This study provides a theoretical explanation of semi-Dirac fermions using the extended classical mechanics framework, emphasizing the duality of mass properties and their implications for technological advancements.
Soumendra Nath Thakur, Tagore's Electronic Lab, WB. India
January 11, 2025.
Abstract
Semi-Dirac fermions are unique quasiparticles that exhibit dual mass properties, being massless in one direction and massive in another. This phenomenon is explained using the extended classical mechanics framework, which distinguishes the behaviour of particles with rest mass (Mᴍ > 0) from those that are massless (Mᴍ = 0). For particles with rest mass, the effective mass (Mᵉᶠᶠ > 0) results in forces aligned with external gravitational influences, ensuring classical motion. Conversely, massless particles with negative effective mass (Mᵉᶠᶠ < 0) experience forces opposing gravitational fields. This duality underpins the behaviour of semi-Dirac fermions, which were recently observed in zirconium silicon sulphide (ZrSiS) crystals. The discovery, published in Physical Review X by researchers at Penn State and Columbia University, marks a significant advancement in condensed matter physics and offers exciting potential for technological innovations, including quantum devices, batteries, and sensors.
Description
The following description provides the explanation of the dual mass properties of semi-Dirac fermions within the framework of extended classical mechanics, their experimental confirmation in ZrSiS crystals.
Semi-Dirac fermions exhibit a unique duality in their mass properties, being massive in one direction and massless in another, for reasons rooted in the extended classical mechanics framework.
For particles with rest mass Mᴍ > 0:
The force equation is expressed as:
F = (Mᴍ − Mᵃᵖᵖ)⋅aᵉᶠᶠ
Where Mᴍ > 0 represents the rest mass, Mᵃᵖᵖ denotes the apparent mass, and Mᵉᶠᶠ = (Mᴍ − Mᵃᵖᵖ) is the effective mass. For such particles, an effective mass Mᵉᶠᶠ > 0 leads to a positive force aligned with the external gravitational influence, ensuring classical motion under gravitational forces.
For massless particles with Mᴍ = 0:
The force equation simplifies to:
F = −Mᵉᶠᶠ ⋅ aᵉᶠᶠ
Where Mᵉᶠᶠ = −Mᵃᵖᵖ < 0. Here, the negative effective mass results in a force opposing the direction of the external gravitational field, distinguishing their behaviour from particles with positive effective mass.
This distinct behaviour of massless particles aligns with the characteristics of semi-Dirac fermions, which exhibit massless motion in one direction while being massive in another. This duality has been experimentally confirmed in zirconium silicon sulphide (ZrSiS) crystals, a semi-metal material. First theorized 16 years ago, semi-Dirac fermions have now been directly observed, representing a significant milestone in condensed matter physics.
A research team from Penn State and Columbia University identified these quasiparticles and published their ground breaking findings in the journal Physical Review X. Their discovery holds immense promise for advancing emerging technologies, such as next-generation batteries and highly sensitive sensors. By bridging the gap between massless and massive particle behaviour, semi-Dirac fermions could provide a foundation for transformative quantum and technological applications, opening new horizons in material science and quantum mechanics.
Conclusion
The observation of semi-Dirac fermions in ZrSiS crystals represents a milestone in the study of quasiparticles and their dual mass properties. Using the framework of extended classical mechanics, their unique behaviour—massless in one direction and massive in another—has been effectively explained. This discovery not only validates theoretical predictions made over 16 years ago but also opens new avenues for research in material science and quantum mechanics. The potential applications of semi-Dirac fermions in advanced technologies such as sensors and energy storage systems underscore their importance. By bridging the gap between massless and massive particle behaviour, this breakthrough paves the way for transformative innovations, highlighting the far-reaching implications of fundamental research in physics.
Links to the discovery, research paper:
References:
[1]. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. doi: https://doi.org/10.20944/preprints202409.1190.v3
[2]. Thakur, S. N. (2024) Photon Dynamics in extended classical mechanics: Effective mass, negative inertia, momentum exchange and analogies with Dark Energy. doi: 10.20944/preprints202411.1797.v1
[3]. Thakur, S.N. (2024) A symmetry and conservation framework for photon energy interactions in gravitational fields. doi: 10.20944/preprints202411.0956.v1
[4]. Thakur, S.N. (2024) Photon interactions with external gravitational fields: True cause of gravitational lensing. doi: 10.20944/preprints202410.2121.v1
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Comment:
The above presentation consistently evaluates the alignment of the discovery research with the theoretical focus, highlighting the following:
Theoretical Framework:
The above presentation acknowledges the accurate emphasis on the extended classical mechanics framework, which forms the foundation of the explanation for the dual mass properties of semi-Dirac fermions.
Mass Properties:
The distinction between rest mass (Mᴍ > 0) and massless (Mᴍ = 0) particles, along with the roles of effective mass (Mᵉᶠᶠ > 0 and Mᵉᶠᶠ < 0) is clearly reiterated, aligning with the presented work.
Observations and Implications:
The above presentation appropriately notes the reference to semi-Dirac fermions' experimental observation in ZrSiS crystals and their technological potential, confirming the coherence of these aspects with the presentation.
Focus:
It recognizes the presentation's intentional narrowing of focus to theoretical insights and technological implications, while omitting experimental details and topological aspects, which were not central to the scope of the presentation.
Conclusion:
The conclusion in the above presentation reaffirms the consistency, clarity, and relevance of the presentation, accurately reflecting the theoretical and applied aspects while justifying the selective omission of experimental specifics.
Final Assessment:
The above presentation effectively supports and reinforces the coherence and focus of the Dual Mass Properties of Semi-Dirac Fermions: Theoretical Insights and Technological Implications. It aligns with the intentions and scope of the presentation while maintaining clarity and logical flow.
