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arxiv: 2504.01059 · v2 · submitted 2025-04-01 · ❄️ cond-mat.str-el

Theory of Linear Magnetoresistance in a Strange Metal

Jaewon Kim , Shubhayu Chatterjee This is my paper

Pith reviewed 2026-05-22 21:37 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords strange metalsquantum critical pointslinear magnetoresistanceT-linear resistivityYukawa interactiondensity wave ordertransport relaxation ratescaling collapse
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The pith

Proximity to quantum critical points produces T-linear resistivity and B-linear magnetoresistance via a disordered Yukawa model with pinned density waves.

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

Strange metals show resistivity linear in temperature and magnetoresistance linear in field, unlike the quadratic laws of ordinary metals. The paper constructs a minimal model in which electrons at the Fermi surface couple to quantum critical bosons through a spatially disordered Yukawa interaction while static pinned density-wave domains are also present. Solving the resulting transport equations yields a relaxation rate that scales as k_B T / ħ when the field is small and as an effective Bohr magneton times B / ħ when the temperature is low. The same model produces a scaling collapse of the magnetoresistance when field and resistance are both rescaled by temperature, reproducing the pattern seen in experiment.

Core claim

A minimal microscopic model coupling electronic excitations at the Fermi surface to quantum critical bosons via a spatially disordered Yukawa interaction, together with static pinned domains of density wave order, produces a transport relaxation rate that scales as k_B T / ħ at low magnetic fields and as μ̃_B B / ħ at low temperatures, with the magnetoresistance exhibiting a scaling collapse upon rescaling field and resistance by temperature.

What carries the argument

Spatially disordered Yukawa coupling of electrons to quantum critical bosons plus static pinned density-wave domains, which together generate the linear scalings in the transport relaxation rate.

If this is right

  • The relaxation rate crosses over from temperature-dominated to field-dominated behavior at a scale set by the ratio of temperature to field.
  • Magnetoresistance data from different temperatures collapse onto a single curve when plotted against B/T.
  • The linear scalings hold only in the vicinity of the quantum critical point and revert to conventional quadratic behavior far from it.
  • The same mechanism accounts for both the zero-field T-linear resistivity and the low-temperature B-linear magnetoresistance within one microscopic framework.

Where Pith is reading between the lines

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

  • If the model is correct, materials tuned away from quantum critical points should recover conventional Fermi-liquid transport coefficients at sufficiently low temperature and field.
  • The required spatial disorder in the Yukawa coupling suggests that controlled introduction of inhomogeneity could be used to test the predicted linear regimes in engineered samples.
  • The effective Bohr magneton appearing in the low-temperature rate may differ from the bare electron value and could be extracted from the slope of the low-T magnetoresistance.

Load-bearing premise

Electrons must couple to quantum critical bosons through a spatially disordered Yukawa interaction while static pinned domains of density wave order are also present.

What would settle it

Observation of quadratic rather than linear magnetoresistance in a strange-metal candidate whose phase diagram shows no nearby quantum critical point, or absence of the predicted B/T scaling collapse in a material where the density-wave domains are demonstrably absent.

Figures

Figures reproduced from arXiv: 2504.01059 by Jaewon Kim, Shubhayu Chatterjee.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A real space schematic of our model, with elec [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Electron self-energy diagrams. (a) Self-energy Σ [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The resistivity [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

A central puzzle in strongly correlated electronic phases is strange metallic transport, marked by $T$-linear resistivity and $B$-linear magnetoresistance, in sharp contrast with quadratic scalings observed in conventional metals. Here, we demonstrate that proximity to quantum critical points, a recurring motif in the phase diagrams of strange metal candidates, can explain both transport anomalies. We construct and solve a minimal microscopic model by coupling electronic excitations at the Fermi surface to quantum critical bosons via a spatially disordered Yukawa interaction, as well as static pinned domains of density wave order. The resultant transport relaxation rate scales as $k_B T/\hbar$ at low magnetic fields, and as an effective Bohr magneton $\tilde{\mu}_B B/\hbar$ at low temperatures. Further, the magnetoresistance in our model shows a scaling collapse upon rescaling the magnetic field and the resistance by temperature, in agreement with experimental observations.

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 / 2 minor

Summary. The paper claims that proximity to quantum critical points explains both T-linear resistivity and B-linear magnetoresistance in strange metals. The authors construct a minimal microscopic model coupling Fermi-surface electrons to quantum critical bosons via a spatially disordered Yukawa interaction together with static pinned domains of density-wave order; solving the model produces a transport relaxation rate scaling as k_B T/ℏ at low B and as an effective Bohr magneton μ̃_B B/ℏ at low T, together with a scaling collapse of the magnetoresistance when B and resistance are rescaled by temperature.

Significance. If the derivations are correct and the model assumptions are justified, the work supplies a unified microscopic mechanism for two central transport anomalies in strange-metal candidates, reproducing the observed linear scalings and the experimental scaling collapse from a single framework built around quantum criticality. This would be a notable contribution to the field.

major comments (2)
  1. [Model construction] Model construction (Hamiltonian definition): the spatially disordered Yukawa vertex and the static pinned density-wave domains are introduced as assumptions required to obtain the linear scalings; the text states that without spatial disorder the vertex is momentum-conserving and the rate reverts to conventional T² or B² behavior, while the pinned domains supply the additional scattering channel that converts the boson spectral function into a linear-in-B rate at T=0. These choices are therefore load-bearing for the central claim.
  2. [Results] Results (scaling derivation): the abstract asserts that the model is 'constructed and solved' to yield the stated scalings and scaling collapse, yet the provided information contains no explicit derivation steps, error analysis, or verification that the linear forms emerge without additional fitting; the degree to which the disorder strength or domain parameters are derived parameter-free versus adjusted to data therefore remains unclear.
minor comments (2)
  1. [Notation] The effective Bohr magneton μ̃_B is used without an explicit definition in terms of the microscopic parameters of the model.
  2. [Abstract and discussion] The claim of agreement with 'experimental observations' would be strengthened by citing specific data sets or materials and showing quantitative comparisons rather than qualitative scaling collapse alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and positive evaluation of the significance of our work. We address each of the major comments below and have revised the manuscript to improve clarity on the model assumptions and derivation details.

read point-by-point responses

  1. Referee: [Model construction] Model construction (Hamiltonian definition): the spatially disordered Yukawa vertex and the static pinned density-wave domains are introduced as assumptions required to obtain the linear scalings; the text states that without spatial disorder the vertex is momentum-conserving and the rate reverts to conventional T² or B² behavior, while the pinned domains supply the additional scattering channel that converts the boson spectral function into a linear-in-B rate at T=0. These choices are therefore load-bearing for the central claim.

    Authors: We agree that the disordered Yukawa interaction and pinned density-wave domains are essential assumptions in our minimal model. These are motivated by the prevalence of disorder and density-wave fluctuations in strange metal materials. In the revised manuscript, we have added further discussion in Section II to elaborate on the physical justification for these choices, drawing from experimental observations in cuprates and other candidates. revision: yes

  2. Referee: [Results] Results (scaling derivation): the abstract asserts that the model is 'constructed and solved' to yield the stated scalings and scaling collapse, yet the provided information contains no explicit derivation steps, error analysis, or verification that the linear forms emerge without additional fitting; the degree to which the disorder strength or domain parameters are derived parameter-free versus adjusted to data therefore remains unclear.

    Authors: The derivations are detailed in the main text (Sections III and IV) and the supplementary information, where we explicitly solve for the scattering rates using disorder-averaged perturbation theory and the Boltzmann equation. The linear scalings arise naturally from the momentum relaxation due to disorder and the form of the quantum critical boson spectrum, without additional fitting. We have added a new appendix providing a step-by-step outline of the calculation and a discussion clarifying that the results are robust to the choice of disorder strength within a range, with the overall scale set by material parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity; linear rates derived from explicit model solution

full rationale

The paper constructs a Hamiltonian incorporating a spatially disordered Yukawa interaction and static pinned density-wave domains, then solves for the transport relaxation rate to obtain the claimed linear scalings. This constitutes a standard forward derivation from stated microscopic inputs rather than any reduction of the output to the inputs by construction, self-definition, or self-citation. No equations are presented in which a fitted parameter is relabeled as a prediction, nor is a uniqueness theorem imported from prior self-work. The derivation chain remains self-contained within the model calculation and does not rely on external benchmarks being presupposed.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the introduction of a spatially disordered Yukawa coupling and pinned density-wave domains whose independent evidence is not supplied in the abstract; several domain assumptions about quantum critical bosons are also required.

free parameters (1)
  • strength and spatial form of disorder in the Yukawa interaction
    The disorder is introduced to generate the linear relaxation rate; its functional form and magnitude are chosen within the model.
axioms (2)
  • domain assumption Strange metals sit near quantum critical points with critical bosons that couple to Fermi-surface electrons
    The model is built on the premise that proximity to QCPs is a recurring motif and sufficient to explain the transport anomalies.
  • ad hoc to paper Static pinned domains of density wave order exist and contribute to magnetotransport
    These domains are added to the model to obtain the B-linear regime.
invented entities (1)
  • spatially disordered Yukawa interaction between electrons and quantum critical bosons no independent evidence
    purpose: to produce T-linear transport relaxation
    The spatial disorder is postulated as part of the minimal model.

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