Excitation of Coherent Phonons in the One-Dimensional Bi(114) Surface

We present time-resolved photoemission experiments from a peculiar bismuth surface, Bi(114). The strong one-dimensional character of this surface is reflected in the Fermi surface, which consists of spin-polarized straight lines. Our results show that the depletion of the surface state and the population of the bulk conduction band after the initial optical excitation persist for very long times. The disequilibrium within the hot electron gas along with strong electron-phonon coupling cause a displacive excitation of coherent phonons, which in turn are reflected in coherent modulations of the electronic states. Beside the well-known $A_{1g}$ bulk phonon mode at 2.76 THz, the time-resolved photoelectron spectra reveal a second mode at 0.72 THz which can be attributed to an optical surface phonon mode along the atomic rows of the Bi(114) surface.

Figure 1

Sketch of the atomic structure of Bi(114). Atoms in the rows are colored. Bottom: Brillouin zones for surface and bulk in the plane of the binary axis and the surface normal; the projection of the bulk $X$ point corresponds to the center of the second surface BZ ${\Gamma }_{10}$. The green shaded (110) plane is tilted out of the image plane. (a)–(e) Photoemission data taken at the Fermi level with $h\nu =21.2\mathrm{eV}$ (a), (b) and with $2\times 3.1\mathrm{eV}$ (c), (d). (a), (c) Fermi surfaces ($\mathrm{\text{black}}=\mathrm{\text{high intensity}}$). (b), (d) Two selected spectra taken for momenta indicated by the blue arrows in (c); the black open diamonds in (b) and (d) show the difference between the two spectra, i.e., the surface state. (e) Band dispersion recorded using $h\nu =21.2\mathrm{eV}$ (spin integrated). Dashed lines are guides to the eye, the color mimics spin polarizations.

Figure 2

(a) Momentum conserving transitions from the fifth to the sixth valence band along [114], which can contribute to the hot electron population close to $\overline{\Gamma }$; energy bands (green lines) were calculated in a tight-binding scheme [33]; electrons are excited by 1.55 eV photons (short red arrows) and accumulate in a minimum of the conduction band (gray shaded), where they are probed by two-photon photoemission (long blue arrows). (b) Spectra (symbols) taken close to $\overline{\Gamma }$ for various delays between $-0.05$ and 4 ps showing the signature of hot electrons above $E_F$. The thick (thin) solid orange line denotes a fit of two Gaussians multiplied with a Fermi-Dirac distribution (bare Fermi-Dirac distribution). (c) Plot of the intensity as function of energy and time delay. (d) Same data after subtraction of the Fermi-Dirac distribution for each individual delay. The black line follows the transient energy position of the conduction band.

Figure 3

(a) Electron temperature $T_{\mathrm{el}}$ and (b) transient position of the conduction band as function of delay [Fig. 2d]. (c) Cross correlation curve obtained from the conduction band at 0.57 eV above $E_F$; the solid line corresponds to a double-exponential fit with two decay constants ${\tau }_i$ and ${\tau }_{ii}$; the dashed lines represent the two distinct contributions. (d) ${\tau }_{ii}$ and ${\tau }_i$ as obtained from the fits as function of energy above $E_F$. The line represents a power law fit $(E-E_F{)}^{-1.5}$.

Figure 4

(a) Transient photoemission intensity at the conduction band for a short pump pulse (top panel) and at $E_F$ for a long pump pulse (bottom panel) as function of time delay. The data are shown as raw data and after subtraction [gray (blue)] of fitted rate equations (solid lines) in order to highlight the oscillations. (b) Fourier transform of the measured intensity cross correlations for the two different temporal pump pulse durations (solid symbols, $\Delta t_{\mathrm{pump}}=160\mathrm{fs}$; open symbols, $\Delta t_{\mathrm{pump}}=280\mathrm{fs}$). Bottom: Calculated phonon DOS $F(\omega )d\omega$ (Ref. 30) weighted by ${\omega }^{-1}$ for the ground state (blue line) and for $n=1\%$ excited valence electrons (red line).