Session B51: Topological Materials: Graphene and Thin films

Live

Recently twisted bilayer graphene(t-BLG) emerges as a new strongly correlated physical platform near a magic twist angle, which hosts many exciting phenomena such as the Mott-like insulating phases, unconventional superconducting behavior and emergent ferromagnetism. Besides the apparent significance of band flatness, band topology may be another critical element in strongly correlated twistronics yet receives much less attention. While an unusual symmetry of t-BLG trivializes Berry curvature, we elucidate that two high-dimensional Z₂ invariants in the Teo-Kane Altland-Zirnbauer table characterize the topology of the moiré Dirac bands, supported by a systematic nonlocal transport study. The moiré band topology of t-BLG manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. Moreover, the nonlocal responses are robust to the interlayer electric field, twist angle, and edge termination, exhibiting a universal scaling law.   

Live

We consider a bilayer Lieb lattice which undergoes an unusual topological transition in the presence of intra-layer spin-orbit coupling (SOC). The specific configuration induces an effective non-symmorphic 2D lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent non-symmorphicity leads to multiple doubly-degenerate bands extending over the edge of the Brillouin zone, i.e. Quadratic Band Crossing Lines. In the presence of intra-layer SOC, these doubly-degenerate bands typically form three 2-band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multi-band subspaces, using specially devised Wilson loop operators to compute non-abelian Berry phases, in order to show that they carry a higher Chern number, 2.   

Live

Recently, non-Hermitian effects on the topology of quantum materials have attracted much interest due to their unusual properties compared to Hermitian topology. A distinct character of non-Hermitian topology is that it breaks the limitation of the requirement of a real band gap. The system may not have a gap in the real spectrum but could still be topological as long as a point gap in the complex spectrum exists. However, the way of realizing non-Hermitian topology in a realistic 1D condensed matter system is still missing. In this work, we study a particular type of graphene nanoribbon with cobalt adatoms (Co-GNR). Due to many-electron interactions, the Hamiltonian characterizing quasiparticle excitations becomes non-Hermitian. The strong spin-orbit coupling brought by the cobalt atoms induces non-trivial non-Hermitian topology in the GW quasiparticle band structure. We extract effective tight-binding parameters with a Wannier function basis and unveil the non-Hermitian skin effect in Co-GNR.   

Live

Topological insulators, along with Chern insulators and Quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. In this letter, we report the experimental realization of the time-reversal invariant Z₂ topological phase [Phys. Rev. Lett. 95, 146802 (2005)] in bilayer graphene-based heterostructures -- a phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising of both a moir\'e superlattice potential and strong spin-orbit coupling; this resulted in materials whose electronic band structure could be tuned from trivial to topological by an external displacement field. We find that the topological phase is characterized by a bulk bandgap and helical edge modes with electrical conductance quantized exactly to 2e²/h in zero external magnetic field. We also present results of a theoretical study of a realistic model of the Z₂ topological insulator which, in addition to replicating our experimental results, explains the origin of the topological insulating bulk and helical edge modes.   

Live

Monolayer tin (Sn) in the stanene form is expected to be a large bandgap two-dimensional (2D) topological insulator. However, electronic properties and growth morphology of Sn thin films highly depend on the supporting substrate. We compare the growth of Sn on a metal substrate with and without the hexagonal boron nitride (hBN) monolayer, which binds weakly to the substrate. Distinct growth morphologies, arising from the different interaction to substrate, are revealed by scanning tunneling microscopy. Most intriguingly, a new Sn phase corresponding to the √7 × √7 superlattice of the underlying metal surface is identified on the hBN/metal substrate, suggesting the influence of metal on Sn through the decoupling hBN monolayer, as our first-principles calculations support. Our study demonstrates that substrates provide a platform to significantly change the electronic and topological properties of 2D material.   

Live

Alpha tin (α-Sn) is an allotrope of tin with a diamond crystal structure, and has been predicted to become topologically nontrivial by applying uniaxial strain. While the topological band structures have been confirmed by angle-resolved photoemission spectroscopy (ARPES), however, the transport properties of α-Sn still need thorough investigations.
We have grown a series of α-Sn films with different thicknesses on InSb and CdTe substrates, respectively, by molecular beam epitaxy (MBE). The high quality has been confirmed by structural characterizations such as X-ray diffraction and transmission electron microscope. The temperature- and thickness-dependent electrical transport of the α-Sn films have been investigated. A large magnetoresistance (MR) has been observed in the α-Sn/InSb heterostructures, up to over 450,000% at 1.5 K and 14 T. On the other hand, multiple transitions in transport type have been observed in the α-Sn films grown on CdTe substrates, which can be well explained by a three-band model. We have established a phase diagram illustrating the transport behaviors of α-Sn. These results can give more insights into the transport mechanism and potential applications of this material system.   

Live

Berry curvature is a key quantity in characterizing the band topology of materials [1]. However, measuring Berry curvature locally in the Brillouin zone (BZ) remains challenging due to decoherence from rapid scattering processes. High-order sideband generation (HSG) avoids this difficulty by using a strong terahertz field to drive electron-hole pairs to collision before scattering. Polarimetry of sidebands has been shown to be sensitive to the local Berry curvature and the Bloch wavefunctions of semiconductors [2,3]. In strained gallium arsenide (GaAs), there is a non-abelian Berry curvature in the valence bands near the BZ center. Here we present a measurement of this non-abelian Berry curvature in GaAs using HSG. We also discuss future applications of this method to characterizing topological materials.

References
[1]
C. Nayak, et al. , "Non-Abelian anyons and topological quantum computing," Rev. Mod. Phys. 80, 1083-, 2008.

[2]
H. B. Banks, Q. Wu, D. C. Valovcin, et al. , "Dynamical Birefringence: Electron-Hole Recollisions as Probes of Berry Curvature," Phys. Rev. X 7, 041042, 2019.

[3]
J. B. Costello, S. D. O'Hara, Q. Wu, et al., Manuscript in Preparation.   

Live

We have performed a thorough study of the many-body physics in twisted bilayer graphene (TBG) through a series of six works. First, we found useful approximations for the Hamiltonian and explained why the bands are flat over the whole Brillouin zone (not only around the Dirac points). Second, we found that, with an approximate particle-hole symmetry, the continuous model of TBG is anomalous, which means that it cannot be realized on lattices. These two properties lead to a projected Coulomb Hamiltonian that can only be written in momentum space. Then we found that the projected Coulomb Hamiltonian hosts a U(4)xU(4) symmetry in the chiral limit and a U(4) symmetry otherwise, and explicitly derived the symmetry generators. Forth, with the help of symmetries, we can write down exact eigenstates of the projected Coulomb Hamiltonian at integer fillings, which are also ground states if the so-called “flat-metric-condition” is satisfied. These ground states are parent states of the valley-polarized states, valley-coherent states, and Chern states. Fifth, given the many-body symmetries and exact ground states, we can also derive the exact charge 1, 2, 0 excitations, with Goldstone modes included. Remarkably, through charge 2 excitations, we prove the absence of Cooper pairs in the project Coulomb Hamiltonian around integer fillings. Finally, we confirmed the analytical results using numerical exact diagonalization, which also suggests phase transitions to other ground states when U(4) or U(4)xU(4) is significantly broken.   

Live

We investigate the single-particle Hamiltonian of Twisted Bilayer Graphene (TBG) model. We provide an analytical perturbative understanding of why the TBG bands are flat over the whole Brillouin zone at the first magic angle, despite it is defined only by vanishing Dirac velocity. We derive a connected "magic manifold": w1=2 \sqrt{1+w0^2} – \sqrt{2+3w0^2}, on which the bands remain extremely flat. We also show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous. The fragile topology of the two flat bands is enhanced to a particle-hole-symmetry-protected stable topology. This stable topology implies 4n+2 Dirac points between the middle two bands. Remarkably, this table topology, as well as the corresponding 4n+2 Dirac points, cannot be realized in lattice models that preserve both C2T and particle-hole symmetries. In other words, the continuous model of TBG is anomalous.   

Live

We investigate 2D Sn on substrates and its electronic, magnetic, and quantum topological properties. Substrates can drastically change the Sn properties. For example, 2D Sn transforms into a 2D Weyl semimetal when large compressive strain is applied by substrates, such as 2D Sn, metals, or insulator substrates. In contrast to the buckled structure of freestanding stanene, the inversion symmetry of tin disappears with large compressive strain, which transforms a 2D topological insulator into a Weyl semimetal. We discuss realistic substrates that can accommodate desirable electronic and topological properties, and even magnetic properties to 2D Sn. Our findings provide a new avenue to experimentally realize new 2D quantum materials.   

Live

Monolayers of Mo and W based transition metal dichalcogenides (TMD) in the 1T’ phase are known to be topological insulators [1]. This has been understood within the Kane-Mele model and is associated with the level inversion between the anion p states and the transition metal d states. However, what is surprising is that this happens across the entire series varying the anion from S to Se to Te for both Mo and W based systems. Examining various families of topological insulators, one finds that while one member of the series would be close to the point of inversion, it is not expected for every member to be close to the point of inversion and therefore become a topological insulator. In this work, we study the 1H , 1T and 1T’ phases of the Mo and W based TMD extensively. We carry out ab-initio electronic structure calculations for each member of the TMD family. To quantify the electronic structure, we map the ab-initio band structure onto a tight binding model. We show that while the level inversion is not specific to the 1T’ phase, and is also present in the other phases, the reason for
realizing a topological insulator in certain instances is elucidated.

[1] X. Qian, J. Liu, L. Feu and J. Li, Science 346, 1344 (2016).   

Live

Bi₂Se₃, widely studied as a topological insulator, has great potential for applications in low power electronics and quantum computing. Intrinsic doping, however, presents a persistent challenge, leading to predominantly bulk conduction. In this work, we use substitutional Sn dopants to control the Fermi level in MBE-grown Bi₂Se₃ films. Scanning Tunneling Microscopy (STM) shows a shift in the local density of states towards the Dirac point as more Sn is incorporated, with density functional theory calculations corroborating the STM results, showing that Sn adds metallic states near the Fermi level that are localized to the defect sites while leaving the Dirac cone undisturbed. Electronic transport measurements show increasing weak antilocalization with doping level, demonstrating that the Sn defects increase the separation between bulk and surface states, though bulk conduction remains a dominant component. However, the macroscopic behavior is still dominated by bulk conduction due to the localized Sn states within the bulk. Overall, we find that Sn doping is a promising method for enhancing the contribution of surface states in Bi₂Se₃.   

Live

Observations of negative longitudinal magnetoresistance (NLMR), anisotropic magnetoresistance (AMR), and the planar Hall effect (PHE) under an in-plane magnetic field are often used as indications of non-trivial topology in non-magnetic material systems. We show NLMR, AMR, and PHE in crystalline epitaxial thin films (< 50 nm) of elemental Bismuth (111) grown by molecular beam epitaxy on intrinsic GaAs (111) substrates. Films were characterized in-situ using scanning tunneling microscopy to confirm topography and density of states. Furthermore, the thickness and temperature dependence of these phenomena are investigated, demonstrating a high degree of tunability. These effects appear robust to contact geometry and addition of a Germanium buffer layer.