Detecting the full photoemission cone from laser-based ARPES experiments by leveraging deflector technology

TL;DR

The paper tackles the limited momentum-space coverage in laser-based ARPES at low photon energy by combining a bias-accelerated approach with deflector-enabled hemispherical analyzers to detect all 2pi photoemitted electrons in a fixed geometry. An extended analytical model incorporating the deflector axis is developed and parameterized by a single weighting factor beta, enabling accurate k-space mapping without rotating the sample. Experimental validation on Au(111), Bi2Sr2CaCu2O8+delta, and WTe2 demonstrates robust momentum-space reconstruction under bias across materials, with observable trade-offs such as slit-induced resolution changes and space-charge effects. The method promises significant advantages for time-resolved ARPES and matrix-element studies, while highlighting practical limitations and general applicability to other ARPES systems with deflector technology.

Abstract

Angle-resolved photoemission spectroscopy (ARPES) provides a direct access to the electronic band structure of solid and molecular systems. The momentum range accessible by this technique depends directly on the photon energy used, and low-photon-energy sources are insufficient to photoemit electrons over the full Brillouin zone of most quantum materials. In addition, while electrons are emitted over a 2$π$ solid angle, conventional hemispherical analyzers only collect a small subset of those electrons. A previous work [RSI 92, 123907 (2021)] demonstrated that electrons emitted over a larger field-of-view can be acquired in one fixed configuration by accelerating them towards the analyzer with a bias voltage. Here, we extend this work by leveraging the deflector technology of novel ARPES hemispherical analyzers. We demonstrate the ability to detect all $2π$ photoemitted electrons in a fixed configuration for various materials such as gold, cuprates and transition-metal dichalcogenides. This approach is especially advantageous for time-resolved ARPES, as electron dynamics over a large momentum range can be accessed with identical measurement conditions.

Figures (7)

• Figure 1: (a-c) Illustration of electron trajectories with the application of different effective bias voltages ($U_B=0$, -10 and -60 V). Electrons are emitted over a $2\pi$ solid angle (delimited by the gray plane), but only the electrons entering the analyzer are colored, with a color gradient reflecting their $k_x$ value. The analyzer deflector deviates those electrons and, in combination with the slit, allows to select which $\theta_X$ (associated to $k_x$) is measured. Here, the positive-$\theta_X$ electrons (blue) are accepted through the slit after being deflected (in a schematically simplified way). In the scenario at $U_B=-60$ V, all photoemitted electrons enter the analyzer and can be measured by scanning the deflector angle. (d) An electron emitted from the sample at an angle $\Theta_S$ propagates in a straight line in the absence of effective bias voltage, as illustrated by the orange arrow. With a voltage bias $U_B$ applied to the sample, the electron is accelerated by the electric field $\vec{E}$ towards the analyzer entrance, arriving at a position $x_A$ and an angle $\Theta_A$. The exact trajectory inside the analyzer depends on these variables and the electron is finally measured at an angle $\Theta_D$ on the detector. (e) Projections of the electron momentum $\vec{k}$ in the $xy$, $xz$ and $yz$ planes to define the measured photoemission angles $\theta_X$ and $\theta_Y$ and the angles converted in spherical coordinates $\Theta$ and $\Omega$.
• Figure 2: Angle-to-momentum conversion for Au(111). (a-c) Isoenergy maps in the $\theta_X-\theta_Y$ plane at $E=E_F$ for $U_B=-2,-10$ and $-30$ V, respectively. (d-f) Spectra along $\theta_X$ for the cut marked by the dashed blue line in the corresponding panels a-c. (g-i) Spectra along $\theta_Y$ for the cut marked by the dashed green line in the corresponding panels a-c. The dashed and dotted red lines in panels (d-i) correspond to the LEC in the angular and position limits, respectively. Panels (j-r) correspond directly to panels a-i, but converted to momenta $k_x$ and $k_y$. The solid red line is the physical LEC curve. We note that regions that do not follow the LEC in panel k at negative $k_x$ are due to distortions arising from imperfect alignment. These distortions vanish at sufficiently large bias voltage.
• Figure 3: (a) Momentum distribution curves (MDCs) of Au(111) along $k_x$ (perpendicular to the slit) taken at $E=E_F$ for $U_B$ from 0 to $-30$ V. (b) MDCs along $k_Y$ (parallel to the slit) in the same conditions. (c) Relative distance between the peaks at positive and negative momenta ($\Delta k$, as illustrated in panel a) as a function of $U_B$ for both momentum directions.
• Figure 4: (a) Fermi surface measured of Au(111) for $U_B=-30$ V. The blue and green boxes, labeled with their center momentum, indicate integration areas used for the EDC analysis. (b) EDCs for the $(0,+k_y)$ integration region as function of $U_B$. (c) Energy resolution determined from the EDC analysis for different momentum regions and $U_B$ values. (d) Offset of the Fermi level position determined from the EDC analysis for different momentum regions and $U_B$ values.
• Figure 5: (a,b) Fermi surface of Au(111) obtained with $U_B=-30$ V, and with slits of 0.1 mm and 0.5 mm, respectively. The spectra for each slit dimension are shown in panels (c-d) for cuts along the deflector direction ($k_x$) and in panels (e-f) for cuts along the slit direction ($k_y$). The solid red line in panels (a-f) corresponds to the physical LEC. (g) Full width at half maximum (FWHM) of the surface states at $E=E_F$ obtained along $k_x$ and $k_y$ as a function of slit dimension. (h,i) MDCs at $E=E_F$ along $k_x$ and $k_y$ for slits of 0.1, 0.3 and 0.5 mm.