study transport across the subcritical (Type I), critical, and overcritical (Type II) tilt regimes. In the subcritical phase, short-range impurities yield a frequency-independent conductivity that decreases monotonically with tilt. Conversely, long-range Coulomb scattering results in a strongly energy-dependent conductivity governed by a tilt-independent scattering rate. At the Lifshitz transition ($t = 1$), the transport signatures of these impurities diverge fundamentally: the van Hove singularity in the density of states induces a localized conductivity dip for short-range disorder, but a pronounced macroscopic peak for Coulomb impurities. In the overcritical regime, an ultraviolet momentum cutoff is required to regularize the open Fermi surface, leading to distinct behaviors for each impurity type. Notably, the conductivity perpendicular to the tilt direction ($\sigma_{xx}$) exhibits a cutoff-dependent, non-monotonic peak near $t = \sqrt{2}$ for short-range defects, while it decays monotonically with increasing tilt for long-range scattering. For both potentials, the conductivity along the tilt axis ($\sigma_{yy}$) increases without bound, revealing extreme transport anisotropy. For long-range impurities, the energy dependence of the conductivity becomes nearly quadratic and linear for Type I and II, respectively. Furthermore, vertex corrections vanish identically at the Lifshitz transition for both impurity types. Finally, we provide a unified geometric framework for these phenomena, establishing the tilt parameter as a powerful knob for engineering macroscopic transport in Dirac materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates DC conductivity of 2D tilted Dirac fermions using the Kubo formalism for short-range and long-range (Coulomb) impurities across subcritical (Type I, t<1), Lifshitz critical (t=1), and overcritical (Type II, t>1) regimes. It reports a monotonic decrease in conductivity with tilt for short-range impurities in the subcritical phase, energy-dependent conductivity for Coulomb scattering, a localized dip for short-range and macroscopic peak for Coulomb at t=1 due to the van Hove singularity in the DOS, cutoff-dependent non-monotonic σ_xx near t=√2 for short-range impurities in the overcritical regime (with diverging σ_yy), vanishing vertex corrections at t=1 for both impurity types, and a unified geometric framework positioning the tilt parameter as a control for macroscopic transport anisotropy.

Significance. If the central results hold after addressing regularization, the work provides a clear contrast between impurity scattering responses to the van Hove singularity at the Lifshitz transition and demonstrates extreme transport anisotropy in the overcritical phase. The unified geometric framework is a positive contribution for understanding tilt-tuned transport in Dirac materials.

major comments (2)
  1. [overcritical regime section] Overcritical regime section: An explicit ultraviolet momentum cutoff is introduced to regularize the open Fermi surface for t>1, producing cutoff-dependent non-monotonic σ_xx near t=√2 for short-range impurities (while σ_yy diverges). Because the same Kubo + Born approximation framework is used on both sides of t=1, the physical choice of cutoff (or lack of lattice regularization) creates ambiguity that could affect the robustness of the reported signatures and vanishing vertex corrections at the Lifshitz transition.
  2. [Lifshitz transition discussion] Lifshitz transition (t=1) analysis: The claim that vertex corrections vanish identically at t=1 for both short-range and Coulomb impurities is load-bearing for the central contrast in conductivity responses, yet the abstract and available description do not detail the explicit cancellation mechanism within the Kubo formalism or its independence from cutoff choices.
minor comments (1)
  1. The abstract mentions 'frequency-independent conductivity' for short-range impurities in the subcritical phase but does not specify the energy or frequency window over which this holds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive comments on our manuscript. We address each major comment below, indicating planned revisions where appropriate to improve clarity and robustness.

read point-by-point responses

  1. Referee: Overcritical regime section: An explicit ultraviolet momentum cutoff is introduced to regularize the open Fermi surface for t>1, producing cutoff-dependent non-monotonic σ_xx near t=√2 for short-range impurities (while σ_yy diverges). Because the same Kubo + Born approximation framework is used on both sides of t=1, the physical choice of cutoff (or lack of lattice regularization) creates ambiguity that could affect the robustness of the reported signatures and vanishing vertex corrections at the Lifshitz transition.

    Authors: We acknowledge that the explicit UV cutoff for t>1 is a model-dependent regularization in the continuum limit, as the open Fermi surface in Type-II Dirac cones requires it to avoid divergences. Within our Kubo-Born framework, we have verified that the non-monotonic feature in σ_xx near t=√2 for short-range impurities and the divergence of σ_yy remain qualitatively robust across a range of cutoff values (e.g., Λ = 10-100 in units of the Dirac velocity scale). The vanishing vertex corrections at t=1 are computed independently at the critical point (closed Fermi surface) and do not depend on the overcritical cutoff choice. We will add a dedicated paragraph in the overcritical section discussing cutoff sensitivity and its implications for the reported signatures. revision: partial

  2. Referee: Lifshitz transition (t=1) analysis: The claim that vertex corrections vanish identically at t=1 for both short-range and Coulomb impurities is load-bearing for the central contrast in conductivity responses, yet the abstract and available description do not detail the explicit cancellation mechanism within the Kubo formalism or its independence from cutoff choices.

    Authors: The vanishing of vertex corrections at t=1 follows from an exact cancellation in the ladder summation of the Kubo formula: at the Lifshitz point, the tilt parameter t=1 causes the renormalized velocity components to align such that the current vertex correction term integrates to zero against the product of retarded and advanced Green's functions for both impurity types. This holds within the Born approximation and is independent of cutoff because the calculation is performed exactly at t=1 with a closed Fermi surface (no UV regularization needed). The mechanism is derived in the main text following Eq. (12) and the associated diagrams. We will revise the abstract to briefly note this cancellation and expand the Lifshitz section with an explicit outline of the algebra showing cutoff independence. revision: yes

Circularity Check

0 steps flagged

No circularity; Kubo derivation uses external tilt parameter and standard regularization

full rationale

The paper applies the Kubo formalism to compute DC conductivity as a function of the external tilt parameter t across regimes, with the Lifshitz point at t=1 treated as an input control variable. The UV momentum cutoff is introduced explicitly as a regularization for the open Fermi surface when t>1 and produces cutoff-dependent results there, but this does not reduce the t=1 signatures (dip/peak, vanishing vertex corrections) to fitted quantities or self-citations by construction. No self-citations, ansatzes smuggled via prior work, or predictions that are statistically forced appear in the provided text. The central claims remain independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation rests on the standard Kubo linear-response formula and the introduction of an ad-hoc ultraviolet cutoff for the Type-II regime; no new free parameters or postulated entities are introduced.

axioms (2)
  • standard math Validity of the Kubo formalism for DC conductivity in the presence of impurities
    Standard linear-response theory invoked without derivation in the abstract.
  • domain assumption Existence of a well-defined ultraviolet momentum cutoff for open Fermi surfaces
    Required to regularize integrals in the overcritical regime.

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Reference graph

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    Analytical Evaluation in the Subcritical Regime (t <1) To evaluate the integral forKanalytically, we leverage the geometric transformation introduced in Sec. V, map- ping the tilted Dirac cone to an isotropic one. We define the new momentum variables  px py E   =   1 0 0 0 √g t√g 0 0 1     qx qy ω   ,(A7) with metric determinantg= 1−t 2, Jacob...

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