Anomalously enhanced photoemission from the Dirac point and other peculiarities in the self-energy of the surface-state quasiparticles in Bi${}_2$Se${}_3$

Line-shape analysis of the photoemission intensity from the surface states of Bi${}_2$Se${}_3$ reveals two unusual features: spectral line asymmetry and anomalously enhanced photoemission from the Dirac point. The former can be described by the one-particle spectral function assuming that the self-energy has an energy-momentum-dependent contribution to the imaginary part, which changes sign when crossing both the dispersion curves and the energy of the Dirac point. The anomalous enhancement can hardly be understood as a self-energy effect, while a final-state interference seems to be a more plausible explanation.

Figure 1

The geometry of our ARPES experiment: LH and LV stand for the linear horizontal and linear vertical polarizations of the incident light.

Figure 2

(a) ARPES image of the Dirac cone in Bi${}_2$Se${}_3$ measured close to the $\Gamma$K direction, $T=20$ K . (b) Energy- and (c) momentum-integrated ARPES spectra represent partial $n\left(k\right)$ and partial DOS, respectively. The difference between 20-eV experimental data and the model, shown in panel (b), refers to the right axis. The arrow in panel (c) marks the position of the Dirac point.

Figure 3

The experimental data (a), the result of the fit-based model (model 1) (b), and their difference (c), superimposed by the MDC dispersion (dashed lines). The spectral function parameters derived from the MDC fit, as described in the text (d): ${\Sigma }^{\prime \prime }$ is an effective imaginary part of the self-energy $M=v{M}_{\omega }$, where $M_{\omega }$ is the MDC area and $v$ is the bare band velocity, $B$ is the momentum-independent background in counts per channel. Examples of the MDC fit at 0.275 eV (e) and 0.302 eV (f) binding energies: experimental data (black symbols), two-Lorentzian fit (red solid line), and their difference (dashed blue line). The experimentally derived band dispersions and the band velocity (g). Partial momentum distribution $n_{\Delta \omega }\left(\mathbf{k}\right)$ (h) and partial DOS (i) derived from experiment (solid black line) and the models 1 and 2 as well as for the case of 10$\%$ nonlinearity applied to the model 1.

Figure 4

A pattern of the energy-dependent part of the self-energy: (a) sign of $S(\omega ,k)$; (b) sign of ${\sigma }^{\prime \prime }(\omega ,k)$; (c) suggested symmetry (center); and (d) their difference; positive is red, negative is blue, zero is white.

Figure 5

Momentum-dependent self-energy. The peaked MDC can be a consequence of a sharp decrease of the scattering rate at $k=0$ (top). Both $n_{\Delta \omega }\left(k\right)$ and DOS${}_{\Delta k}\left(\omega \right)$ can only be fitted to the experiment if the Kramers-Kronig consistency is not taken into account (bottom).

Figure 6

Two-slit-like interference pattern models the photoelectron intensity for coherent emission from $k_{\omega }$ and $-k_{\omega }$ states: $I(\alpha ,\theta \propto k_{\omega })$. The sum of such distributions for all pairs of states, $n\left(\alpha \right)$, models the momentum distribution function (see text).

Figure 7

Simulation of a finite band gap (top row), not exact position in $\mathbf{k}$ space (middle row), and a finite momentum resolution (bottom row). All images are shown in the same absolute color scale. The dispersion, if shown, is presented by a white dotted line over corresponding images.

Figure 8

The intensity of each pixel of one ARPES spectrum, $D_n({\omega }_i,k_j)$, vs the intensity of the corresponding pixel of another, $D_1$, spectrum: spectra #2 vs #1 (left); #3 vs #2 (right); and simulated based on spectrum #1 with $n=2.5$ and $\alpha =0$, 0.1, and 0.4 (center), as described in the text.