Yu-Shiba-Rusinov bound states of exciton condensate

Abstract

Quantum condensed states in solids often reveal their fundamental nature via interactions with impurities, as epitomized by Yu-Shiba-Rusinov (YSR) bound states at magnetic impurities in superconductors. Although analogous YSR bound states were predicted within quantum condensates of excitons several decades ago, their existence has been elusive. Here, we directly visualize in-gap electronic states bound to impurities inside an exciton condensate phase of a van der Waals crystal Ta2Pd3Te5, utilizing scanning tunneling microscopy and spectroscopy. We find that the energies of in-gap states are strongly correlated with the excitonic band gap, which is systematically tuned by local strain and carrier injection. Our theoretical analyses reveal that these in-gap states are induced by charge dipoles associated with Ta vacancies through a charge-exciton version of the YSR mechanism. Our findings establish both the YSR physics in exciton condensates and a novel microscopic tool to probe and control quantum properties in exciton condensates persisting up to room temperature.

Figures (20)

• Figure 1: Atomic structures, excitonic transition, and defects of Ta$_2$Pd$_3$Te$_5$.a. Top and side views of the schematic atomic structure. Topmost Te atoms and their bonding are highlighted by red circles and lines, respectively. b. STM topography images obtained at sample bias of 300 mV and -300 mV. The structure of topmost Te atoms is overlaid with red circles and lines. The lattice unit cell is indicated by a black box. Scale bars represent 1 nm. c. STM topographies simulated by DFT calculations in the given bias conditions match well with the experimental results in b. d. ARPES intensity maps along the c (x) axis measured near and below the excitonic transition temperature. Colored lines guide distinct dispersions of two valence bands (VB1 and VB2) and a conduction band (CB1). CB1 and VB1 open the excitonic band gap. e. dI/dV curve measured by STM and averaged for a unit cell. f. Large-area STM topography images obtained at 300 and 100 mV, respectively. Atomic scale defects appear at a lower bias as bright protrusions or points. g. dI/dV maps obtained at -25 and 40 meV, respectively, within the band gap for the same area as f. In-gap electronic states appear on bright defects of the topography. Scale bars in f and g and their inset represent 20 nm and 2 nm, respectively.
• Figure 2: Identification of defects with in-gap bound states.a-e. STM topography images (sample bias of 100 mV) of defects exhibiting in-gap states with 1 nm scale bars. Images for $\alpha$ and $\alpha$' ($\beta$ and $\beta$') are mirror symmetric. f-j. dI/dV STS data measured along white dashed arrows in a-e. Each spectrum is shifted vertically for clarity. The in-gap states in the filled ($E^-$) and empty ($E^+$) states are indicated by red and blue arrows, respectively. k-o. Grid dI/dV maps on each defect measured at its in-gap state energies $E^-$ (top) and $E^+$ (bottom). Scale bars represent 2 nm and the in-gap states are distributed over approximately 5 nm. .
• Figure 3: a. STM topography of a locally strained area (a stripe of bright protrusion). The scale bar represents 5 nm. Ta-vacancy defects are marked by circles or boxes. b. Enlarged topography of $\alpha$, $\beta$ and $\beta'$ defects within the strained area. c. Height profile and dI/dV maps across the strained area (along the dashed arrows in a). The dI/dV map shows the excitonic gap closed. d. Normalized dI/dV curves of the three defects in b. Similar dI/dV curves in the strained area away from defects distribute in the grey part. e. Changes of the dI/dV curves upon the variation of the tip height on (left) a pristine area and a defect $\alpha$ (right). The zero tip height corresponds to the normal tunneling condition. (Left) The turn-on of the dI/dV signal is indicated at the dashed lines, which indicate conservatively the gap edges and the gap edge spectral features are outside of the shaded region. (Right) The in-gap states are indicated by dashed lines. f. dI/dV curves at given ${\Delta}Z$ on defect $\alpha$ taken from e. g. Summary of ${\Delta}Z$ sweeps on different defects. In-gap state energies are plotted against the gap edge positions of the pristine area (e).
• Figure 4: a,b. Enlarged STM topography and simulated STM images of a Ta vacancy ($\alpha$ defect) at unoccupied (top) and occupied (bottom) states. The yellow shades indicate the major topographic features. The Ta vacancy position is shown in a, b, c by the red dashed lines. d. Charge density difference due to the Ta vacancy from the pristine structure in the DFT calculation. e. xz(xy)-plane averaged charge density difference in the vicinity of the Ta vacancy along the y (b) (top) and x-axis (bottom), indicating the charge dipole formation along the y-axis. f. Numerical solution of 2D tight-binding Hamiltonian of the exciton insulator with the local charge dipole (top) and monopole (bottom) potential V, indicating the emergence of the symmetric twin in-gap state from the gap edges only in the case of charge dipole.
• Figure 5: a,b. DFT-calculated electronic band structure of monolayer (a) and bi-layer (b) Ta$_2$Pd$_3$Te$_5$. The band gap from the calculation is much smaller than the experimental excitonic gap, since electron-hole manybody interactions are not sufficiently included in DFT. These results are consistent with the previous DFT reportsTPT1TPT2TPT3TPT4TPT9