Holographic Particles Reveal How Materials’ Internal Structure Boosts Electrical Flow

Researchers investigate the behaviour of holographic Fermions interacting with ionic lattices undergoing charge density wave (CDW) transitions, a phenomenon linked to spontaneous translational symmetry breaking. Kai Li and Yi Ling, both from the Institute of High Energy Physics, Chinese Academy of Sciences and the School of Physics, University of Chinese Academy of Sciences, alongside Peng Liu, Chao Niu, and Meng-He Wu et al. detail how CDW formation impacts the structure of the Fermi surface and the emergence of band gaps in momentum space. This work is significant because it demonstrates that CDW enhances spectral function amplitude and Fermi surface momentum, revealing a doping-dependent expansion of the Fermi surface radius potentially crossing the first Brillouin zone, and a lattice amplitude-dependent widening of the band gap, findings consistent with experimental observations.

This work focuses on the structure of the Fermi surface within different Brillouin zones, demonstrating how the presence of charge density waves affects the formation of band gaps in momentum space.

Specifically, researchers have discovered that the formation of charge density waves enhances the amplitude of the spectral function and the momentum of the Fermi surface. Furthermore, the study examines changes in the Fermi surface with varying doping parameters and lattice amplitudes. Interestingly, the radius of the Fermi surface expands as the doping parameter increases, potentially crossing the first Brillouin zone.
This expansion provides insight into the behaviour of electrons within the material as its composition is altered. Additionally, the width of the band gap increases with the lattice amplitude, aligning with observations from condensed matter experiments and confirming the model’s accuracy. This research builds upon advancements in holographic techniques, rooted in the AdS/CFT correspondence, which have provided new avenues for studying strongly correlated systems.

By employing fermions as a probe over a lattice background with charge density waves, scientists are able to analyse non-Fermi liquid behaviour and fermionic spectral functions, offering data comparable to that obtained from Angle-Resolved Photoemission Spectroscopy and Scanning Tunneling Microscopy. The investigation reveals that the interplay between the ionic lattice and charge density wave enhances the spectral function amplitude while reducing band gaps through charge screening.

The study demonstrates that charge density wave-induced charge redistribution partially compensates for the ionic lattice potential, resulting in smaller band gaps at Brillouin zone boundaries compared to systems with only a lattice. This nuanced understanding of symmetry breaking effects is crucial for connecting holographic models with experimental observations and could pave the way for designing materials with tailored electronic properties. The detailed analysis of the Fermi surface’s response to doping and lattice amplitude provides a comprehensive picture of electron behaviour in these complex systems.

Investigating Fermionic Behaviour via Holography on Pre-existing Ionic Lattices

Holographic techniques, rooted in the AdS/CFT correspondence, underpin this work investigating the behaviour of fermions in strongly correlated systems. Researchers employed a holographic approach, utilising fermions as a probe on a background featuring an ionic lattice and charge density wave (CDW). This methodology allows analysis of non-Fermi liquid behaviour and fermionic spectral functions, facilitating comparisons with experimental data from Angle-Resolved Photoemission Spectroscopy and Scanning Tunneling Microscopy.

The study specifically examines the structure of the Fermi surface within different Brillouin zones, focusing on how the presence of CDW affects band gap formation in momentum space. A key innovation lies in considering CDW formation over a pre-existing lattice background, mirroring the conditions found in real materials, rather than generating the CDW first and then introducing the lattice.

This sequence allows investigation of commensurate and incommensurate states arising from the coexistence of lattice and CDW. Spectral functions and Fermi surface structures were analysed with varying doping parameters and lattice amplitudes to understand their influence on symmetry breaking effects. Calculations reveal that the CDW enhances the amplitude of the spectral function and the momentum of the Fermi surface.

Furthermore, the radius of the Fermi surface expands with increasing doping parameter, potentially crossing the first Brillouin zone. Consistent with experimental observations, the width of the band gap increases with the lattice amplitude, demonstrating the method’s ability to model realistic material properties.

Charge density waves and ionic lattices modify electronic band structure and Fermi surface properties

Spectral function amplitudes are enhanced alongside the formation of a band gap within the momentum space due to the presence of charge density waves. Investigations into the interplay between ionic lattices and charge density waves reveal an enhancement of the spectral function amplitude coupled with a reduction in the band gap, attributable to charge screening effects.

Systematic reductions in band gaps at Brillouin zone boundaries, compared to scenarios with only ionic lattices, result from partial compensation of the ionic lattice potential by CDW-induced charge redistribution. Fermi momentum is demonstrably enhanced when both ionic lattices and charge density waves contribute to symmetry breaking, highlighting the non-additive nature of these combined mechanisms.

The radius of the Fermi surface expands proportionally with increases in the doping parameter, eventually crossing the first Brillouin zone and leading to the development of complex band structures containing multiple gaps and Fermi pockets. Specifically, the research demonstrates that the spectral function amplitude increases while the band gap decreases as a result of charge screening.

Band gap widths increase with increasing lattice amplitude, aligning with experimental observations. Numerical analysis focused on the spectral function of fermions within backgrounds incorporating both ionic lattices and charge density waves was performed. The study reveals that the combined effect of ionic lattices and CDW leads to a smaller band gap at Brillouin zone boundaries than that observed with only an ionic lattice present.

This suggests a complex interplay between the two phenomena, where charge redistribution partially offsets the potential created by the ionic lattice. Furthermore, the Fermi momentum is demonstrably larger in the presence of both symmetry-breaking mechanisms than in systems with only one. The holographic setup utilizes a gravity model with two gauge fields and a dilaton field in four dimensions, with the dilaton field serving as the order parameter for the charge density wave.

The background solutions incorporate both ionic lattices and charge density waves, allowing for the investigation of their combined effects on fermionic excitations. The doping parameter and lattice amplitude are treated as independent variables, enabling a detailed exploration of their influence on the system’s properties. Commensurate states are constructed when the wave-vector of the CDW has a rational ratio with the wave-vector of the ionic lattice, providing a basis for studying Mott insulator behavior.

Holographic Fermions exhibit expanded Fermi surfaces and amplified spectral functions with charge density wave formation

Researchers investigated the behaviour of holographic fermions in a background containing an ionic lattice, potentially undergoing a phase transition to form a charge density wave. Their work focused on analysing the structure of the Fermi surface within different Brillouin zones and determining how the presence of a charge density wave affects band gap formation in momentum space.

Results indicate that the formation of the charge density wave amplifies the spectral function and the momentum of the Fermi surface. Specifically, the radius of the Fermi surface expands as the doping parameter increases, potentially extending beyond the first Brillouin zone. Furthermore, the width of the band gap increases with the amplitude of the lattice, aligning with experimental observations.

This holographic setup allows independent control over the doping parameter and the strength of the ionic lattice, enabling detailed investigation of the interplay between these factors and the resulting electronic properties. The authors acknowledge that their analysis relies on specific parameter choices within the holographic model, such as the fixed value of β and the AdS radius.

Future research could explore the impact of varying these parameters and investigating the behaviour of the system in different holographic settings. The findings contribute to understanding the electronic structure of complex materials, particularly those relevant to high-temperature superconductivity and related quantum phenomena, by providing insights into the effects of charge density waves and ionic lattices on the Fermi surface and band structure.