Two-dimensional Surface States Research Articles

Nanoscale mapping of relativistic photocarrier transports in epitaxial graphene surface and edge states

We report the direct mapping of photo-transport properties of relativistic carriers generated on terrace-surface and terrace-edge structures of epitaxial graphene grown on silicon carbide. In this method, a conductive probe made a direct contact with epitaxial graphene and scanned the surface, allowing us to map the topography, current, and noise of graphene with nanoscale resolutions via a scanning noise microscopy. The maps were further analyzed by a two-dimensional network model to obtain the sheet-conductance (S□) and noise-source density (neff) distributions of epitaxial graphene. The topography image showed the formation of terraces, which could be attributed to the different decomposition rate of silicon atoms during the graphene growth. The terraces of graphene exhibited uniform S□, being separated by one-dimensional terrace-edges. Interestingly, terrace-edges exhibited a rather large neff with a power-law relationship of S□ ∝ neff−0.5, indicating a typical hopping conduction. However, in terrace-surfaces, sheet-conductance was nearly independent on neff, which was attributed to the relativistic nature of charge carriers unaffected by charge-trapping potential. Notably, under illumination, we observed the relativistic behavior of photocarriers in overall graphene terraces, presumably because photocarriers were generated through charge-transfer complexes formation at epitaxial graphene/substrate interface without the participation of noise-sources. Interestingly, we observed nearly homogeneous photoconductance and neff, which could be possibly due to the merger of one-dimensional edge-states into two-dimensional surface-states. The mapping of photoconductance and photo-traps provides valuable insights into the generation of relativistic photocarriers in epitaxial graphene.

Probing surface states: A study of UCF and WAL in Bi1.9Sb0.1Te2Se topological insulator

In the exploration of three-dimensional quaternary topological insulators, understanding surface states has become pivotal for unraveling the underlying physics and tapping into potential applications. Our study delves into the temperature and magnetic field-angle dependence of universal conductance fluctuations (UCF) and weak anti-localization (WAL) effects in a Bi1.9Sb0.1Te2Se topological insulator-based mesoscopic device. Conventionally, other low-temperature transport phenomena in probing surface states may inevitably face interference from three-dimensional bulk conductance. However, we experimentally demonstrate that, at low temperatures, UCF reflects the properties of two-dimensional topological surface states more accurately, thereby providing a more reliable and distinct way to confirm their existence. Moreover, we carefully analyze the temperature-dependent WAL using the Hikami–Larkin–Nagaoka model, proposing a crucial role for charge puddles associated with electrostatic fluctuations in the electron dephasing process. Our findings not only emphasize the key role of UCF in unveiling the underlying behavior of topological surface states but also offer a deeper understanding of phase-coherent transport in quaternary topological insulators.

Finite size effects on helical hinge states in three-dimensional second-order topological insulators

We investigate the finite size effects of a three-dimensional second-order topological insulator with fourfold rotational symmetry and time-reversal symmetry. Starting from the effective Hamiltonian of the three-dimensional second-order topological insulator, we derive the effective Hamiltonian of four two-dimensional gapped surface states by perturbative methods. Then, the sign alternation of the mass term of the effective Hamiltonian on the adjacent surface leads to the hinge state. In addition, we obtain the effective Hamiltonian and its wave function of one-dimensional gapless hinge states with semi-infinite boundary conditions based on the effective Hamiltonian of two-dimensional surface states. In particular, we find that the hinge states on the two sides of the same surface can couple to produce a finite energy gap.

Room Temperature Spin-to-Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers.

Disordered topological insulator (TI) films have gained intense interest by benefiting from both the TI's exotic transport properties and the advantage of mass production by sputtering. Here, we report on the clear evidence of spin-charge conversion (SCC) in amorphous Gd-alloyed BixSe1-x (BSG)/CoFeB bilayers fabricated by sputtering, which could be related to the amorphous TI surface states. Two methods have been employed to study SCC in BSG (tBSG = 6-16 nm)/CoFeB(5 nm) bilayers with different BSG thicknesses. First, spin pumping is used to generate a spin current in CoFeB and detect SCC by the inverse Edelstein effect (IEE). The maximum SCC efficiency (SCE) is measured to be as large as 0.035 nm (IEE length λIEE) in a 6 nm thick BSG sample, which shows a strong decay when tBSG increases due to the increase of BSG surface roughness. The second method is THz time-domain spectroscopy, which reveals a small tBSG dependence of SCE, validating the occurrence of a pure interface state-related SCC. Furthermore, our angle-resolved photoemission spectroscopy data show dispersive two-dimensional surface states that cross the bulk gap until the Fermi level, strengthening the possibility of SCC due to the amorphous TI states. Our studies provide a new experimental direction toward the search for topological systems in amorphous solids.

Kagome surface states and weak electronic correlation in vanadium-kagome metals

RVSn (R = Y and lanthanides) with two-dimensional vanadium-kagome surface states is an ideal platform to investigate kagome physics and manipulate the kagome features to realize novel phenomena. Utilizing the micron-scale spatially resolved angle-resolved photoemission spectroscopy and first-principles calculations, we report a systematical study of the electronic structures of RVSn (R = Gd, Tb, and Lu) on the two cleaved surfaces, i.e. the V- and RSn1-terminated (001) surfaces. The calculated bands without any renormalization match well with the main ARPES dispersive features, indicating the weak electronic correlation in this system. We observe ‘W’-like kagome surface states around the Brillouin zone corners showing R-element-dependent intensities, which is probably due to various coupling strengths between V and RSn1 layers. Our finding suggests an avenue for tuning electronic states by interlayer coupling based on two-dimensional kagome lattices.

Flexible dimensional hierarchy of higher-order topology in the stacked Kagome-chain acoustic crystal

Manipulating wave propagation and energy collection plays a core role in modern physics, for which topological insulators hosting robust boundary states offer an ideal platform. However, there exist challenges in integrating multiple topological states like two-dimensional (2D) surface state, one-dimensional (1D) hinge state, and zero-dimensional (0D) corner state into a single three-dimensional (3D) architecture. Here we introduce a dimensional hierarchy acoustic structure with a piled 3D Kagome-chain crystal. By tuning the inter- and intra-layer hopping, we lift the 3D bulk states into 2D surface states. A further distortion on the in-plane unit cell makes the system support the 1D hinge and 0D corner states simultaneously. This hierarchy keeps the parent architecture unchanged. Analytically, we prove the robustness of our framework in different geometrical configurations. Our research offers insight for the practical use of the sonic or optical device with diversified topological modes like wave concentrations and transmissions.

Transport properties of a 1000 nm HgTe film: the interplay of surface and bulk carriers

We report on systematic study of transport properties of a 1000 nm HgTe film. Unlike thinner and strained HgTe films, which are known as high-quality three-dimensional topological insulators, the film under study is much thicker than the limit of pseudomorphic growth of HgTe on a CdTe substrate. Therefore, the 1000 nm HgTe film is expected to be fully relaxed and has the band structure of bulk HgTe, i.e. a zero gap semiconductor. Additionally, the system is characterized by the bands inversion, so that the two-dimensional topological surface states (TSSs) are expected to exist. To check this claim we studied classical and quantum transport response of the system. We demonstrate that by tuning the top-gate voltage one can change the electron-dominating transport to the hole one. The highest electron mobility is found to be more than cm2 Vs−1. The system exhibits Shubnikov-de Haas (SdH) oscillations with a complicated pattern and shows up to five independent frequencies in corresponding Fourier spectra. These Fourier peaks are attributed to the TSSs, Volkov-Pankratov states and spin-degenerate bulk states in the accumulation layer near the gate. The observed peculiarities of the quantum transport are the strong SdH oscillations of the Hall resistance, and the suppressed oscillatory response of the TSSs.

Gate-tunable transport in van der Waals topological insulator Bi4Br4 nanobelts

Bi4Br4 is a quasi-one-dimensional van der Waals topological insulator with novel electronic properties. Several efforts have been devoted to the understanding of its bulk form, yet it remains a challenge to explore the transport properties in low-dimensional structures due to the difficulty of device fabrication. Here we report for the first time a gate-tunable transport in exfoliated Bi4Br4 nanobelts. Notable two-frequency Shubnikov–de Haas oscillations oscillations are discovered at low temperatures, with the low- and high-frequency parts coming from the three-dimensional bulk state and the two-dimensional surface state, respectively. In addition, ambipolar field effect is realized with a longitudinal resistance peak and a sign reverse in the Hall coefficient. Our successful measurements of quantum oscillations and realization of gate-tunable transport lay a foundation for further investigation of novel topological properties and room-temperature quantum spin Hall states in Bi4Br4.

Observation of spin-momentum locked surface states in amorphous Bi2Se3.

Crystalline symmetries have played a central role in the identification and understanding of quantum materials. Here we investigate whether an amorphous analogue of a well known three-dimensional strong topological insulator has topological properties in the solid state. We show that amorphous Bi2Se3 thin films host a number of two-dimensional surface conduction channels. Our angle-resolved photoemission spectroscopy data are consistent with a dispersive two-dimensional surface state that crosses the bulk gap. Spin-resolved photoemission spectroscopy shows this state has an anti-symmetric spin texture, confirming the existence of spin-momentum locked surface states. We discuss these experimental results in light of theoretical photoemission spectra obtained with an amorphous topological insulator tight-binding model, contrasting it with alternative explanations. The discovery of spin-momentum locked surface states in amorphous materials opens a new avenue to characterize amorphous matter, and triggers the search for an overlooked subset of quantum materials outside of current classification schemes.

Metal to Wigner-Mott insulator transition in two-leg ladders

We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $\nu = 1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insulator is a ladder analog of the two-dimensional spinon surface state. In both cases, a charge neutral spinless mode remains gapless across the Wigner-Mott transition. We discuss physical properties of these transitions, and comment on insights obtained for thinking about continuous Wigner-Mott transitions in two-dimensional systems which are being studied in moire materials.

Unusual Magnetotransport from two-dimensional Dirac Fermions in Pd3Bi2Se2

Pd$_{3}$Bi$_{2}$Se$_{2}$ has been proposed to be topologically non-trivial in nature. However, evidence of its non-trivial behavior is still unexplored. We report the growth and magneto-transport study of Pd$_{3}$Bi$_{2}$Se$_{2}$ thin films, revealing for the first time the contribution of two-dimensional (2D) topological surface states. We observe exceptional non-saturated linear magnetoresistance which results from Dirac fermions inhabiting the lowest Landau level in the quantum limit. The transverse magnetoresistance changes from a semi-classical weak-field $B^{2}$ dependence to a high-field $B$ dependence at a critical field $B^{\star}$. It is found that $B^{\star} \propto T^2$, which is expected from the Landau level splitting of a linear energy dispersion. In addition, the magnetoconductivity shows signatures of 2D weak anti-localization (WAL). These novel magnetotransport signatures evince the presence of 2D Dirac fermions in Pd$_{3}$Bi$_{2}$Se$_{2}$ thin films.

Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators.

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.

Floquet-Weyl semimetals generated by an optically resonant interband transition

Floquet-Weyl semimetals (FWSMs) generated by irradiation of a continuous-wave laser with left-hand circular polarization (rotating in counterclockwise sense with time) on the group II--V narrow-gap semiconductor ${\mathrm{Zn}}_{3}{\mathrm{As}}_{2}$ are theoretically investigated, where the frequency of the laser is set nearly resonant with the band gap of the crystal. It is found that the excitation of the crystal by such a laser induces two types of FWSM phases that differ absolutely in character. To be specific, the associated two pairs of Weyl points are stably formed by band touching between Floquet sidebands ascribable to a valence band labeled ${J}_{z}=\ifmmode\pm\else\textpm\fi{}3/2$ and a conduction band labeled ${J}_{z}=\ifmmode\pm\else\textpm\fi{}1/2$, where ${J}_{z}$ represents the $z$ component of total angular-momentum quantum number of the $\mathrm{\ensuremath{\Gamma}}$ point and a double sign corresponds. Here, one FWSM state composed of the up-spin Floquet sidebands relevant to ${J}_{z}=3/2$ and $1/2$ shows almost quadratic band-touching in the vicinity of the associated pair of Weyl points, while the other FWSM state composed of the down-spin Floquet sidebands relevant to ${J}_{z}=\ensuremath{-}3/2$ and $\ensuremath{-}1/2$ shows linear band-touching. Furthermore, it is revealed that both up-spin and down-spin sidebands host nontrivial two-dimensional surface states that are pinned to the respective pairs of the Weyl points. Both surface states also show different energy dispersions and physical properties. A more detailed discussion is presented in the text on the origin of the above findings, the chirality of the FWSM phases, the alteration of topological order, laser-induced magnetic properties, and so on.

Planar magnetic texture on the surface of a topological insulator

We study the planar magnetic textures coupled to a two-dimensional Dirac surface state, where both the magnetic texture and surface state form in the magnetic topological insulator surface layer. It is shown that the radial vortex with winding number $w=\ifmmode\pm\else\textpm\fi{}1$ leads to the confinement of Dirac states, where a mapping to the Schr\"odinger equation of a two-dimensional hydrogen atom is found. The fully spin-polarized zero-energy bound state forms a flat band that resembles the zeroth Landau level of Dirac electrons in a uniform out-of-plane magnetic field. Remarkably, the number of the zero-energy state is topologically robust. Interestingly, when such a system is proximity coupled to an $s$-wave superconductor, the existence of Majorana zero modes at the Abrikosov vortex depends only on the relative value of the magnetic exchange coupling and the pairing strength. We conclude with a brief discussion on the physical realization with such magnetic textures.

Identifying Majorana vortex modes via nonlocal transport

The combination of two-dimensional Dirac surface states with s-wave superconductivity is expected to generate localized topological Majorana zero modes in vortex cores. Putative experimental signatures of these modes have been reported for heterostructures of proximitized topological insulators, iron-based superconductors or certain transition metal dichalcogenides. Despite these efforts, the Majorana nature of the observed excitation is still under debate. We propose to identify the presence of Majorana vortex modes using a nonlocal transport measurement protocol originally employed for one-dimensional settings. In the case of an isolated subgap state, the protocol provides a spatial map of the ratio of local charge- and probability-density which offers a clear distinction between Majorana and ordinary fermionic modes. We show that these distinctive features survive in the experimentally relevant case of hybridizing vortex core modes.

Emergent plasmonic excitations in Mexican-hat and bell-shaped bands of hybridized Dirac electrons in graphene/topological insulator heterostructures

Stacking a graphene monolayer onto a three-dimensional topological insulator results in a van der Waals heterostructure that can serve as a versatile platform for rich emergent exotic physics. In particular, the Dirac electrons of the graphene and that of the two-dimensional surface states of the topological insulator hybridize effectively, leading to the emergence of two distinct electronic bands around the Fermi level, with respective Mexican-hat and bell shapes. In this paper, we explore the emergent collective plasmonic excitations in the representative heterostructure of graphene/${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$, combining first-principles calculations and low-energy effective Hamiltonian descriptions. We discover two different plasmon modes of the system, and our band-resolved analysis allows us to attribute the two modes to the intraband transitions within the Mexican-hat and bell-shaped bands, respectively. We also analyze the relative strengths and damping rates of the plasmon modes upon variations of the bias potential across the heterojunction, enabling potential experimental detections of those collective excitations. These findings provide alternate avenues for regulating the electronic states and plasmonic excitations in the hybridized Dirac electron systems for potential device applications.

Chiral symmetry protected topological nodal superconducting phase and Majorana Fermi arc

With an external in-plane magnetic field, we show the emergence of a topological nodal superconducting phase of the two-dimensional topological surface states. This nodal superconducting phase is protected by the chiral symmetry with a non-zero magnetic field, and there are corresponding Majorana Fermi arcs (also known as flat band Andreev bound states) connecting the two Majorana nodes along the edges, similar to the case of Weyl semimetal. The topological nodal superconductor is an intermediate phase between two different chiral superconductors, and is stable against the effects of substrates. The two-dimensional effective theory of the nodal superconducting phase also captures the low energy behavior of a three-dimensional lattice model which describes the iron-based superconductor with a thin film geometry. The localizations of the Majorana nodes can be manipulated through external in-plane magnetic fields, which may introduce a non-trivial topological Berry phase between them.

Magnetotransport and high-resolution angle-resolved photoelectron spectroscopy studies of palladium-doped Bi2Te3

We have performed magnetotransport and high-resolution angle-resolved photoelectron spectroscopy (ARPES) measurements on topological insulator ${\mathrm{Pd}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}(0\ensuremath{\le}x\ensuremath{\le}0.20)$ single crystals. We have observed unusually high values of magnetoresistance ($\ensuremath{\sim}1500%$) and mobility $(\ensuremath{\sim}93\phantom{\rule{0.16em}{0ex}}000\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.28em}{0ex}}{\mathrm{V}}^{--1}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{--1})$ at low temperatures for pristine ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ that decrease upon Pd doping. Shubnikov--de Haas (SdH) oscillations were detected for $x=0.05$, 0.10, confirming the presence of two-dimensional topological surface states (TSSs) for these samples. Hall measurement shows the crossover from $n$-type charge carriers in pristine ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ to $p$-type charge carriers upon Pd doping. The ARPES measurements show that the conduction band crosses the Fermi level for pristine ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and the Dirac point of the TSSs and bulk-derived valence bands indicated a shift to lower binding energy upon Pd doping in a rigid-band-like way up to $x\ensuremath{\sim}0.10$. Based on the comparison of the parameters obtained from the SdH and ARPES measurements, the reduction in the ${k}_{\mathrm{F}}$ value in the magnetotransport measurements is likely due to the band bending induced by the Schottky barrier.

Realizing Kagome Band Structure in Two-Dimensional Kagome Surface States of RV_{6}Sn_{6} (R=Gd, Ho).

We report angle resolved photoemission experiments on a newly discovered family of kagome metals RV_{6}Sn_{6} (R=Gd, Ho). Intrinsic bulk states and surface states of the vanadium kagome layer are differentiated from those of other atomic sublattices by the real-space resolution of the measurements with a small beam spot. Characteristic Dirac cone, saddle point, and flat bands of the kagome lattice are observed. Our results establish the two-dimensional (2D) kagome surface states as a new platform to investigate the intrinsic kagome physics.

Spin-valley locking and bulk quantum Hall effect in a noncentrosymmetric Dirac semimetal BaMnSb2

Spin-valley locking in monolayer transition metal dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a Dirac semimetal BaMnSb2. This is revealed by comprehensive studies using first principles calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy measurements. Moreover, this material also exhibits a stacked quantum Hall effect (QHE). The spin-valley degeneracy extracted from the QHE is close to 2. This result, together with the Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we also observed a plateau in the z-axis resistance, suggestive of a two-dimensional chiral surface state present in the quantum Hall state. These findings establish BaMnSb2 as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states.