Anisotropic Two-Dimensional Screening at the Surface of Black Phosphorus

Electronic screening can have direct consequences for structural arrangements on the nanoscale, such as on the periodic ordering of adatoms on a surface. So far, such ordering phenomena have been explained in terms of isotropic screening of free electronlike systems. Here, we directly illustrate the structural consequences of anisotropic screening, making use of a highly anisotropic two-dimensional electron gas (2DEG) near the surface of black phosphorous. The presence of the 2DEG and its filling is controlled by adsorbed potassium atoms, which simultaneously serve to probe the electronic ordering. Using scanning tunneling microscopy, we show that the anisotropic screening leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band bending-induced 2DEG near the surface. The electronic dispersion of the 2DEG inferred by electronic ordering is consistent with that measured by angle-resolved photoemission spectroscopy.

Figure 1

Clean and K-doped black phosphorus. (a) STM constant-current image showing pristine black phosphorus with characteristic vacancies ($V_s=-400\mathrm{mV}$, $I_t=20\mathrm{pA}$, scale $\mathrm{bar}=10\mathrm{nm}$). The inset shows an atomically resolved image of the black phosphorus surface ($V_s=-100\mathrm{mV}$, $I_t=40\mathrm{pA}$). The notation used here is $\mathrm{armchair}=x=[100]$ and $\mathrm{zig}z\text{ag}=y=[010]$. (b) K-doped black phosphorus at areal adatom density $n_K=7.0\times {10}^{11}{\mathrm{cm}}^{-2}$ after low-temperature deposition at $T=4.4\mathrm{K}$. K adatoms appear as isotropic protrusions with an apparent height of approximately 200 pm ($V_s=1\mathrm{V}$, $I_t=10\mathrm{pA}$, scale $\mathrm{bar}=10\mathrm{nm}$).

Figure 2

Temperature-dependent distribution of K adatoms. (a) Large-scale STM constant-current image of K-doped BP (adatom density $n_K=2.0\times {10}^{12}{\mathrm{cm}}^{-2}$) after low-temperature deposition at $T=4.4\mathrm{K}$ ($V_s=-1\mathrm{V}$, $I_t=3\mathrm{pA}$, scale $\mathrm{bar}=20\mathrm{nm}$). The $x$,$y$ orientation refers to the atomic lattice in Fig. 1 and is the same for (b)–(d). (b)–(d) STM constant current images taken at $T=4.4\mathrm{K}$ after annealing the K-doped BP sample for ten minutes to $T_{\text{anneal}}=5.6\text{K}$, 8.0 K, and 14.8 K, respectively ($V_s=-1\mathrm{V}$, $I_t=3\mathrm{pA}$, scale $\mathrm{bar}=20\mathrm{nm}$). (e)–(h) Mean interaction potentials for single K dopant at (0,0) calculated from multiple images. Line cuts from mean interaction potential (i) along $x$ and (j) along $y$. The arrows in (e) refer to the directions of these line cuts.

Figure 3

Density-dependent mean interaction potentials. Mean interaction potentials for varying K adatom density ($n_K$) are shown after annealing the samples to 13.4 K (lowest density), 14.8 K (medium and high density), and approximately 18.0 K (highest density). (a) Mean interaction potential for lowest K density ($n_K=7.0\times {10}^{11}{\mathrm{cm}}^{-2}$) showing isotropic screening behavior. (b) Mean interaction potential at $n_K=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$, revealing the onset of screening anisotropy. (c),(d) Mean interaction potential for $n_K=2.0\times {10}^{12}{\mathrm{cm}}^{-2}$ and $n_K=1.8\times {10}^{13}{\mathrm{cm}}^{-2}$, respectively.

Figure 4

Relation between electron filling and screening. (a) Line profiles of the oscillatory mean interaction potential along $y$ for samples doped with $n_K=1.4\times {10}^{12}{\mathrm{cm}}^{-2}$ (dark blue), $n_K=2.0\times {10}^{12}{\mathrm{cm}}^{-2}$ (red), and $n_K=1.8\times {10}^{13}{\mathrm{cm}}^{-2}$ (orange). Points indicate measured data from Fig. 3, while the solid lines show fits of the data to Eq. (1) described in the text. (Inset) Illustration of the anisotropic CB of BP with colored slices indicating doping levels from Figs. 3 and 4. (b) and (c) ARPES data taken after dosing K onto BP with $n_K=1.5\times {10}^{13}{\mathrm{cm}}^{-2}$ showing a 2D electronlike band along (b) $\overline{\mathrm{\Gamma }}-\overline{X}$ and (c) $\overline{\mathrm{\Gamma }}-\overline{Y}$ directions. Momentum distribution cuts (red) at $E_F$ show distinct $k_F$ peaks (red arrows) that yield $2*k_{F,y}=0.28{\AA }^{-1}$ and $2*k_{F,x}=0.13{\AA }^{-1}$, respectively. (d) Comparison of the Fermi wave vectors along $\overline{\mathrm{\Gamma }}-\overline{X}$ and $\overline{\mathrm{\Gamma }}-\overline{Y}$ as a function of potassium density ($n_K$) for ARPES data (solid and dashed lines) and STM data (points). The coverage for the ARPES data in (b) and (c) approximately corresponds to the orange markers of the STM data. Dopant density for ARPES data was calculated using Luttinger’s theorem under the assumption that a single electron per K atom is transferred to the BP surface layer (black) and 0.8 electrons are transferred (gray).