Anomalous impurity-induced charge modulations in black phosphorus

TL;DR

This work investigates how ionized indium impurities on black phosphorus induce anomalous, energy-independent charge modulations. Using scanning tunneling microscopy with tip-induced band bending, the authors image a distorted triangular charge order that is strictly confined to the impurity's Coulomb potential disk and exhibits a constant wavevector $|\mathbf{q}|\approx0.32~\text{Å}^{-1}$. The modulation's spatial anisotropy is opposite to the Fermi-surface anisotropy, challenging simple Friedel-like or screening explanations and suggesting a role for nonlocal impurity potentials, quantum geometric effects, and local correlations. Moreover, by tuning the impurity potential via bias and current, they demonstrate controllable expansion and merger of modulations, indicating impurity engineering can realize macroscopic charge-ordered states in anisotropic 2D semiconductors.

Abstract

We observe anomalous charge modulations induced by ionized indium impurities on the surface of the semiconductor black phosphorus by scanning tunneling microscopy (STM). When the impurities are switched into a negatively charged state by the STM tip, periodic charge modulations emerge around the impurity center, but strictly confined by the nanoscale impurity potential. These modulations form a distorted triangular pattern, whose periodicity remains unchanged in a wide range of positive bias. Furthermore, these local charge orders exhibit an anisotropy opposite to that expected based on the anisotropy of the Fermi surface, challenging a simple band-structure interpretation. Our experiment demonstrates the possibility of creating and manipulating macroscopic charge orders through impurity engineering.

Figures (4)

• Figure 1: Charge modulations near ionized adatom impurities. (a) Schematic illustration of the experimental setup. The STM tip is brought close to the sample (gray), and the electric field between them (cyan) locally penetrates the sample. A neutral impurity (white ball) is placed on the surface. When the tip is away from the impurity, the surface electrons (blue) remains spatially uniform. The inset shows the crystal structure of the (001) surface of the black phosphorus (BP) samples used. The darker and brighter balls represent surface and subsurface phosphorus atoms, respectively. (b) Local energy diagram near the impurity for the case in (a). $E_\mathrm{C}$ and $E_\mathrm{V}$ denote band edges of the conduction (white) and valence (gray) bands, respectively. The red line indicates the Fermi level, $E_\mathrm{F}$. The blue shades illustrate the density of states on the surface. The impurity level (white) above $E_\mathrm{F}$ indicates the impurity’s charge-neutral (Imp$^0$) state. (c) Ionization (yellow ball) occurs when the local electric field reaches the impurity, and the impurity’s Coulomb potential disturbs locally the energy of surface electrons (blue). (d) Local energy diagram near the impurity for the case in (c). $V_\mathrm{B}$ is the applied bias voltage. Ionization (Imp$^-$) is represented by the impurity level (yellow) moving below the $E_\mathrm{F}$. While the dashed curves illustrate tip-induced band bending, the Coulomb potential of ionized impurity further lifts the bands (solid curves). The blue arrows represent the tunneling channels, with their lengths indicating the tunneling probabilities. (e) STM image taken near indium adatoms showing charge modulations. Setup conditions: $V_\mathrm{B}$ = 0.7 V, $I_\mathrm{set}$ = 0.1 nA. (f) Fourier-filtered image of (e), highlighting the charge modulations. Scale bar, 2 nm.
• Figure 2: Charge modulations controlled by the electric field between tip and sample. (a)--(c) Fourier-filtered STM images taken at a fixed current setpoint but with varying bias voltages. As the bias voltage increases, the size of the disk decreases. The orange arrows indicate that a charge modulation peak shown in (a) disappears at the same location in (c). (d)--(f) Fourier-filtered STM images taken at a fixed bias but with varying current setpoints. Scale bar, 2 nm.
• Figure 3: Energy dependence of charge-modulation periodicity. (a) STM image taken near a two-adatom impurity. Setup conditions: $V_\mathrm{B}$ = 1.2 V, $I_\mathrm{set}$ = 0.1 nA. (b) The normalized differential conductance $(\mathop{}\!\mathrm{d}{I}/\mathop{}\!\mathrm{d}{V})/(I/V)$ spectra along the line marked by the arrow in (a). Setup conditions: $V_\mathrm{B}$ = 1.2 V, $I_\mathrm{set}$ = 0.2 nA. (c) Band edge (black dots) appearing near $V_\mathrm{B}$ = 0.8 V in (b), extracted by finding the bias that corresponds to a maximum in the first derivative of each spectrum above 0.7 V. The impurity potential (purple) is estimated by a screened Coulomb potential SI. (d) Line-wise Fourier transform of (b). The periodic feature of the charge order is marked with the green arrow. The blue dashed curve corresponds to the expected dispersion of quasiparticle interference along the zigzag direction in the conduction band.
• Figure 4: Fourier-filtered STM images taken around two nearby cluster impurities. The bias is fixed at 0.6 V, while the current setpoint decreases from 500 pA to 50 pA. The charge modulations around both impurities are initially separated at 500 pA, and gradually expand their extensions and start to merge at 50 pA. Scale bar, 2 nm.