Field-Induced Weyl-Like Crossings and Longitudinal Magnetoconductivity in Dirac Systems

arXiv:2402.16859 · cond-mat.mes-hall, hep-ph · Submitted 2024-01-19 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Field-Induced Weyl-Like Crossings and Longitudinal Magnetoconductivity in Dirac Systems".

Mira: Here's the gist of the paper. The gist: The introduction of a pseudoscalar associated to longitudinal photons propagating along a magnetic field B could transforms a Dirac semimetal into a Weyl semimetal with a pair of Weyl nodes for each point of Dirac, leading to negative longitudinal magnetoresistance in Dirac systems via an axial anomaly relation Theoretical Framework A low-energy model is built to study systems such as Dirac/Weyl semimetals, according to statistical quantum electrodynamics formalism.

Kai: The paper investigates three-dimensional crystals with linear dispersion fermionic excitations, which are describe by the massless 3 + 1 Weyl and Dirac equations Topological Transition The introduction of a pseudoscalar, associated to longitudinal photons propagating along a magnetic field B, could transforms a Dirac semimetal into a Weyl semimetal with a pair of Weyl nodes for each point of Dirac.

Mira: The nodes are separated by a pseudovector electric field induced dynamically along B associated to a chiral effect on the Fermi surface A topological quantum transition is produced between a chiral-and non chiral symmetry phase.

Kai: This Fermi surface modification implies that a Dirac semimetal is transformed into a Weyl semimetal.

Paper summary: Kai: So to recap, this paper investigates three-dimensional crystals with linear dispersion fermionic excitations described by massless three + one Weyl and Dirac equations <ref:2402.16859#pg2,three-dimensional crystals with linear dispersion fermionic excitations>.

Mira: The thesis is that a specific pseudoscalar associated with longitudinal photons propagating along a magnetic field B can transform a Dirac semimetal into one with Weyl nodes, which are paired up for each point of the original Dirac system.

Lev: That transformation happens because there's a pseudovector electric field induced dynamically along B that has an effect on the Fermi surface, leading to this chiral-and non-chiral symmetry phase transition.

Kai: This implies a topological quantum transition between these two phases, which is the main mechanism driving the change in particle behavior.

Mira: The paper then shows how this leads to a general expression for longitudinal magnetoconductivity without needing an independent phenomenological internode relaxation time.

Lev: The crucial part they highlight is that the chiral contribution to this conductivity has an explicit B squared prefactor, and its coefficient depends on the magnetic field and temperature through Landau-level thresholds and Fermi-Dirac occupation factors.

Kai: They also found that the resulting conductivity exhibits a nonmonotonic magnetic field dependence, along with an inverse-temperature regime under appropriate conditions.

Mira: The main significance is that this provides a direct link between the longitudinal electromagnetic response, these field-induced Weyl-like crossings, and longitudinal magnetotransport in Dirac systems.

Lev: It's useful for understanding how to predict transport signatures in materials where we might have these kinds of topological phase boundaries driven by external fields.

Kai: So, they are using this to study things like Na3Bi and ZrTe5, which are real materials in the literature.

Conclusion: Kai: Looking at the paper, I think the real power here is how they tie these fundamental topological concepts—the Weyl nodes—to something incredibly measurable: the longitudinal magnetoconductivity.

Mira: They aren't just doing a calculation; they are proposing a mechanism where the field configuration dictates the topology of the system itself. It’s about controlling phase transitions using electromagnetism in condensed matter.

Lev: If this holds up, it means that you could potentially design materials where changing the magnetic field isn't just nudging some parameters around, but fundamentally altering what kind of excitations are allowed to propagate through them.

Kai: Exactly. It suggests that in systems like these Dirac semimetals, the external fields aren't just causing minor corrections; they’re driving a phase change where new types of nodes appear.

Mira: This has implications for designing sensors or devices where you need to precisely tune transport properties by applying magnetic fields at specific temperatures.

Lev: For error correction, it means we have to be careful because the underlying physics might shift entirely depending on the field strength you're dealing with, which affects how much overhead your code needs.

Kai: So, in short, this paper shows that longitudinal photons interacting with a magnetic field can engineer Weyl nodes and link that directly to measurable conductivity changes.

Mira: It’s a neat piece of condensed matter physics because it connects topology to transport observables in a very concrete way.

Instituto Superior de Tecnologƭas y Ciencias Aplicadas Instituto de Cibernética, Matemƭica y F༿isica

cond-mat.mes-hall, hep-ph

Submitted: 2024-01-19

Updated: 2026-10-21

Comments: Title changed. Manuscript substantially revised, including abstract, text, and conclusions. 9 pages and 3 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 68/100

The gist: The gist: The introduction of a pseudoscalar associated to longitudinal photons propagating along a magnetic field B could transforms a Dirac semimetal into a Weyl semimetal with a pair of Weyl nodes

Key concepts

Dirac/Weyl Semimetals: These are materials with linear energy dispersion for their charge carriers, described by Dirac or Weyl equations. They can exhibit unique electronic properties due to the presence of nodes in their energy spectrum, which are crucial for understanding topological phenomena like the one studied here.
Pseudoscalar Invariant (${f E} imes{f B}$): This term represents a combination of electric and magnetic fields that has a specific mathematical property. Its non-vanishing value is key because it drives the topological transition, causing a Dirac semimetal to change its fundamental electronic structure into one resembling a Weyl semimetal with distinct nodes.
Longitudinal Magnetoconductivity: This refers to how the electrical conductivity of a material changes when subjected to both an electric field and a magnetic field applied parallel to each other. The paper derives an analytical expression for this effect, showing it can be negative under certain conditions due to the chiral current generation.
Chiral Current Generation: This describes the process where the magnetic field and electric field together induce a net flow of charge that breaks the statistical balance of particle densities. This is a direct consequence of the topological transition, as it leads to a specific type of current that influences transport properties.

Terminology

Accuracy — 1× in this paper · explained in 1 episode
Chiral Symmetry — 1× in this paper · explained in 2 episodes

Summary

The gist: The introduction of a pseudoscalar associated to longitudinal photons propagating along a magnetic field B could transforms a Dirac semimetal into a Weyl semimetal with a pair of Weyl nodes for each point of Dirac, leading to negative longitudinal magnetoresistance in Dirac systems via an axial anomaly relation

Theoretical Framework

A low-energy model is built to study systems such as Dirac/Weyl semimetals, according to statistical quantum electrodynamics formalism. The paper investigates three-dimensional crystals with linear dispersion fermionic excitations, which are describe by the massless 3 + 1 Weyl and Dirac equations

Topological Transition

The introduction of a pseudoscalar, associated to longitudinal photons propagating along a magnetic field B, could transforms a Dirac semimetal into a Weyl semimetal with a pair of Weyl nodes for each point of Dirac. The nodes are separated by a pseudovector electric field induced dynamically along B associated to a chiral effect on the Fermi surface A topological quantum transition is produced between a chiral-and non chiral symmetry phase. This Fermi surface modification implies that a Dirac semimetal is transformed into a Weyl semimetal.

Chiral Effect and Current Generation

The pseudovector electric field E3 is associated with longitudinal photons propagating in the direction of B, and it produces an axial current leading to the breaking of the previously existing statistical chiral balance of the densities of charged particles. In parallel directions, electrons decrease their negative momentum and holes increase their positive momentum, producing a chiral Rcurrent. The sign of the pseudoscalar G = 1/4E · B plays a fundamental role in giving a phenomenological basis to our chirality-changing transitions (chiral current generation) between the Weyl nodes.

Negative Longitudinal Magnetoresistance

The most prominent signature of the chiral magnetic effect in Dirac systems in parallel electric and magnetic fields is a positive contribution to the conductivity that has a quadratic dependence on magnetic field. The paper reports a general expression for the negative longitudinal magnetoresistance induced by longitudinal photons in semimetals. This relation corresponds to a negative longitudinal magnetoresistance related to a chiral current generation along B.

General Expression and Results

The general expression for the magnetoconductivity at finite temperature and density associated to the scattering and pair creation was calculated in 37,38. This relation (20) could describe the negative longitudinal magnetoresistance of a wide variety of Dirac/Weyl semimetals such as Na3Bi and ZrTe5. The quadratic dependence on field B is associated with a positive contribution to the magnetoconductivity, which is a prominent signature of the chiral magnetic effect in Dirac/Weyl systems in parallel electric and magnetic fields. The relation (23) gives an expression for the magnetoconductivity when ε1 ≥ µ.

Experimental Validation

The curves (c, d) reproduced with a high level of accuracy some of the experimental results, in the low temperature region, reported to be for ZrTe5 and Na3Bi. The function f(B, k3, µ, T) in (20) provides the possibility of generalizing the usual expressions of the magnetoconductivity reported in the literature. The relation (17) corresponds to a negative longitudinal magnetoresistance related to a chiral current generation along B.

Conclusion

The authors conclude that as a consequence of a pseudoscalar, associated to longitudinal photons propagating along B, a Dirac semimetal could be transformed into a Weyl semimetal with a pair of Weyl nodes for each point of Dirac. The nodes are separated by a pseudovector electric field induced dynamically along B. A topological quantum transition is produced between a chiral-and non chiral symmetry phase in presence of a pseudovector electric current parallel to B. The pseudovector field E3 is not just changing the relative position of the Weyl nodes in momentum space a magnitude k3, but also to induce a chiral effect on the Fermi surface. A general expression to longitudinal magnetoconductivity was calculated in 38. The function f(T, k3, B, µ) in (20) provides the possibility of generalizing the usual expressions of the magnetoconductivity reported in the literature and to study the influence of the magnetic field B and the pseudovector electric field in these semimetals. The authors believe that a wide variety of these semimetals can be studied by using our general expression to the negative longitudinal magnetoresistance. The relation (20) could describe the negative longitudinal magnetoresistance of a wide variety of Dirac/Weyl semimetals such as Na3Bi and ZrTe5. The function f can be written as f(B, k3, µ, T) = 1/T 1/k3ε1 1 1 + cosh[(ε1−µ)T]. The quadratic dependence on field B is associated with a positive contribution to the magnetoconductivity, which is a prominent signature of the chiral magnetic effect in Dirac/Weyl systems in parallel electric and magnetic fields. The relation (20) could describe the negative longitudinal magnetoresistance of a wide variety of Dirac/Weyl semimetals such as Na3Bi and ZrTe5. The relation (17) corresponds to a negative longitudinal magnetoresistance related to a chiral current generation along B. The authors report a chiral effect induced by longitudinal photons associated to a negative longitudinal magnetoresistance in Dirac systems. This negative magnetoresistance is valid for relativistic quantum systems associated to the scattering and pair creation. The function f(B, k3, µ, T) in (20) provides the possibility of generalizing the usual expressions of the magnetoconductivity reported in the literature and to study the influence of the magnetic field B and the pseudovector electric field in these semimetals. The authors believe that a wide variety of these semimetals can be studied by using our general expression to the negative longitudinal magnetoresistance.

Appendix A Summary

From the structure of Πµν in a magnetized plasma, in the case of non-vanishing temperature T and chemical potential µ, we can find the polarization properties of three electromagnetic eigenmodes propagating in the system. Under those conditions the polarization tensor may be expanded in terms of six independent transverse tensors. In the case of C-symmetric (µ = 0), the mode b(3)µ is a transverse plane polarized wave, whose electric unit vector is E(3) u = e⊥ × e3, orthogonal to the plane (B, k). In the case of C-non-symmetric (µ!= 0), the second mode b(2)µ is the same pure longitudinal wave that in the C-symmetric case. The transverse modes b(1,3)µ describe circularly polarized waves in the plane orthogonal to B having different eigenvalues, typical of Faraday effect.

Calculation of Im[s] Summary

The denominator D of the integral s (see (7), which have singularities due to D) given by D = 4z1p3(p3 + k3) + z 2 1 − 4ω 2ε 2n,0, it can be written in the form symmetric under the exchange εq ↔ εq', ω ↔ -ω.

Improvements for AI systems

Improved AI can model topological phase transitions in Dirac/Weyl semimetals by predicting whether a system will transform from a Dirac to a Weyl semimetal based on applied magnetic fields and electric fields. This allows for the design of materials exhibiting specific chiral symmetry breaking phenomena, such as the chiral-and non chiral symmetry phase.
Improved AI can calculate the negative longitudinal magnetoresistance in Dirac systems using a general expression that has a quadratic dependence on B, which is identified as a prominent signature of the chiral magnetic effect in Dirac/Weyl systems in parallel electric and magnetic fields.
Improved AI can predict the real conductivity associated with the pseudovector mode, given by sigma equals Im[Πij] over omega, allowing for a quantitative description of charge transport driven by longitudinal photons. This includes separating the Ohm current term from the Hall current.
Improved AI can generalize experimental magnetoconductivity expressions by using the function f(B, k3, µ, T) which depends on field B and momentum k3 associated with the pseudovector E3. This allows for studying the influence of magnetic fields and pseudovector electric fields in various semimetals like Na3Bi and ZrTe5.
Improved AI can predict the temperature dependence of negative longitudinal magnetoresistance, showing that the upward curvature of the magnetoresistance decrease when the temperature increase and identifying conditions where T2 greater than eB could have positive contribution to the longitudinal magnetoresistance.