Single-Scale Magnetoelastic Landau Quantization: Thermodynamics, Quantum Oscillations, and Metrology

TL;DR

This paper introduces a unified theoretical framework for understanding thermodynamics and quantum oscillations in dislocated electronic systems under magnetic fields, revealing universal behaviors and metrological applications.

Contribution

It develops a single-scale description linking thermodynamics and quantum oscillations in dislocated systems, enabling precise dislocation density measurement and device design.

Findings

Universal hyperbolic kernels describe thermodynamic observables.

Sharp signatures of magnetoelastic interference in heat capacity.

Phase-unwarping protocol for dislocation metrology from a single field sweep.

Abstract

We develop a unified, single-scale description of thermodynamics and quantum oscillations in electronic systems with a uniform areal density of screw dislocations under a uniform magnetic field. A single tunable gap, $\hbar|\omega_{eff}|$ with $\omega_{eff}=\omega_{c}+\omega_{cl}$, organizes all equilibrium observables obtained from a compact harmonic-oscillator partition function: free energy, internal energy, entropy, heat capacity, magnetization, magnetic susceptibility, and magnetocaloric responses collapse onto universal hyperbolic kernels in $x=\hbar|\omega_{eff}|/(2k_{B}T)$. We identify a compensated-field regime where the transverse gap closes and the heat capacity reaches an equipartition plateau, providing a sharp signature of magnetoelastic interference. In transport and torque, the same scale rigidly shifts the Hall fan and compresses the $1/B$ period of de Haas-van Alphen and Shubnikov-de Haas oscillations when expressed in $1/B_{eff}$, enabling a phase-unwarping protocol that metrologizes the dislocation density from a single field sweep. In mesoscopic samples, boundary corrections to the Landau degeneracy generate finite-size calorimetric oscillations that diagnose the effective magnetic length. Moderate disorder and weak interactions preserve the kernel structure while smoothing amplitudes. We outline an experimental roadmap combining on-chip calorimetry, torque magnetometry, and transport, and discuss device-level opportunities in caloritronics and strain engineering, magnetocaloric microcooling, magnetoelastic heat switching, and dilatometric transduction, where the single scale $\hbar|\omega_{eff}|$ enables rational design and optimization.