Charge density waves (CDWs) are collective quantum phenomena involving charge modulation in solids, often arising from the condensation of electron-hole pairs with finite momentum. However, distinguishing CDWs from lattice symmetry breaking is challenging due to the simultaneous softening of phonon modes. This study investigates the low-dimensional semimetal HfTe₂, focusing on its potential to exhibit an excitonic insulator phase, a state where electron-hole pairs condense at low temperatures due to weak screening and a low carrier density. The reduced screening in layered materials makes them ideal candidates for observing excitonic insulators. Previous studies have reported signatures like band renormalization and gap opening, but these are not exclusive to excitonic insulators and can also occur in lattice instability-driven transitions. Therefore, observing a metal-insulator transition without phonon softening is crucial for confirming an excitonic insulator phase. HfTe₂, with its indirect band overlap and absence of bulk phase transitions, is a promising material for this investigation. This study explores the thickness and doping dependence of the CDW formation mechanism, aiming to understand the conditions favoring exciton condensation and to open up opportunities for realizing novel quantum states.

Extensive research has been conducted on charge density waves (CDWs), a collective phenomenon where electron density modulates periodically in a solid. The Peierls instability, a lattice distortion driving CDW formation, has been extensively studied. However, excitonic insulators, where CDWs result from electron-hole pair condensation, have garnered significant attention recently. The theoretical framework for excitonic insulators was established in the 1960s, predicting their formation in semimetals with small carrier density and weak screening. Experimental evidence has emerged in various materials, including transition metal dichalcogenides (TMDs). Studies on TMDs have demonstrated the signatures of exciton condensation, such as band renormalization and gap opening. However, distinguishing between excitonic insulators and lattice-driven transitions remains a challenge because both can display similar spectral features. The need to identify a metal-insulator transition without phonon softening is crucial for unambiguous identification of an excitonic insulator phase. The research on HfTe2 builds upon this body of work, focusing on the impact of dimensionality and carrier concentration on the occurrence of this exotic quantum state.

High-quality single-layer and multi-layer HfTe₂ films were grown using molecular beam epitaxy (MBE) on highly oriented pyrolytic graphite (HOPG) and SiC substrates. Atomic layer-by-layer growth was monitored via reflection high-energy electron diffraction (RHEED). Angle-resolved photoemission spectroscopy (ARPES) using both lab-based and synchrotron-based setups characterized the band structures of the HfTe₂ thin films. Raman spectroscopy probed the phonon response, while synchrotron X-ray diffraction investigated the structural changes associated with the phase transition. First-principles calculations based on density functional theory (DFT) were performed to understand the electronic and structural properties of the films. Electron doping was achieved by growing the films on SiC substrates with varied resistivities, introducing bilayer graphene. The carrier density was determined from the Luttinger area of the Fermi surface, using ARPES data and analyzing Fermi surface maps. The transition temperature (Tc) was extracted by fitting the temperature-dependent energy gap data to a semi-phenomenological BCS mean-field equation. The Raman spectroscopic measurements involved non-polarized Raman spectra acquired under normal incidence using a HeNe laser, analyzing the reflected radiation with a grating spectrometer equipped with a liquid-nitrogen-cooled CCD to measure Raman shift, analyzing the phonon modes, and investigating potential collective excitations and lattice distortions. DFT calculations using the Vienna ab initio simulation package (VASP) were used to compute the phonon dispersion and band structure, determining topological properties using the Z2pack package.

The ARPES measurements revealed a metal-insulator transition in single-layer HfTe₂ at low temperatures, indicated by a full gap opening, band renormalization, and the appearance of replica bands at the M point. Importantly, Raman spectroscopy and synchrotron X-ray diffraction showed no signs of lattice distortion within the detection limit. This suggests that the observed CDW is primarily electronic in origin, supporting the excitonic insulator scenario. The CDW state was observed to persist in films with thickness up to 2 TL, but it was suppressed and completely destroyed at 3 TL due to increased screening. Electron doping significantly increased the transition temperature (Tc), reaching ~2.3 times that of the undoped sample. This effect is attributed to a reduced screening effect and a more balanced electron-hole carrier density, thus promoting exciton formation. Analysis of the transition temperature as a function of electron-hole density imbalance and total carrier density demonstrated the significant role of screening in the formation of the excitonic insulating state. The energy gap was found to be relatively independent of doping within a specific range despite significant changes in Tc, suggesting a complex interplay between doping, screening, and exciton condensation. The experimental findings were consistent with DFT calculations, which did not predict any structural instability. Furthermore, calculations indicated the presence of a topological nontrivial character for films with 2 TL or more, opening up the possibility of exploring topological excitonic insulating phases. The combination of experimental and computational techniques strongly suggests the observation of an intrinsic excitonic insulator phase in low-dimensional HfTe₂.

The findings directly address the research question of whether an excitonic insulator phase exists in low-dimensional HfTe₂. The observation of a metal-insulator transition without discernible lattice distortion, coupled with the doping dependence of Tc, strongly supports the excitonic insulator scenario. The thickness dependence of the CDW state underscores the critical role of screening in suppressing exciton formation. The unusual doping effect on Tc, increasing with doping in contrast to typical Peierls-type CDW materials, further emphasizes the distinct nature of the excitonic mechanism. The observation of topological nontrivial properties in thicker films opens a new avenue for exploring the interplay between excitonic and topological orders. These results significantly advance our understanding of excitonic insulators, particularly in low-dimensional systems and provide insights into controlling and manipulating such phases through doping and dimensionality.

This research provides compelling evidence for the existence of an intrinsic excitonic insulator phase in low-dimensional HfTe₂. The absence of observable lattice distortion, coupled with the doping-dependent transition temperature and thickness-dependent suppression, strongly points to an electronic mechanism driven by exciton condensation. The study highlights the unique behavior of HfTe₂ compared to other CDW materials and opens exciting possibilities for exploring the interplay between excitonic and topological order in future research. Further investigations could focus on other 2D materials and detailed theoretical modeling to gain deeper understanding of the complex interplay between doping, screening, and the excitonic transition.

The study is limited by the experimental resolution of the techniques used. The absence of lattice distortion observed in Raman and X-ray diffraction might not fully exclude the possibility of extremely subtle structural changes beyond the detection limits of the current measurements. The DFT calculations, while providing valuable insights, are subject to inherent limitations in accurately describing correlated electron systems. The model used to extract the transition temperature assumes a BCS-type mean-field behavior which might not perfectly capture the true nature of the phase transition. The range of doping levels achievable in this study may not cover the full extent of the excitonic phase diagram.