Material’s Unusual Electronic Structure Unlocks Secrets of Conductivity Changes

Researchers have long sought to fully elucidate the mechanisms driving charge density wave transitions in quasi-one-dimensional materials like ZrTe3. Josu Diego and Matteo Calandra, both from the Dipartimento di Fisica at the Universit`a di Trento, alongside their colleagues, now demonstrate that the interplay between Fermi surface geometry and momentum-dependent electron-phonon coupling is critical to understanding this phenomenon. Their first-principles calculations reveal that accurate reproduction of the Fermi surface requires consideration of Hubbard interactions, subsequently enabling a soft harmonic phonon mode at the charge density wave wavevector. Significantly, the team found variations in electron-phonon coupling with phonon momentum to be the dominant factor, establishing a cooperative origin for the charge density wave in ZrTe3 and offering insights applicable to other related quasi-1D systems such as trichalcogenides.

Hubbard interactions and electron-phonon coupling drive charge density wave formation in ZrTe3, leading to its unique electronic properties

Scientists have uncovered a crucial link between electronic structure and lattice dynamics in the quasi-one-dimensional material ZrTe3, resolving a long-standing question regarding the origin of its charge density wave (CDW). This research demonstrates that the CDW transition, occurring at 63 K, arises not solely from the geometry of the Fermi surface, but from a cooperative effect dominated by momentum-dependent electron-phonon coupling.
First principles calculations revealed that accurately reproducing the Fermi surface of ZrTe3 necessitates incorporating Hubbard interactions on the tellurium atoms, a step essential for the emergence of a soft harmonic phonon mode at the CDW wavevector. Analyzing the behaviour of electron-phonon coupling across different phonon momenta, researchers found that its variations significantly outweigh purely electronic effects in driving the CDW formation.

This work unambiguously identifies the CDW in ZrTe3 as a result of both Fermi surface geometry and the momentum-dependent electron-phonon coupling, with the latter playing the predominant role in stabilizing the ordered phase. The study employed density functional theory calculations, utilising ultrasoft pseudopotentials and a plane-wave basis set truncated at a kinetic energy cutoff of 35 Ry for the wavefunctions and 350 Ry for the charge density.
Furthermore, DFT+U calculations were performed to account for electron-electron interactions on the Te 5p states, with on-site Hubbard U parameters determined from first principles using a linear-response method. These calculations were crucial in revealing the soft phonon mode at the experimentally observed CDW wavevector of (0.07, 0, 0.33) reciprocal lattice units.

The findings have direct implications for understanding similar phenomena in other quasi-one-dimensional systems, including trichalcogenides and compounds exhibiting Peierls-like chains, potentially guiding the design of novel materials with tailored electronic and structural properties. This detailed analysis of lattice dynamics and electron-phonon interactions provides a comprehensive understanding of the microscopic origins of the charge modulated state in ZrTe3.

Computational parameters for density functional theory calculations were carefully optimized for accuracy and efficiency

Ultrasoft pseudopotentials incorporating 4s² 4p⁶ 4d² 5s² valence electrons for zirconium and 5s² 5p⁴ for tellurium initiated the computational workflow. A plane-wave basis set, truncated at a kinetic energy cutoff of 35 Ry for wavefunctions and 350 Ry for the charge density, was employed to define the electronic states.

Density functional theory with the BE exchange-correlation functional underpinned all calculations, enabling accurate modelling of the material’s electronic structure. To account for electron-electron interactions on tellurium 5p states, DFT+U calculations were performed. The on-site Hubbard U parameters were computed ab initio using the linear-response method, utilizing a 3 × 3 × 3 q-point grid and projectors constructed from Te 5p atomic orbitals.

Spin-orbit coupling was also incorporated via projector augmented wave pseudopotentials, increasing energy cutoffs to 90 Ry for wavefunctions and 360 Ry for charge density. Both structural relaxation, maintaining original crystal symmetry, and electronic calculations utilized a 20 × 25 × 10 k-point grid alongside a Methfessel-Paxton smearing of 0.001 Ry.

Phonon frequencies were then calculated within the harmonic approximation using density functional perturbation theory, implemented in Quantum ESPRESSO, with DFPT+U for correlated calculations. This approach facilitated exact harmonic phonon calculations at each q-point without requiring supercells. Recognizing the quasi-one-dimensional character of ZrTe₃ and the importance of phonon convergence along kx, a dense 35 × 15 × 6 k-point mesh and 0.001 Ry smearing were used.

The electron-phonon linewidth γμ(q) was evaluated using a converged 100 × 30 × 12 k-point grid and a Gaussian smearing of 0.001 Ry to approximate the electronic Dirac delta functions. Nesting function ζ(q) and the real part of the non-interacting electronic susceptibility χ0(q) were computed on a 200 × 100 × 60 k-point grid using the EPIq code.

Maximally localized Wannier functions, generated with the Wannier90 package from a 15 × 15 × 6 k-point mesh projecting onto Zr d and Te p orbitals, facilitated dense sampling of the Brillouin zone, with a total of 28 MLWFs generated. A broadening of 0.008 eV was applied to the Dirac delta functions in ζ(q).

Momentum-dependent electron-phonon coupling drives charge density wave formation in ZrTe3, leading to its unique electronic properties

First principles calculations reveal that the Fermi surface of ZrTe3 is accurately reproduced only with the inclusion of Hubbard interaction on the tellurium atoms. This inclusion is essential for the appearance of a soft harmonic phonon mode at the charge density wave wavevector. Analysis of the electron-phonon coupling demonstrates that variations with phonon momentum dominate over electronic effects.

These findings unambiguously identify the charge density wave origin in ZrTe3 as a cooperative effect of Fermi surface geometry and momentum-dependent electron-phonon coupling, with the latter playing the leading role. The research establishes a connection between the electronic structure and lattice dynamics in the formation of the charge density wave.

A soft phonon mode emerges at the experimentally determined CDW wavevector of (0.07, 0, 0.33) reciprocal lattice units. Detailed examination of the electron-phonon interaction reveals its significant momentum dependence, exceeding the influence of purely electronic effects in driving the lattice distortion.

This momentum-dependent coupling actively contributes to the observed lattice modulation. Calculations were performed on the high-symmetry phase of ZrTe3, necessitating the inclusion of correlation effects on the tellurium 5p orbitals to accurately model the Fermi surface. The emergence of the soft phonon mode at the CDW wavevector confirms the interplay between electronic instabilities and lattice dynamics.

The observed dominance of momentum-dependent electron-phonon coupling provides insight into the microscopic origin of the charge modulated state in this quasi-one-dimensional material. These mechanisms are directly applicable to other quasi-1D systems, including trichalcogenides and compounds exhibiting Peierls-like chains.

Zirconium telluride’s charge density wave transition arises from coupled Fermi surface topology and electron-phonon interactions, leading to a complex electronic reconstruction

Researchers have identified the origin of the charge density wave transition in zirconium telluride as a cooperative effect stemming from both the geometry of its Fermi surface and momentum-dependent electron-phonon coupling. First principles calculations reveal that accurately reproducing the Fermi surface requires incorporating Hubbard interaction on the tellurium atoms, which is also crucial for the emergence of a soft harmonic phonon mode at the charge density wave wavevector.

Analysis of the electron-phonon coupling demonstrates that its variation with phonon momentum dominates over purely electronic effects, establishing a leading role for lattice dynamics in this phenomenon. These findings clarify a long-standing question regarding the relative importance of electronic and lattice contributions to the charge density wave instability in quasi-one-dimensional materials.

The research demonstrates that while Fermi surface nesting is a necessary condition, it is the momentum-dependent electron-phonon coupling that ultimately drives the structural instability observed in zirconium telluride. The results are directly applicable to other similar systems, including trichalcogenides and compounds exhibiting Peierls-like chains, offering insights into their charge ordering behaviour.

The authors acknowledge that further investigation is needed to determine whether the observed Fermi surface kink alone is sufficient to initiate the charge density wave transition or if it functions in conjunction with the electron-phonon coupling. Future research will likely focus on quantifying the precise contributions of each mechanism and exploring the behaviour of similar materials under varying conditions to broaden the understanding of charge density wave phenomena.