[Paper Review] Charge-Density-Waves Tuned by Crystal Symmetry

A. Gallo–Frantz, A. A. Sinchenko+11 more|arXiv (Cornell University)|Jun 27, 2023

High-pressure geophysics and materials4 citations

TL;DR

This study demonstrates that biaxial mechanical deformation of TbTe₃ induces a reversible switch in charge density wave (CDW) orientation from the c-axis to the a-axis as the a/c lattice ratio increases, with a coexistence region near a/c = 1.000. The transition is driven by strain-induced changes in CDW transition temperature Tc, which varies linearly with a/c and is quantitatively explained by a 2D tight-binding model, revealing a direct link between crystal symmetry and electronic order in RTe₃ systems.

ABSTRACT

The electronic orders appearing in condensed matter systems are originating from the precise arrangement of atoms constituting the crystal as well as their nature. This teneous relationship can lead to highly different phases in condensed matter, and drive electronic phase transitions. Here, we show that a very slight deformation of the crystal structure of TbTe$_3$ can have a dramatic influence on the electronic order that is stabilized. In particular, we show that the Charge Density Wave (CDW) developping along the $\vec{c}$ axis in the pristine state, switches to an orientation along $\vec{a}$ when the naturally orthorhombic system is turned into a tetragonal system. This is achieved by performing true biaxial mechanical deformation of a TbTe$_3$ sample from 250K to 375K, and by measuring both structural and electronic parameters with x-ray diffraction and transport measurements. We show that this switching transition is driven by the tetragonality parameter $a/c$, and that the transition occurs for $a=c$, with a coexistence region for $0.9985< a/c < 1.002$. The CDW transition temperature $T_c$ is found to have a linear dependence with $a/c$, with no saturation in the deformed states investigated here, while the gap saturates out of the coexistence region. The linear dependence of $T_c$ is accounted for within a tight-binding model. Our results question the relationship between the gap and $T_c$ in RTe$_3$ systems. More generally, our method of applying true biaxial deformation at cryogenic temperatures can be applied to many systems displaying electronic phase transitions, and opens a new route towards the study of coexisting or competing electronic orders in condensed matter.

Motivation & Objective

• To investigate how crystal symmetry, specifically the a/c lattice ratio, controls the orientation of charge density waves (CDWs) in TbTe₃.
• To explore the role of mechanical strain in driving electronic phase transitions in quasi-2D quantum materials.
• To establish a direct quantitative link between structural deformation and CDW transition temperature Tc in RTe₃ compounds.
• To examine the relationship between CDW gap and Tc under varying lattice symmetry, challenging conventional assumptions.
• To develop and apply a cryogenic biaxial deformation setup enabling in-situ XRD and resistivity measurements for real-time monitoring of structural and electronic responses.

Proposed method

• True biaxial tensile stress was applied to TbTe₃ crystals using a custom-designed device with force applied along both a and c crystallographic directions via a polyimide cross-shaped substrate.
• In-situ x-ray diffraction (XRD) was used to measure structural parameters, including CDW satellite peak intensities and lattice constants a and c, to track the a/c ratio during deformation.
• Transport measurements along both a and c directions were performed using four-terminal resistivity configuration to detect CDW formation and orientation via resistivity anomalies.
• The CDW transition temperature Tc was extracted from resistivity curves as a function of temperature under varying strain conditions.
• A 2D tight-binding model with electron-electron and electron-phonon coupling was used to explain the linear dependence of Tc on the a/c ratio, incorporating the screened Coulomb interaction U(Q) and Lindhard susceptibility χ(T,Q).
• Theoretical calculations of χ(T,Q₀) and its temperature derivative were performed to derive the sensitivity of Tc to strain, using parameters from TbTe₃: t∥ ≈ 2 eV, t⊥ ≈ 0.37 eV, EF ≈ 1.48 eV, and ζ ≈ 0.23 Å⁻¹.

Experimental results

Research questions

• RQ1 How does biaxial mechanical strain with controlled a/c ratio influence the orientation of charge density waves in TbTe₃?
• RQ2 What is the quantitative relationship between the CDW transition temperature Tc and the lattice parameter ratio a/c in strained TbTe₃?
• RQ3 Does the CDW gap saturate while Tc continues to increase under strain, and what does this imply about the Tc-gap relationship in RTe₃ systems?
• RQ4 Can a 2D tight-binding model with screened Coulomb interaction quantitatively explain the observed linear Tc(a/c) dependence?
• RQ5 What is the nature of the electronic state at the tetragonal point (a/c = 1), and does it support coexisting CDW order along both a and c directions?

Key findings

• The CDW orientation switches from the c-axis to the a-axis as the a/c ratio increases, with a continuous transition and a coexistence region for 0.9985 < a/c < 1.002.
• The CDW transition temperature Tc varies linearly with the a/c ratio, with a minimum at a/c = 1.000, and increases by approximately 20 K for a 0.2% increase in the a lattice parameter.
• The linear dependence of Tc on a/c is quantitatively explained by a 2D tight-binding model incorporating the screened Coulomb interaction and Lindhard susceptibility, with a theoretical δTc/δa ≈ 26 K per 0.1% strain, in good agreement with experiment.
• The CDW gap saturates in the pure CDW phases along a or c, while Tc continues to increase with strain, indicating a decoupling between gap and Tc in RTe₃ systems.
• At a/c = 1.000, the system is degenerate with equal Tcx and Tcy, leading to coexisting CDW order along both directions and enhanced fluctuations.
• The study demonstrates that true biaxial strain at cryogenic temperatures enables precise tuning of electronic order and provides a new platform for probing competing or coexisting electronic phases in quantum materials.