Revealing the Empty-State Electronic Structure of Single-Unit-Cell $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$

We use scanning tunneling spectroscopy to investigate the filled and empty electronic states of superconducting single-unit-cell FeSe deposited on ${\mathrm{SrTiO}}_3(001)$. We map the momentum-space band structure by combining quasiparticle interference imaging with decay length spectroscopy. In addition to quantifying the filled-state bands, we discover a $\mathrm{\Gamma }$-centered electron pocket 75 meV above the Fermi energy. Our density functional theory calculations show the orbital nature of empty states at $\mathrm{\Gamma }$ and explain how the Se height is a key tuning parameter of their energies, with broad implications for electronic properties.

Figure 1

(a) Typical topography of in situ–grown $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$. Set point: 4 V, 5 pA. (b) Line cut along the arrow in (a). The inset illustrates the underlying crystal structure. (c) Atomically resolved topography of single-unit-cell (1UC) $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$. Set point: 50 mV, 250 pA. (d) $dI/dV$ spectrum of 1UC $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$, $T=4.3\mathrm{K}$. Bias oscillation $V_{\mathrm{rms}}=0.7\mathrm{mV}$.

Figure 2

Quasiparticle interference imaging, real space. (a) Topography (set point: 50 mV, 500 pA) and (b)–(e) conductance maps $g(\mathbf{r},\omega )$ (set point: $100\mathrm{M}\mathrm{\Omega }$, $V_{\mathrm{rms}}=1.4\mathrm{mV}$) of a $20\mathrm{nm}\times 20\mathrm{nm}$ field of view with as-grown defects. Images were drift corrected following Ref. [16].

Figure 3

Quasiparticle interference imaging, momentum transfer ($\mathit{q}$) space. (a)–(f) Theoretical simulations, $A(\mathit{k},\omega )$ and its autocorrelation, for three representative energies. (g)–(i) Fourier transform amplitudes $|g(\mathit{q},\omega )|$ of conductance maps (fourfold symmetrized for increased signal). (j) Azimuthally averaged intensity plot of $|g(q_r,\omega )|$, where $q_r$ is measured relative to $\mathit{G}=(2\pi /a,0)$. The superconducting gap is marked by $2\mathrm{\Delta }$.

Figure 4

(a),(b) Energy dependent decay length $\lambda (\omega )$, extracted from exponential fits to the tunneling current as the tip is retracted from the sample at a fixed bias (inset schematic). Fits were performed in the current range [10 pA, 500 pA], two of which (250 and 50 meV) are shown in (a). Dashed horizontal lines indicate calculated values of $\lambda$ at the $\mathrm{\Gamma }$ and $M$. (c) $dI/dV$ spectrum. $V_{\mathrm{rms}}=2.8\mathrm{mV}$. Vertical lines mark extrema in the numerical derivatives of $\lambda (\omega )$ and $dI/dV$.

Figure 5

(a) Band structure of free-standing single-unit-cell (1UC) FeSe, calculated in the generalized gradient approximation (GGA). Structural parameters: lattice constant $a=3.90\AA$, Se height $h_{\mathrm{Se}}=1.45\AA$. (b) Energies of the five $\mathrm{\Gamma }$ bands shown in (a) vs $h_{\mathrm{Se}}$ (the band represented by orange is degenerate). The GGA values of $h_{\mathrm{Se}}$ for 1UC FeSe ($a=3.90\AA$ fixed) and bulk FeSe ($a=3.68\AA$ relaxed) are marked, as well as the experimental value for bulk FeSe. The Fermi energy $E_F$ expected from electron doping is marked in (a),(b). (c) Charge density isosurfaces (yellow) at $\mathit{k}=0$ for the five $\mathrm{\Gamma }$ bands, shown in two perspectives. The histograms depict the orbital compositions.