Atomic Valley Filter Effect Induced by an Individual Flower Defect in Graphene

Yu Zhang(张钰)$^{1,2\hyperlink{s}{*}}$, Rong Liu(刘榕)$^{1}$, Lili Zhou(周丽丽)$^{1}$, Can Zhang(张璨)$^{1}$,\\ Guoyuan Yang(杨国元)$^{2}$, Yeliang Wang(王业亮)$^{1}$, and Lin He(何林)$^{3\hyperlink{s}{*}}$

doi:10.1088/0256-307X/40/9/096801

⇦Chinese Physics Letters, 2023, Vol. 40, No. 9, Article code 096801⇨ Atomic Valley Filter Effect Induced by an Individual Flower Defect in Graphene Yu Zhang (张钰)1,2*, Rong Liu (刘榕)1, Lili Zhou (周丽丽)1, Can Zhang (张璨)1, Guoyuan Yang (杨国元)2, Yeliang Wang (王业亮)1, and Lin He (何林)3* Affiliations 1School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China 2Advanced Research Institute of Multidisciplinary Sciences, Beijing Institute of Technology, Beijing 100081, China 3Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China Received 22 June 2023; accepted manuscript online 8 August 2023; published online 23 August 2023 ^*Corresponding authors. Email: yzhang@bit.edu.cn; helin@bnu.edu.cn Citation Text: Zhang Y, Liu R, Zhou L L et al. 2023 Chin. Phys. Lett. 40 096801 Abstract Owing to the bipartite nature of honeycomb lattice, the electrons in graphene host valley degree of freedom, which gives rise to a rich set of unique physical phenomena including chiral tunneling, Klein paradox, and quantum Hall ferromagnetism. Atomic defects in graphene can efficiently break the local sublattice symmetry, and hence, have significant effects on the valley-based electronic behaviors. Here we demonstrate that an individual flower defect in graphene has the ability of valley filter at the atomic scale. With the combination of scanning tunneling microscopy and Landau level measurements, we observe two valley-polarized density-of-states peaks near the outside of the flower defects, implying the symmetry breaking of the $K$ and $K'$ valleys in graphene. Moreover, the electrons in the $K$ valley can highly penetrate inside the flower defects. In contrast, the electrons in the $K'$ valley cannot directly penetrate, instead, they should be assisted by the valley switch from the $K'$ to K. Our results demonstrate that an individual flower defect in graphene can be regarded as a nanoscale valley filter, providing insight into the practical valleytronics.

DOI:10.1088/0256-307X/40/9/096801 © 2023 Chinese Physics Society Article Text Apart from spin degree of freedom, the electrons in graphene host valley degree of freedom, owing to the bipartite nature of honeycomb lattice.[1] A rich set of intrinsic valley-based physical phenomena, such as chiral tunneling, Klein paradox, and quantum Hall ferromagnetism, are expected to exhibit in graphene.[1-3] Previous studies have been demonstrated that single-atom defects in graphene, including an individual C-atom vacancy, H-atom absorption, and N-atom substitution, can efficiently break the local sublattice symmetry of graphene, and hence, give rise to valley-polarized states.[4,5] Topological defects are another kind of atomic defects that are usually ubiquitous and unavoidable in graphene during the epitaxial growth.[6] For each topological defect, the local hexagonal lattice prefers to reconstruct into networks of five- and seven-membered rings, nesting in the intrinsic graphene lattice and leaving no unsatisfied bonds. Over the past decade, extensive investigations have been focused on the effect of topological defects on the structural, mechanical, and electronic properties of graphene.[7-11] However, to the best of our knowledge, a microscopic exploration of valley-based physical properties modulated by topological defects has still been experimentally lacking. To address this problem, in the present work, we perform high-precision Landau level (LL) measurements on individual flower defects, a class of topological defects with the lowest formation energy,[12,13] at the atomic scale via scanning tunneling microscopy/spectroscopy (STM/STS) under out-of-plane magnetic fields. Near the outside of a flower defect, the zeroth LL exhibits two valley-polarized density-of-states (DOS) peaks, implying the local symmetry breaking of the $K$ and $K'$ valleys in graphene. Moreover, the electrons in the $K$ valley can highly penetrate inside the flower defects. In contrast, the electrons in the $K'$ valley cannot directly penetrate, instead, they should be assisted by the valley switch from the $K'$ to $K$ valley. Our results demonstrate that an individual flower defect in graphene can be regarded as a nanoscale valley filter, providing insight into the practical valleytronics. In our experiments, we directly synthesize multilayer graphene on Ni foils by using a chemical vapor deposition (CVD) method, as we previously reported.[14] The graphene layers are usually rotationally misaligned, resulting in moiré patterns presented in STM images. Figure 1(a) shows a representative large-scale STM image of our as-grown graphene samples. The superlattice period of the moiré pattern $\lambda$ is about 2.5 nm, yielding the twisted angle $\theta$ between the topmost two graphene sheets of about 6$^{\circ}$ ($\lambda =a/[2\sin(\theta/2)]$, $a = 0.246$ nm is the atomic lattice of monolayer graphene). In such a case, the topmost monolayer graphene usually electronically decouples with the underlying graphene sheets, and hence, is expected to behave as a freestanding monolayer graphene, as we will discuss later. Owing to the substrate imperfections and kinetic factors of the CVD growing process, there is usually a concentration of flower defects in the topmost monolayer graphene,[12] exhibiting as protrusions in the large-scale STM images. Figures 1(b) and 1(c) show zoom-in STM image of an individual flower defect and its corresponding atomic structure, respectively. In each flower defect, the central seven six-membered rings are cut and rotate relatively to the pristine graphene lattice, and thus, form a grain boundary loops consisting of close-packed five- and seven-membered rings with hexagonal symmetry and leave no unsatisfied bonds.[12,13,15] In fact, flower defect is the most common topological defects appearing in graphene, because it possesses the lowest energy per dislocation core, as demonstrated by density functional theory (DFT) calculations.[12]

Fig. 1. Intervalley scattering induced by an individual flower defect in graphene. (a) Large-scale STM topographic image of graphene with flower defects. (b) Fourier transform of panel (a). The outer and inner bright spots marked by the white and yellow circles correspond to the reciprocal lattices of topmost monolayer graphene and graphene moiré superlattice. The central six bright spots marked by the green circles correspond to the intervalley scattering induced by flower defects. (c) Atomically resolved STM image of an individual flower defect in graphene. (d) Fourier transform of panel (c). (e) Atomic structure of an individual flower defect in graphene. The five- and seven-membered rings of the flower defect are filled with yellow and green, respectively. (f) Schematic of intervalley scattering process in monolayer graphene.

Fig. 2. Electronic properties of an individual flower defect in graphene in the absence of magnetic field. (a) Typical STM image of an individual flower defect in graphene. (b) Typical STS spectra recorded on the flower defect (blue line) and pristine graphene (red line) in the absence of magnetic field. [(c), (d)] STS maps recorded at the same location of panel (a) under the sample biases of 0.4 and 0.5 V, respectively. The center of the flower defect is marked by the blue dots.

Figure 1(d) shows the Fourier transform of the large-scale STM image in Fig. 1(a). The reciprocal lattices of the topmost monolayer graphene lattice and moiré superlattice can be clearly identified, as marked by the white and yellow circles, respectively. Moreover, there are additional six bright spots (marked by green circles) appearing at the corners of graphene Brillouin zone, which correspond to the $\sqrt 3 \times \sqrt 3 R~{30}^{\circ}$ interference pattern in the STM image. In addition, these bright spots become much more evident for the atomically resolved measurements of an individual flower defect, as exhibited in Figs. 1(b) and 1(e). Such a signature can be attributed to the flower-defect-induced intervalley scattering, as depicted in Fig. 1(f), since the local sublattice symmetry is broken.[16-21] Now we concentrate on the electronic properties modulated by an individual flower defect in graphene in the absence of magnetic field. Away from the flower defects, the STS spectrum exhibits the typical V shape, which reflects the local DOS of massless Dirac fermions in pristine monolayer graphene. When approaching the center of an individual flower defect, there is a DOS peak emerging at the energy of about 0.4 eV [Figs. 2(a) and 2(b)], in excellent agreement with the previous studies.[22,23] Moreover, there is almost no difference in the peak energy for the STS spectra acquired inside the five- and seven-membered rings of the flower defect. The electronic states induced by an individual flower defect can be further characterized by the high-resolution STS maps. From Figs. 2(c) and 2(d), we can find out that the electronic states at the energy of the DOS peak mainly localize on the flower defect [Fig. 2(c) for 0.4 eV]. However, in contrast, there is less electronic concentration in the vicinity of the flower defect when the acquired energy is not at the DOS peak [Fig. 2(d) for 0.5 eV as an example]. High-resolution LL spectra of an individual flower defect in graphene, acquired via STM/STS measurements under out-of-plane magnetic fields, allow us to directly detect rich valley-based phenomena. Figure 3(a) shows the evolution of the series of LLs as a function of magnetic field $B$ from 5 T to 10 T when recorded near the outside of an individual flower defect. All the LLs exhibit sharp DOS peaks and are well defined (the LL indices are marked accordingly), and satisfy the characteristic of the massless Dirac fermion in monolayer graphene (For the massless Dirac fermions in monolayer graphene, the energies of the discrete Landau levels can be described by $E_{n}={\rm sgn}(n)\sqrt {2e\hslash v_{\scriptscriptstyle{\rm F}}|n|B} +E_{0}$, where $E_{0}$ is the energy of Dirac point, $e$ is the electron charge, $n = \ldots, -2, -1, 0, 1, 2,\ldots$ is the Landau index, $\hslash$ is Planck's constant, and $v_{\scriptscriptstyle{\rm F}}$ is the Fermi velocity).[24-28] As a result, the topmost graphene layer is electronically decoupled from the underlying graphene sheets, as mentioned above. Among all the LLs, the zeroth LL is of great significance. On the one hand, the quasiparticle lifetimes are inversely proportional to energy, yielding the longest lifetime and the sharpest DOS peaks for the zeroth LL.[29] On the other hand, there are spin and valley fourfold degeneracy for pristine monolayer graphene. The spin and/or valley symmetry breaking, as a consequence, can be directly captured by the splitting behavior of the zeroth LL.

Fig. 3. Electronic properties outside flower defects of monolayer graphene under magnetic fields. (a) STS spectra recorded outside a flower defect in graphene under different magnetic fields. The Landau level indices are labeled in the panel. (b) High-resolution STS spectra of the zeroth Landau level recorded outside a flower defect under different magnetic fields. (c) Schematic DOS of Landau levels in monolayer graphene under high magnetic fields. The zeroth Landau level exhibits fourfold valley and spin degeneracies. Owing to the existence of flower defects, the zeroth Landau level splits into two valley-polarized DOS peaks. (d) Energy separations of two valley-polarized states in monolayer graphene as a function of magnetic field, yielding a linear relation with the slope of $1.5 \pm 0.1$ meV/T and an effective g factor of about 24.

A close examination of the zeroth LL evolution as a function of out-of-plane magnetic fields near the outside of an individual flower defect shows that the zeroth LL splits into two DOS peaks, with their intensities roughly equal and the energy separation of several meV, as exhibited in Fig. 3(b). Around flower defects, the local sublattice symmetry of graphene is expected to be broken,[29,30] and therefore, these two DOS peaks of the zeroth LL can be unambiguously attributed to the valley-polarized states, i.e., $K$ and $K'$, as schematically depicted in Fig. 3(c). By further summarizing the energy of valley splitting $\Delta E$ as a function of magnetic fields $B$ in Fig. 3(d), we can observe a linear relation between $\Delta E$ and $B$ with the slope of $1.5 \pm 0.1$ meV/T, as well as an effective $g$ factor of about 24 based on a Zeeman-like dependence $\Delta E=g\mu_{\scriptscriptstyle{\rm B}}B$ ($\mu_{\scriptscriptstyle{\rm B}}$ is the Bohr magneton). Such a value of the effective $g$ factor is reasonable for the valley splitting of the zeroth LL, in consistence with the previous studies.[31,32] The evolution of the zeroth LL across an individual flower defect in monolayer graphene is of particular interest. Figure 4(b) shows the zeroth LL recorded near the outside and at the center of a flower defect, as marked in Fig. 4(a). We should first mention that the central seven six-membered rings of a flower defect are unable to generate LLs by themselves, because their size is much smaller than the LL-formation size of about the magnetic length $l_{\scriptscriptstyle{\rm B}}=\sqrt \hslash/(eB)$. As a consequence, the detected LLs inside the flower defect, i.e., within the grain boundary loops consisting of five- and seven-membered rings, are expected to originate from the spatial extent of the wave functions for the corresponding LLs outside the defect. From Fig. 4(b), we can observe an obvious contrast in intensity for the splitting zeroth LL measured outside and inside the flower defect. Specifically, for the zeroth LL measured outside the flower defect [red line in Fig. 4(b)], the intensities of the DOS peaks for the $K$ and $K'$ valleys are nearly the same. However, for the inside case [blue line in Fig. 4(b)], the intensity of the DOS peak for the $K'$ valley is dramatically suppressed and almost vanished, while the intensity for the $K$ valley is strongly enhanced, reaching approximately twice the value of the outside case. To make the result more convinced, we carry out STS measurement across an individual flower defect under different out-of-plane magnetic fields. Figures 4(c)–4(e) show spatially resolved STS spectra of the zeroth LL along the red arrow in Fig. 4(a) under $B = 10$, 8, and 6 T, respectively, where the center of the flower defect is set as $x = 0$ nm. Consistent with the above description, the intensity of the DOS peak inside the flower defect for the $K'$ valley is almost vanished while for the $K$ valley is strongly enhanced. Similar observations have been obtained for several flower defects in graphene, which help us rule out any possible artifacts. Considering that the detected LLs inside the flower defect originates from the spatial extent of the wave functions for the corresponding LLs outside the defect, we can conclude that the incoming electrons in the $K$ valley can highly penetrate inside the flower defects. However, in contrast, the incoming electrons in the $K'$ valley cannot directly penetrate, instead, they should be assisted by the valley switch from the $K'$ valley to the $K$ valley, as schematically depicted in Fig. 4(f). Therefore, our results provide direct evidence that an individual flower defect can be regarded as a nanoscale valley filter.

Fig. 4. Electronic properties inside flower defects of monolayer graphene under magnetic fields. (a) Typical STM image of an individual flower defect in graphene. (b) Typical STS spectra recorded outside (red line) and inside (blue line) the flower defect under $B = 10$ T. (c)–(e) Spatially resolved STS spectra recorded across the flower defect along the red arrow in panel (a) under $B = 10$, 8, and 6 T, respectively. (f) Schematic of atomic valley filter effect induced by flower defects in graphene.

Indeed, valley filter effect in graphene systems has been widely studied in the past decade, since it is the central component in valleytronics. For example, line defects in graphene, which are composed of five- and eight-membered rings, are theoretically proposed to exhibit a valley filter effect that the incident electrons in the $K$ or $K'$ valley can be well transmitted or reflected, owing to energy and momentum conservation along the defects.[33] Another example is zigzag graphene nanoribbon with a designed geometry, where the incident electrons in the $K$ valley can be either reflected or transmitted into the $K'$ valley, depending on the width of the nanoribbon.[34] In addition, valley filter effect is also expected to take place around the ballistic point contacting with zigzag edges[35] and strained structures graphene.[36,37] However, we cannot provide an exact verification for the physical origin of such a valley filter effect induced by an individual flower defect observed in our experiments at present, which needs further exploration. In summary, we have systematically studied the nanoscale valley filter effect in monolayer graphene induced by individual flower defects via the high-precision LL spectra. Flower defects can locally break the sublattice symmetry in graphene, thus giving rise to the valley-polarized states. Moreover, the electrons in the $K$ valley can highly penetrate inside the flower defects, while the electrons in the $K'$ valley cannot directly penetrate, instead, they should be assisted by the valley switch from the $K'$ to $K$ valley. Our results demonstrate that an individual flower defect in graphene can be regarded as a nanoscale valley filter, opening a road to realize and tailor valley-based nanodevices. Methods. The low-pressure chemical-vapor-deposition method was employed to grow controllable layers of graphene on Ni(111) single crystal. The Ni(111) single crystal was first heated from room temperature to 900 ℃ in 40 min under an argon (Ar) flow of 100 SCCM (SCCM stands for standard cubic centimeters per minute) and hydrogen (H$_2$) flow of 100 SCCM, and keep this temperature and flow ratio for 20 min. Next CH$_4$ gas was introduced with a flow ratio of 20 SCCM, the growth time is $\sim$ 15 min, and then cooled down to room temperature. Then samples are transferred into the ultrahigh vacuum condition for further characterizations. STM/STS measurements. STM/STS measurements were performed using a custom-designed STM system at 4.2 K under ultrahigh-vacuum conditions (USM-1300, Unisoku). An electrochemically etched tungsten tip was used as the STM probe, which was calibrated by using a standard graphene lattice and a Si(111)-($7 \times 7$) lattice. The STS measurements were taken by a standard lock-in technique with the bias modulation of 2 mV at 973 Hz. Acknowledgments. This work was supported by the National Key R&D Program of China (Grant Nos. 2022YFA1402502, 2022YFA1402602, 2021YFA1400103, and 2020YFA0308800), the National Natural Science Foundation of China (Grant Nos. 92163206 and 12274026), and China Postdoctoral Science Foundation (Grant No. 2021M700407). 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