Researchers have, for the first time, visualized in-gap electronic states bound to impurities within an exciton condensate phase of the van der Waals crystal Ta₂Pd₃Te₅ at 4.4 K, utilizing scanning tunnelling microscopy and spectroscopy. This observation establishes an analogue to the Yu-Shiba-Rusinov state, typically seen in superconductors, but within this distinct quantum condensate.
The energies of these impurity-bound states correlate with the excitonic band gap, a property tunable by local strain and carrier injection, potentially allowing control of quantum properties even at room temperature. These findings introduce a microscopic tool to probe and control quantum properties in exciton condensates.
Ta₂Pd₃Te₅ Crystal Structure and Excitonic Transition
The van der Waals crystal Ta₂Pd₃Te₅ exhibits a structural arrangement of alternating one-dimensional chains of tantalum and palladium, sandwiched between tellurium layers; this specific layering is critical to its observed properties. Unit cells of the material contain two Ta₂Pd₃Te₅ layers, with tellurium atoms forming alternating dimer and trimer chains along the c-axis, a configuration clearly visualized through scanning tunneling microscopy and corroborated by density functional theory calculations.
These calculations also detail the electronic band structure, providing a foundational understanding of the material’s electronic behavior. A transition from a zero-gap semimetal to an insulating state with a 100 meV gap occurs below 365 K, as determined by transport measurements and angle-resolved photoemission spectroscopy.
Recent confirmation of the excitonic nature of this transition came with the identification of a direct exciton photoemission signal in angle-resolved photoemission spectroscopy, solidifying the understanding of the material’s unique phase behavior. STM topographies show the arrangement of topmost tellurium atoms, overlaid with simulated DFT calculations for comparison, demonstrating a close match between theoretical models and experimental observations. The observed transition is a fundamental shift in the material’s electronic structure, driven by the formation of excitons, bound electron-hole pairs, and their subsequent condensation.
ARPES and DFT Confirm Dirac Crossing & Band Gap Formation
ARPES and DFT calculations consistently revealed a Dirac crossing formed by one conduction band (CB1) and two valence bands (VB1 and VB2) near the Fermi energy, establishing the metallic nature of the material in its normal phase. This crossing provides the foundation for exciton formation, a process expected to induce symmetry breaking and open an energy gap below 370 K, as detailed in recent publications including (X 14, 011046 (2024)).
The resulting band gap, fully saturated at approximately 100 meV as observed in ARPES spectra at 80 K, is also discernible in scanning tunnelling spectroscopy (STS) spectra recorded at 4. 4 K, demonstrating its stability at cryogenic temperatures. The asymmetry of this gap and the local density of states across the Fermi level stems from the presence of the additional valence band, VB2.
The existence of impurity-induced in-gap states, previously suggested by transport and ARPES measurements, has now been directly visualized. These states manifest as sharp or broad peaks splitting from the valence and conduction band edges, exhibiting characteristics analogous to Yu-Shiba-Rusinov (YSR) states typically observed in superconductors, as described in “Tetrahedral coordination of palladium in Ta₂Pd₃Te₅: a compound with a “stuffed” Ta₂NiSe₅ structure”.
Detailed analysis of spectral functions calculated using a YSR Hamiltonian for varying exciton insulator band gaps and charge dipole strengths further elucidates the nature of these states, revealing their sensitivity to both the overall gap size and local charge distribution. Calculations show that the charge density distributions associated with these in-gap states are localized around defect sites, indicated by red circles in accompanying structural models.
The theoretical framework employed utilizes a tight-binding model to describe the conduction and valence orbitals, incorporating a uniform coupling term mediated by the excitonic condensate. Parameters within this model reproduce the observed electronic structure and in-gap state behavior. This confirms the role of the exciton condensate in mediating interactions between electrons and holes, ultimately leading to the formation of these defect-bound states.
Observation of In-Gap States via Scanning Tunneling Microscopy
At 4 Kelvin, detailed analysis of defect sites revealed characteristic in-gap states manifesting both filled and empty electronic signatures, indicated by red and blue arrows in differential conductance measurements. These states appear localized around imperfections in the crystal lattice, as evidenced by scanning tunneling microscopy topography images. Five distinct defect types were identified, each exhibiting these in-gap states, with mirror symmetry observed between certain configurations.
The correlation between in-gap state energies and the exciton insulator band gap is further substantiated by experiments varying the distance between the scanning tip and the defect. Measurements show that the in-gap state energies shift in relation to the gap edge positions of the pristine, defect-free areas of the material.
This tunability, achieved through local strain and carrier injection, suggests a pathway toward controlling quantum properties within exciton condensates, potentially extending functionality to higher temperatures. This highlights the potential for external control over these delicate quantum states.
Defect-Bound States Analogous to Yu-Shiba-Rusinov Resonance
The observation of paired in-gap states proximal to intrinsic defects within an exciton condensate establishes a striking parallel to the well-known Yu-Shiba-Rusinov (YSR) resonance, typically observed in superconducting materials. These states, appearing as localized disruptions of the excitonic order, offer a new means of investigating the complex many-body interactions inherent to these quantum condensates and potentially manipulating their properties.
Computational modeling suggests these states arise from tantalum sites occupied by palladium, creating local charge dipoles that induce a double resonance within the excitonic gap, mirroring the excitonic analogue of the YSR mechanism. This resonance isn’t merely a theoretical curiosity; researchers demonstrated a direct relationship between these defect-bound states and the excitonic order through precise control of local strain and carrier density.
The ability to tune the properties of these in-gap states opens possibilities for designing novel quantum devices and exploring the fundamental limits of exciton condensation. This control is particularly significant given the sensitivity of these states to the surrounding electronic environment, making them ideal probes of the condensate’s underlying physics. Just as YSR states can reveal insights into pairing mechanisms and magnetism in superconductors, these impurity-induced states within the exciton condensate promise to illuminate the intricacies of exciton pairing and the interplay of various quantum phenomena.
The work builds on prior theoretical predictions suggesting that charged impurities could locally disrupt electron-hole pairing, forming bound states within the exciton condensate, a concept now supported by experimental observation in the van der Waals crystal Ta₂Pd₃Te₅. The implications extend beyond fundamental understanding, as the ability to engineer these impurity-bound states could create tailored quantum systems.
Analogous to the use of magnetic impurities to induce quantum phase transitions and design quantum states in superconductors, these defects within the exciton condensate offer a similar degree of control. This precise manipulation of quantum states, achieved through localized control of the material’s electronic structure, represents a step toward utilizing the potential of exciton condensates for advanced quantum technologies.
Strain and Carrier Injection Tune Excitonic Gap Energies
This precise control was achieved using scanning tunnelling microscopy and spectroscopy at a remarkably low temperature of 4. 4 K, providing a stable platform for further investigation of these quantum phenomena. The ability to manipulate the excitonic gap opens avenues for exploring exciton condensates under a wider range of conditions, potentially extending functionality to less cryogenic environments. A corrugated stripe region, approximately 8 nm wide, exhibited a substantial strain variation of around 2. 4%, leading to a collapse of the excitonic gap and the emergence of a metallic pseudogap of roughly 30 meV.
This pseudogap suggests heightened excitonic fluctuations and the presence of preformed excitons, characteristics anticipated during a Bose-Einstein condensation transition. The sensitivity of the excitonic gap to strain, previously observed in transport measurements under pressure, is further confirmed by these localized experiments.
The research team employed a technique involving systematic variation of tip height during tunnelling spectroscopic measurements, shifting the tip from a position where tunnelling current was barely detectable by -100 pm. This allowed for investigation of the excitonic energy gap’s evolution as a function of tip-sample distance, revealing the influence of external factors on the condensate’s properties.
The direct effect of an electric field on exciton binding was estimated to be an order of magnitude smaller than the effect of carrier doping, highlighting the dominant role of carrier concentration in modulating the excitonic gap. Angle-resolved photoemission spectroscopy (ARPES) experiments, utilizing a laser with 11 eV photons and an energy resolution better than 0. 6 meV, complemented the scanning tunnelling spectroscopy, providing a broader picture of the material’s electronic structure.
Crystals of Ta₂Pd₃Te₅ were prepared through cleavage at 80 K in ultra-high vacuum conditions, ensuring a pristine surface for accurate measurements. These combined techniques provide a robust methodology for probing and manipulating the delicate balance of interactions within the exciton condensate.
Pd-Ta Charge Dipoles Explain Resonance in Exciton Condensate
Theoretical analyses now connect in-gap electronic states within the exciton condensate Ta₂Pd₃Te₅ to charge dipoles formed by palladium atoms occupying tantalum sites, offering a novel explanation rooted in an excitonic version of the Yu-Shiba-Rusinov (YSR) mechanism. This connection establishes a parallel between the behavior of excitonic condensates and superconductors, where YSR states typically arise from magnetic impurities, and provides a new means of probing quantum phenomena.
The observed defect-bound states exhibit a strong correlation with the excitonic order, a relationship confirmed through local control of both strain and carrier density within the material. These dipoles, aligned perpendicular to the crystal chain direction, possess a moment of 0. 14 × 10⁻¹² C m for a single palladium atom, as detailed in supplementary figures. A tight-binding Hamiltonian, incorporating excitonic pairing and local perturbations from dipole charges, was employed to simulate the system’s behavior and validate these findings.
This approach mirrors the YSR Hamiltonian used to describe impurity effects in superconductors, but adapted for the unique properties of exciton insulators. The implications of this discovery extend beyond a deeper understanding of exciton condensates; the ability to manipulate these states through defects opens avenues for engineering quantum phenomena. The presence of similar in-gap states near Majorana zero modes in topological superconductors underscores their importance in unambiguously identifying these elusive particles.
The researchers suggest that controlled manipulation of these defects could lead to the design of quantum phase transitions and tailored quantum states, potentially extending functionality beyond current limitations. The observation of these states in Ta₂Pd₃Te₅, a van der Waals crystal, provides experimental validation of these concepts and establishes a specific material platform for further investigation.
The researchers note that while analogous YSR resonances have been predicted in other bosonic quasiparticle condensates, experimental confirmation has remained elusive until now. Evidence for exciton condensation in related materials, such as monolayer WTe₂, and the observation of exciton insulator states in Ta₂Pd₃Te₅, provide a foundation for this new understanding of defect-bound states and their influence on quantum behavior.
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