arXiv subjects

Cheng-Cheng Liu

Publications and source records attributed to Cheng-Cheng Liu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Stable Higher-Order Topological Dirac Semimetals with $\mathbb{Z}_2$ Monopole Charge in Alternating-twisted Multilayer Graphenes and beyond

We demonstrate that a class of stable $\mathbb{Z}_2$ monopole charge Dirac point ($\mathbb{Z}_2$DP) phases can robustly exist in real materials, which surmounts the understanding: that is, a $\mathbb{Z}_2$DP is unstable and generally considered to be only the critical point of a $\mathbb{Z}_2$ nodal line ($\mathbb{Z}_2$NL) characterized by a $\mathbb{Z}_2$ monopole charge (the second Stiefel-Whitney number $w_2$) with space-time inversion symmetry but no spin-orbital coupling. For the first time, we explicitly reveal the higher-order bulk-boundary correspondence in the stable $\mathbb{Z}_2$DP phase. We propose the alternating-twisted multilayer graphene, which can be regarded as 3D twisted bilayer graphene (TBG), as the first example to realize such stable $\mathbb{Z}_2$DP phase and show that the Dirac points in the 3D TBG are essential degenerate at high symmetric points protected by crystal symmetries and carry a nontrivial $\mathbb{Z}_2$ monopole charge ($w_2=1$), which results in higher-order hinge states along the entire Brillouin zone of the $k_z$ direction. By breaking some crystal symmetries or tailoring interlayer coupling we are able to access $\mathbb{Z}_2$NL phases or other $\mathbb{Z}_2$DP phases with hinge states of adjustable length. In addition, we present other 3D materials which host $\mathbb{Z}_2$DPs in the electronic band structures and phonon spectra. We construct a minimal eight-band tight-binding lattice model that captures these nontrivial topological characters and furthermore tabulate all possible space groups to allow the existence of the stable $\mathbb{Z}_2$DP phases, which will provide direct and strong guidance for the realization of the $\mathbb{Z}_2$ monopole semimetal phases in electronic materials, metamaterials and electrical circuits, etc.

cond-mat.mes-hall↗

arXiv2023

Majorana corner modes and tunable patterns in an altermagnet heterostructure

The mutual competition and synergy of magnetism and superconductivity provide us with a very valuable opportunity to access topological superconductivity and Majorana Fermions. Here, we devise a heterostructure consisting of an $s$-wave superconductor, a 2D topological insulator and an altermagnet, which is classified as the third magnet and featured by zero magnetization but spin polarization in both real and reciprocal spaces. We find that the altermagnet can induce mass terms at the edges that compete with electron pairing, and mass domains are formed at the corners of sample, resulting in zero-energy Majorana corner modes (MCMs). The presence or absence of MCMs can be engineered by only changing the direction of the Néel vector. Moreover, uniaxial strain can effectively manipulate the patterns of the MCMs, such as moving and interchanging MCMs. Experimental realization, remarkable advantages of our proposal and possible braiding are discussed.

cond-mat.supr-con↗

arXiv2023

Design monolayer iodinenes based on halogen bond and tiling theory

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, X from group-IIIA to group-VIA elements have bonding characteristics of covalent bonds. In this work, we for the first time unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes, encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e. diatomic-kagome, and gyrated hexagonal tiling pattern. These iodinene structures exhibit a wealth of properties, such as flat bands, nontrivial topology, and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our work not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens a new avenue for designing other non-covalent bonding 2D materials.

cond-mat.mtrl-sci↗

arXiv2023

Layer Construction of Three-Dimensional Z2 Monopole Charge Nodal Line Semimetals and prediction of the abundant candidate materials

The interplay between symmetry and topology led to the concept of symmetry-protected topological states, including all non-interacting and weakly interacting topological quantum states. Among them, recently proposed nodal line semimetal states with space-time inversion ($\mathcal{PT}$) symmetry which are classified by the Stiefel-Whitney characteristic class associated with real vector bundles and can carry a nontrivial $\mathbb{Z}_2$ monopole charge have attracted widespread attention. However, we know less about such 3D $\mathbb{Z}_2$ nodal line semimetals and do not know how to construct them. In this work, we first extend the layer construction previously used to construct topological insulating states to topological semimetallic systems. We construct 3D $\mathbb{Z}_2$ nodal line semimetals by stacking of 2D $\mathcal{PT}$-symmetric Dirac semimetals via nonsymmorphic symmetries. Based on our construction scheme, effective model and combined with first-principles calculations, we predict two types of candidate electronic materials for $\mathbb{Z}_2$ nodal line semimetals, namely 14 Si and Ge structures and 108 transition metal dichalcogenides $MX_2$ ($M$=Cr, Mo, W, $X$=S, Se, Te). Our theoretical construction scheme can be directly applied to metamaterials and circuit systems. Our work not only greatly enriches the candidate materials and deepens the understanding of $\mathbb{Z}_2$ nodal line semimetal states but also significantly extends the application scope of layer construction.

cond-mat.mtrl-sci↗

arXiv2023

High-temperature Majorana corner modes in a $d+id'$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors

The realization of Majorana corner modes generally requires unconventional superconducting pairing or $s$-wave pairing. However, the bulk nodes in unconventional superconductors and the low $T_c$ of $s$-wave superconductors are not conducive to the experimental observation of Majorana corner modes. Here we show the emergence of a Majorana corner mode at each corner of a two-dimensional topological insulator in proximity to a $d+id'$ pairing superconductor, such as heavily doped graphene or especially a twisted bilayer of a cuprate superconductor, e.g., Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, which has recently been proposed as a fully gapped chiral $d_{x^2-y^2}+id_{xy}$ superconductor with $T_c$ close to its native 90 K, and an in-plane magnetic field. By numerical calculation and intuitive edge theory, we find that the interplay of the proximity-induced pairing and Zeeman field can introduce opposite Dirac masses on adjacent edges of the topological insulator, which creates one zero-energy Majorana mode at each corner. Our scheme offers a feasible route to achieve and explore Majorana corner modes in a high-temperature platform without bulk superconductor nodes.

cond-mat.supr-con↗

arXiv2023

Optical bulk-boundary dichotomy in a quantum spin Hall insulator

The bulk-boundary correspondence is a key concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi4Br4, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits a strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.

cond-mat.mes-hall↗

arXiv2023

2D Ladder polyborane: an ideal Dirac semimetal with a multi-feld-tunable band gap

Hydrogen, a simple and magic element, has attracted increasing attention for its effective incorporation within solids and powerful manipulation of electronic states. Here, we show that hydrogenation tackles common problems in two-dimensional borophene, e.g., stability and applicability. As a prominent example, a ladder-like boron hydride sheet, named as 2D ladder polyborane, achieves the desired outcome, enjoying the cleanest scenario with an anisotropic and tilted Dirac cone, that can be fully depicted by a minimal two-band tight-binding model. Introducing external fields, such as an electric field or a circularly-polarized light field can effectively induce distinctive massive Dirac fermions, whereupon four types of multi-field-driven topological domain walls hosting tunable chirality and valley indexes are further established. Moreover, the 2D ladder polyborane is thermodynamically stable at room temperature and supports highly switchable Dirac fermions, providing an ideal platform for realizing and exploring the various multi-field-tunable electronic states.

cond-mat.mes-hall↗

arXiv2022

Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene

Starting from a realistic extended Hubbard model for a $p_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the MA-TBG near the van Hove (VH) dopings. Here we focus on the interplay between the approximate SU(2)$\times$SU(2) symmetry and the $D_3$ symmetry, which leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic RPA based calculations followed by a succeeding mean-field energy minimization for the ground state energy. At the SU(2)$\times$SU(2) symmetric point, the degenerate inter-valley SDW and VDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-valley DW. This state simultaneously hosts three 4-component vectorial spin-valley DW orders with each adopting one wave vector, and the polarization directions of the three DW orders are mutually perpendicular to one another. %in the $\mathbb{R}^4$ space. In the presence of a tiny inter-valley exchange interaction with coefficient $J_H\to 0^{-}$ which breaks the SU(2)$\times$SU(2) symmetry, a pure chiral SDW state is obtained. In the case of $J_H\to 0^{+}$, a nematic VDW+SDW state emerges which possesses a stripy distribution of the charge density, consistent with the recent STM observations. On the aspect of SC, while the triplet $p+ip$ and singlet $d+id$ topological SCs are degenerate at $J_H=0$ near the VH dopings, the former (latter) is favored for $J_H\to 0^{-}$ ($J_H\to 0^{+}$). In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments.

cond-mat.str-el↗

arXiv2021

From Atomic Semimetal to Topological Nontrivial Insulator

Topological band insulators and (semi-) metals can arise out of atomic insulators when the hopping strength between electrons increases. Such topological phases are separated from the atomic insulator by a bulk gap closing. In this work, we show that in many (magnetic) space groups, the crystals with certain Wyckoff positions and orbitals being occupied must be semimetal or metals in the atomic limit, e.g. the hopping strength between electrons is infinite weak but not vanishing, which then are termed atomic (semi-)metals (ASMs). We derive a sufficient condition for realizing ASMs in spinless and spinful systems. Remarkably, we find that increasing the hopping strength between electrons may transform an ASM into an insulator with both symmetries and electron fillings of crystal are preserved. The induced insulators inevitably are topologically non-trivial and at least are obstructed atomic insulators (OAIs) that are labeled as trivial insulator in topological quantum chemistry website. Particularly, using silicon as an example, we show ASM criterion can discover the OAIs missed by the recently proposed criterion of filling enforced OAI. Our work not only establishes an efficient way to identify and design non-trivial insulators but also predicts that the group-IV elemental semiconductors are ideal candidate materials for OAI.

cond-mat.mes-hall↗

arXiv2021

$C_n$-symmetric higher-order topological crystalline insulators in atomically thin transition-metal dichalcogenides

Based on first-principles calculations and symmetry analysis, we predict atomically thin ($1-N$ layers) 2H group-VIB TMDs $MX_2$ ($M$ = Mo, W; $X$ = S, Se, Te) are large-gap higher-order topological crystalline insulators protected by $C_3$ rotation symmetry. We explicitly demonstrate the nontrivial topological indices and existence of the hallmark corner states with quantized fractional charge for these familiar TMDs with large bulk optical band gaps ($1.64-1.95$ eV for the monolayers), which would facilitate the experimental detection by STM. We find that the well-defined corner states exist in the triangular finite-size flakes with armchair edges of the atomically thin ($1-N$ layers) 2H group-VIB TMDs, and the corresponding quantized fractional charge is the number of layers $N$ divided by 3 modulo integers, which will simply double including spin degree of freedom.

cond-mat.mes-hall↗

arXiv2021

Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates

We propose two mechanisms to realize the second order topological insulator (SOTI) state in spinless hexagonal lattices, viz., chemical modification and anti-Kekulé/Kekulé distortion of hexagonal lattice. Correspondingly, we construct two models and demonstrate the nontrivial band topology of the SOTI state characterized by the second Stiefel-Whitney class $w_2$ in the presence of inversion symmetry ($\textit{P}$) and time-reversal symmetry ($\textit{T}$). Based on the two mechanisms and using first-principles calculations and symmetry analysis, we predict three categories of real light element material candidates, i.e., hydrogenated and halogenated 2D hexagonal group IV materials XY (X=C, Si, Ge, Sn, Y=H, F, Cl), 2D hexagonal group V materials (blue phosphorene, blue arsenene, and black phosphorene, black arsenene), and the recent experimentally synthesized anti-Kekulé/Kekulé order graphenes and the counterparts of silicene/germanene/stanene. We explicitly demonstrate the nontrivial topological invariants and existence of the protected corner states with fractional charge for these candidates with giant bulk band gap (up to 3.5 eV), which could facilitate the experimental verification by STM. Our approaches and proposed abundant real material candidates will greatly enrich 2D SOTIs and promote their intriguing physics research.

cond-mat.mes-hall↗

arXiv2020

$\textit{Ab initio}$ four-band Wannier tight-binding model for generic twisted graphene systems

The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and accurate model of the systems is of vital importance for the further study. Here, we construct the symmetry-adapted localized Wannier functions and the corresponding $\textit{ab initio}$ minimal two-valley four-band effective tight-binding models for generic twisted graphene systems with small twist angle. Such two-valley model evades the Wannier obstruction caused by the fragile topology in one-valley model. The real space valley operator is introduced to explicitly describe the valley $U_{v}\left(1\right)$ symmetry. Each symmetry-adapted Wannier orbital shows a peculiar three-peak form with its maximum at AA spots and its center at AB or BA spots. An extended Hubbard model is also given and the related parameters are presented explicitly. We provide an approach to systematically build the Wannier tight-binding model for generic twisted graphene systems. Our model provides a firm basis for further study of the many-body effects in these systems.

cond-mat.mes-hall↗

arXiv2020

Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A$_2$Cr$_3$As$_3$ (A=Na, K, Rb, Cs) superconductors

A spin-U(1)-symmetry protected momentum-dependent integer-$Z$-valued topological invariant is proposed to time-reversal-invariant (TRI) superconductivity (SC) whose nonzero value will lead to exactly flat surface band(s). The theory is applied to the weakly spin-orbit coupled quasi-1D A$_2$Cr$_3$As$_3$ (A=Na, K, Rb, Cs) superconductors family with highest $T_c$ up to 8.6 K with $p_z$-wave pairing in the $S_z=0$ channel. It's found that up to the leading atomic spin-orbit-coupling (SOC), the whole (001) surface Brillouin zone is covered with exactly-flat surface bands, with some regime hosting three flat bands and the remaining part hosting two. Such exactly-flat surface bands will lead to very sharp zero-bias conductance peak in the scanning tunneling microscopic spectrum. When a tiny subleading spin-flipping SOC is considered, the surface bands will only be slightly split. The application of this theory can be generalized to other unconventional superconductors with weak SOC, particularly to those with mirror-reflection symmetry.

cond-mat.supr-con↗

arXiv2020

Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice

The Kohn-Luttinger mechanism for unconventional superconductivity (SC) driven by weak repulsive electron-electron interactions on a periodic lattice is generalized to the quasicrystal (QC) via a real-space perturbative approach. The repulsive Hubbard model on the Penrose lattice is studied as an example, on which a classification of the pairing symmetries is performed and a pairing phase diagram is obtained. Two remarkable properties of these pairing states are revealed, due to the combination of the presence of the point-group symmetry and the lack of translation symmetry on this lattice. Firstly, the spin and spacial angular momenta of a Cooper pair is de-correlated: for each pairing symmetry, both spin-singlet and spin-triplet pairings are possible even in the weak-pairing limit. Secondly, the pairing states belonging to the 2D irreducible representations of the $D_5$ point group can be time-reversal-symmetry-breaking topological SCs carrying spontaneous bulk super current and spontaneous vortices. These two remarkable properties are general for the SCs on all QCs, and are rare on periodic lattices. Our work starts the new area of unconventional SCs driven by repulsive interactions on the QC.

cond-mat.str-el↗

arXiv2020

Quasi-One-Dimensional Higher-Order Topological Insulators

Quasi-1D materials Bi$_{4}$X$_{4}$ (X=Br,I) are prototype weak topological insulators (TI) in the $β$ phase. For the $α$ phases, recent high-throughput database screening suggests that Bi$_{4}$Br$_{4}$ is a rare higher-order TI (HOTI) whereas Bi$_{4}$I$_{4}$ has trivial symmetry indicators. Here we show that in fact the two $α$ phases are both pristine HOTIs yet with distinct termination-dependent hinge state patterns by performing first-principles calculations, analyzing coupled-edge dimerizations, inspecting surface lattice structures, constructing tight-binding models, and establishing boundary topological invariants. We reveal that the location of inversion center dictates Bi$_{4}$Br$_{4}$ (Bi$_{4}$I$_{4}$) to feature opposite (the same) dimerizations of a surface or intrinsic (bulk or extrinsic) origin at two side cleavage surfaces. We propose a variety of experiments to examine our predictions. Given the superior hinges along atomic chains, the structural transition at room temperature, and the extreme anisotropies in three axes, our results not only imply the possible existence of many topological materials beyond the scope of symmetry indicators but also establish a new TI paradigm and a unique material platform for exploring the interplay of geometry, symmetry, topology, and interaction.

cond-mat.mes-hall↗

arXiv2020

Spectroscopic evidence for a spin and valley polarized metallic state in a non-magic-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 non-magic-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 that when one of its VHS is partially filled, the one associated peak in the spectrum splits into four peaks. 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, lifting both the spin and valley degeneracies. Our results for this non-magic-angle TBG reveal a new symmetry-breaking phase, which has not been identified in the MA-TBG or in other systems.

cond-mat.mtrl-sci↗

arXiv2019

Nodal Line Spin-gapless Semimetals and High-quality Candidate Materials

Spin-gapless semimetals (SGSMs), which generate 100\% spin polarization, are viewed as promising semi-half-metals in spintronics with high speed and low consumption. We propose and characterize a new $\mathbb{Z_{\mathrm{2}}}$ class of topological nodal line (TNL) in SGSMs. The proposed TNLSGSMs are protected by space-time inversion symmetry or glide mirror symmetry with two-dimensional (2D) fully spin-polarized nearly flat surface states. Based on first-principles calculations and effective model analysis, a series of high-quality materials with $\textit{R}\overline{3}\textit{c}$ and $\textit{R}{3}\textit{c}$ space groups are predicted to realize such TNLSGSMs (chainlike). The 2D fully spin-polarized nearly flat surface states may provide a route to achieving equal spin pairing topological superconductivity as well as topological catalysts.

cond-mat.mtrl-sci↗

arXiv2018

Chiral SDW and d + id superconductivity in the magic-angle twisted bilayer-graphene

We model the newly synthesized magic-angle twisted bilayer-graphene superconductor with two $p_{x,y}$-like Wannier orbitals on the superstructure honeycomb lattice, where the hopping integrals are constructed via the Slater-Koster formulism by symmetry analysis. The characteristics exhibited in this simple model are well consistent with both the rigorous calculations and experiment observations. A van Hove singularity and Fermi-surface (FS) nesting are found in the doping levels relevant to the correlated insulator and unconventional superconductivity revealed experimentally, base on which we identify the two phases as weak-coupling FS instabilities. Then, with repulsive Hubbard interactions turning on, we performed random-phase-approximation (RPA) based calculations to identify the electron instabilities. As a result, we find chiral $d+id$ topological superconductivity bordering the correlated insulating state near half-filling, identified as noncoplanar chiral spin-density wave (SDW) ordered state, featuring quantum anomalous Hall effect. The phase-diagram obtained in our approach is qualitatively consistent with experiments.

cond-mat.supr-con↗