Low-energy Van Hove Singularities Research Articles

Real-Space Mapping of Local Subdegree Lattice Rotations in Low-Angle Twisted Bilayer Graphene.

In two-dimensional small-angle twisted bilayers, van der Waals (vdW) interlayer interaction introduces an atomic-scale reconstruction, which consists of a moiré-periodic network of local subdegree lattice rotations. However, real-space measurement of the subdegree lattice rotation requires extremely high spatial resolution, which is an outstanding challenge in an experiment. Here, a topmost small-period graphene moiré pattern is introduced as a magnifying lens to magnify sub-Angstrom lattice distortions in small-angle twisted bilayer graphene (TBG) by about 2 orders of magnitude. Local moiré periods of the topmost graphene moiré patterns and low-energy van Hove singularities of the system are spatially modified by the atomic-scale reconstruction of the underlying TBG, thus enabling real-space mapping of the networks of the subdegree lattice rotations both in structure and in electronic properties. Our results indicate that it is quite facile to study subdegree lattice rotation in vdW systems by measuring the periods of the topmost moiré superlattice.

Loop currents in AV3Sb5 kagome metals: Multipolar and toroidal magnetic orders

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a ``real" charge density-wave (rCDW), but also time-reversal symmetry-breaking, typical of loop currents described by an ``imaginary" charge density-wave (iCDW). Here, we combine density-functional theory, group-theory, and phenomenological modeling to investigate the complex charge-ordered states that arise from interactions between the low-energy van Hove singularities present in the electronic structure of $A$V$_3$Sb$_5$. We find two broad classes of mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, triple-$\mathbf{Q}$ rCDW order, dubbed $3\mathbf{Q}$-$3\mathbf{Q}$, and double-$\mathbf{Q}$ iCDW, single-$\mathbf{Q}$ rCDW order, dubbed $2\mathbf{Q}$-$1\mathbf{Q}$. Moreover, we identify seven different types of iCDW order, stemming from the different vanadium-orbital and kagome-sublattice structures of the two pairs of van Hove singularities present above and below the Fermi level. While the $2\mathbf{Q}$-$1\mathbf{Q}$ states trigger an orthorhombic distortion that breaks the threefold rotational symmetry of the kagome lattice, the $3\mathbf{Q}$-$3\mathbf{Q}$ states induce various types of subsidiary uniform magnetic orders, from conventional ferromagnetism to magnetic octupolar, magnetic toroidal, and even magnetic monopolar order. We show that these exotic orders display unique magneto-striction, magneto-electric, and magneto-electric-striction properties that can be probed experimentally to identify which iCDW state is realized in these compounds. We briefly discuss the impact of an out-of-plane modulation of the charge order and the interplay between these complex charge-ordered states and superconductivity.

Twist angle dependent absorption feature induced by interlayer rotations in CVD bilayer graphene

Abstract Bilayer graphene (BLG) grown via chemical vapor deposition (CVD) tends to exhibit twisted stacking. The twist angle θ t in twisted BLG (tBLG) provides a new degree of freedom for engineering its electronic and optical properties. In this paper, we investigate the θ t-dependent optical absorption in tBLG and deeply understand the electronic structure-optical properties correlations. New absorption peaks, whose wavelengths are modified by θ t, are observed on the feature of optical contrast (OC) in tBLG. Under the corresponding energy excitation, the Raman G mode in tBLG exhibits a significant enhancement. Furthermore, the results of θ t obtained by OC absorption peak are verified to be consistent with those by the Raman R mode. All these properties are proved to be related to the energy difference between low-energy Van Hove singularities (E VHS) in the density of states of tBLGs. This work builds a relation between optical absorption and twist angle, providing a viable method to identifying twist angles in tBLGs.

Enhanced third-harmonic generation by manipulating the twist angle of bilayer graphene

Twisted bilayer graphene (tBLG) has received substantial attention in various research fields due to its unconventional physical properties originating from Moiré superlattices. The electronic band structure in tBLG modified by interlayer interactions enables the emergence of low-energy van Hove singularities in the density of states, allowing the observation of intriguing features such as increased optical conductivity and photocurrent at visible or near-infrared wavelengths. Here, we show that the third-order optical nonlinearity can be considerably modified depending on the stacking angle in tBLG. The third-harmonic generation (THG) efficiency is found to significantly increase when the energy gap at the van Hove singularity matches the three-photon resonance of incident light. Further study on electrically tuneable optical nonlinearity reveals that the gate-controlled THG enhancement varies with the twist angle in tBLG, resulting in a THG enhanced up to 60 times compared to neutral monolayer graphene. Our results prove that the twist angle opens up a new way to control and increase the optical nonlinearity of tBLG, suggesting rotation-induced tuneable nonlinear optics in stacked two-dimensional material systems.

Spectroscopic Evidence for a Spin- and Valley-Polarized Metallic State in a Nonmagic-Angle Twisted Bilayer Graphene.

In the magic-angle twisted bilayer graphene (MA-TBG), strong electron-electron (e-e) correlations caused by the band-flattening lead to many exotic quantum phases such as superconductivity, correlated insulator, ferromagnetism, and quantum anomalous Hall effects, when its low-energy van Hove singularities (VHSs) are partially filled. Here our high-resolution scanning tunneling microscope and spectroscopy measurements demonstrate that the e-e correlation in a nonmagic-angle TBG with a twist angle θ = 1.49° still plays an important role in determining its electronic properties. Our most interesting observation on that sample is when one of its VHSs is partially filled, the one associated peak in the spectrum splits into four peaks. Simultaneously, the spatial symmetry of electronic states around the split VHSs is broken by the e-e correlation. Our analysis based on the continuum model suggests that such a one-to-four split of the VHS originates from the formation of an interaction-driven spin-valley-polarized metallic state near the VHS, which is a symmetry-breaking phase that has not been identified in the MA-TBG or in other systems.

Twistronics in graphene-based van der Waals structures

The electronic properties of van der Waals (vdW) structures can be substantially modified by the moiré superlattice potential, which strongly depends on the twist angle among the compounds. In twisted bilayer graphene (TBG), two low-energy Van Hove singularities (VHSs) move closer with decreasing twist angles and finally become highly non-dispersive flat bands at the magic angle (∼ 1.1°). When the Fermi level lies within the flat bands of the TBG near the magic angle, Coulomb interaction is supposed to exceed the kinetic energy of the electrons, which can drive the system into various strongly correlated phases. Moreover, the strongly correlated states of flat bands are also realized in other graphene-based vdW structures with an interlayer twist. In this article, we mainly review the recent scanning tunneling microscopy (STM) advances on the strongly correlated physics of the magic-angle TBG (MATBG) and the small-angle twisted multilayer graphene. Lastly we will give out a perspective of this field.

Correlation-induced valley splitting and orbital magnetism in a strain-induced zero-energy flatband in twisted bilayer graphene near the magic angle

In the vicinity of the magic angle in twisted bilayer graphene (TBG), many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed because the two low-energy Van Hove singularities (VHSs) become exceedingly narrow, i.e., become flatbands. Heterostrain, strain in van der Waals structures where each layer is strained independently, can modify the single-particle band structure of the TBG and lead to various properties. Here, we show that heterostrain in a TBG near the magic angle generates a zero-energy flatband between the two VHSs. Doping the TBG to partially fill the zero-energy flatband, we observe a correlation-induced valley-polarized gap of \ensuremath{\sim}10 meV. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the large orbital magnetic moments in TBG. The measured orbital magnetic moment per moir\'e unit cell is $\ensuremath{\sim}15\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ in the TBG, which is well consistent with our calculations.

Magnetism near half-filling of a Van Hove singularity in twisted graphene bilayer

Twisted graphene bilayers (TGBs) have low-energy van Hove singularities (VHSs) that are strongly localized around AA-stacked regions of the moire pattern. Therefore, they exhibit novel many-body electronic states, such as Mott-like insulator and unconventional superconductivity. Unfortunately, these strongly correlated states were only observed in magic angle TGBs with the twist angle theta~1.1{\deg}, requiring a precisely tuned structure. Is it possible to realize exotic quantum phases in the TGBs not limited at the magic angle? Here we studied electronic properties of a TGB with theta~1.64{\deg} and demonstrated that a VHS splits into two spin-polarized states flanking the Fermi energy when the VHS is close to the Fermi level. Such a result indicates that localized magnetic moments emerge in the AA-stacked regions of the TGB. Since the low-energy VHSs are quite easy to be reached in slightly TGBs, our result therefore provides a facile direction to realize novel quantum phases in graphene system.

Scanning tunneling microscopy and spectroscopy of twisted trilayer graphene

Twist, as a simple and unique degree of freedom, could lead to enormous novel quantum phenomena in bilayer graphene. A small rotation angle introduces low-energy van Hove singularities (VHSs) approaching the Fermi level, which result in unusual correlated states in the bilayer graphene. It is reasonable to expect that the twist could also affect the electronic properties of few-layer graphene dramatically. However, such an issue has remained experimentally elusive. Here, by using scanning tunneling microscopy/spectroscopy (STM/STS), we systematically studied a twisted trilayer graphene (TTG) with two different small twist angles between adjacent layers. Two sets of VHSs originating from the two twist angles were observed in the TTG, indicating that the TTG could be simply regarded as a combination of two different twisted bilayer graphene. By using high-resolution STS, we observed split of the VHSs and directly imaged spatial symmetry breaking of electronic states around the VHSs. These results suggest that electron-electron interactions play an important role in affecting the electronic properties of graphene systems with low-energy VHSs.

Landau quantization and Fermi velocity renormalization in twisted graphene bilayers

Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHSs, the observed Landau quantization in the twisted bilayers is identical to that of massless Dirac fermions in graphene monolayer, which allows us to measure the Fermi velocity directly. Our result indicates that the Fermi velocity of the twisted bilayers depends remarkably on both the twisted angles and the interlayer coupling strengths. This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data.

Tuning the Interlayer Coupling of the Twisted Bilayer Graphene by Molecular Adsorption

We describe a facile method to modulate the local interlayer coupling by adsorption of single-molecule magnets (SMMs) onto twisted bilayer graphene and report the characterization of its electronic band structure using scanning tunneling microscopy and spectroscopy. Low-energy Van Hove singularities (VHSs) and superlattice Dirac cones, induced by the interlayer coupling and graphene-on-graphene moiré, respectively, are observed in the tunneling spectra. Our experiments demonstrate that the energy difference of the two VHSs, which reflects the magnitude of interlayer coupling, can be tuned by the local coverage density of molecular adsorption.

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer

It is well established that strain and geometry could affect the band structure of graphene monolayer dramatically. Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature, which are found to strongly affect the local band structures of the twisted graphene bilayer. The energy difference of the two low-energy van Hove singularities decreases with increasing lattice deformation and the states condensed into well-defined pseudo-Landau levels, which mimic the quantization of massive chiral fermions in a magnetic field of about 100 T, along a graphene wrinkle. The joint effect of strain and out-of-plane distortion in the graphene wrinkle also results in a valley polarization with a significant gap. These results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.

Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer

Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows ΔE(vhs)∼ℏν(F)ΔK between 1.0° and 3.0° [here ν(F)∼1.1 × 10(6) m/s is the Fermi velocity of monolayer graphene, and ΔK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle θ∼1.3°, the observed ΔE(vhs)∼0.11 eV is much smaller than the expected value ℏν(F)ΔK∼0.28 eV at 1.3°. The origin of the reduction of ΔE(vhs) at 1.3° is discussed.

Observation of Van Hove singularities in twisted graphene layers

When a Van Hove singularity exists near the Fermi energy of a solid’s density of states, it can cause a variety of exotic phenomena to emerge. Scanning tunnelling microscope measurements indicate that when graphite’s graphene sheets are rotated out of their usual alignment, it can generate low-energy Van Hove singularities for which the position is controlled by the angle of rotation. Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity1 in the density of states often lead to new phases of matter such as superconductivity2,3, magnetism4 or density waves5. However, in most materials this condition is difficult to control. In the case of single-layer graphene, the singularity is too far from the Fermi energy6 and hence difficult to reach with standard doping and gating techniques7. Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states measured by scanning tunnelling spectroscopy. We demonstrate that a rotation between stacked graphene layers can generate Van Hove singularities, which can be brought arbitrarily close to the Fermi energy by varying the angle of rotation. This opens intriguing prospects for Van Hove singularity engineering of electronic phases.

Re-examination of the Lattice Dynamics of White Tin Using a Modified Axially Symmetric Model

Experimental measurements of both the specific heat and the Debye-Waller factor for (white) Sn suggest the presence of low-lying phonon branches. In addition, recent experiments by Rowell et al. displayed structure in the Sn-Sn superconductors tunneling characteristic curve associated with very low-energy Van Hove singularities in the Sn vibrational spectrum. A previous theoretical calculation of the Sn phonon spectrum using the elastic constants of Mason and B\"ommel does not predict the existence of such low-lying phonon branches. A subsequent calculation based on the elastic data of Rayne and Chandrasekhar, on the other hand, clearly indicates the presence of a very low-energy acoustic branch along the [110] direction. However, in this calculation complete elastic consistency was not possible because of the constraint imposed by the $A\ensuremath{-}S$ (axially symmetric) lattice dynamics model. Consequently, we have re-examined the lattice vibrational spectrum of Sn on the basis of a generalized $A\ensuremath{-}S$ lattice dynamics model which allows complete elastic consistency to be obtained. The specific heat, the magnitude of the Debye-Waller factor and the low-energy structure in the tunneling experiments calculated from the dispersion curves obtained from our modified A-S model are in quantitative agreement with experimental observations. The anisotropy factor $\ensuremath{\epsilon}$ of the Debye-Waller factor is increased from 1.2 to 1.56 and remains in disagreement with experiment. It appears to us that with the present elastic data it is not possible to obtain a mean-square displacement larger in the $z$ direction than that in the $x$ direction. Furthermore, we conclude that the Mason and B\"ommel elastic data are incapable of explaining the present experimental data on white tin.