We show that the chiral multifold fermions present a dual Haldane sphere problem in momentum space. Owing to the Berry monopole at the degenerate point, a dual Landau level emerges in the trace of quantum metric, with which a quantized geometric invariant is defined through a surface integration. We further demonstrate potential manifestations in the measurable, physical observables. With a lower bound derived for the finite spread of Wannier functions, anomalous phase coherence is identified accordingly for the flat band superconductivity. We briefly comment on the stability of these results under perturbations. Potential experimental probes of the quantum metric are also discussed.
So far, the circular photogalvanic effect (CPGE) is the only possible quantized signal in Weyl semimetals. With inversion and mirror symmetries broken, Weyl and multifold fermions in band structures with opposite chiralities can stay at different energies and generate a net topological charge. Such kind of net topological charge can present as a quantized signal in the circular polarized light induced injection current. According to current theoretical understanding, RhSi and its counterparts are believed to be the most promising candidate for the experimental observation of the quantized CPGE…
Chiral multifold fermions are quasiparticles described by higher spin generalizations of the Weyl equation, and are realized as low energy excitations near symmetry protected band crossings in certain chiral crystals. In this work we calculate the linear optical conductivity of all chiral multifold fermions. We show that it is enhanced with respect to that of Weyl fermions with the same Fermi velocity, and features characteristic activation frequencies for each multifold fermion class, providing an experimental fingerprint to detect them. We calculate the conductivity for realistic chiral mult…
Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and non-linear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of …
Multifold fermions are generalizations of two-fold degenerate Weyl fermions with three-, four-, six- or eight-fold degeneracies protected by crystal symmetries, of which only the last type is necessarily non-chiral. Their low energy degrees of freedom can be described as emergent particles not present in the Standard Model of particle physics. We propose a range of experimental probes for multifold fermions in chiral symmetry groups based on the gyrotropic magnetic effect (GME) and the circular photo-galvanic effect (CPGE). We find that, in contrast to Weyl fermions, multifold fermions can hav…
We reassert our statement that the non-quantized Weyl node contribution to the anomalous Hall conductivity is not a Fermi surface property, contrary to the claim by Vanderbilt, Souza and Haldane.
Topological semimetals in crystals with a chiral structure (which possess a handedness due to a lack of mirror and inversion symmetries) are expected to display numerous exotic physical phenomena, including fermionic excitations with large topological charge [1], long Fermi arc surface states [2,3], unusual magnetotransport [4] and lattice dynamics [5], as well as a quantized response to circularly polarized light [6]. To date, all experimentally confirmed topological semimetals exist in crystals that contain mirror operations, meaning that these properties do not appear. Here, we show that Al…
We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk energy gap, corresponding to the two zero points of the Bloch function on the complex-energy Riemann surface. The edge-state energy loops move around the hole of the Riemann surface in appropriate system parameter regimes. The quantized Hall conductance can be expressed by the winding numbers of the edge states, which reflects the topological feature of the…
The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light's polarization, known as the circular photogalvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material par…
To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square ($C^2$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this $C^2$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the $\mathbb{Z}_2$ topological number robust to interactions can be measured locally from a correspondence between the pfaff…
New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong（新Cornerstone科学实验室，香港大学物理系）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（香港大学光学量子材料国家重点实验室）；Department of Electrical and Electronic Engineering, The University of Hong Kong（香港大学电子电气工程系）；Quantum Science Center of Guangdong-Hong Kong-Macao Great Bay Area（粤港澳大湾区量子科学中心）；Materials Innovation Institute for Life Sciences and Energy (MILES), HKU-SIRI, Shenzhen（深圳港大西丽研究院生命科学与能源材料创新研究所）
Quantized Hall drift in a frequency-encoded photonic Chern insulator
Université de Montréal（蒙特利尔大学）；INO-CNR（意大利国家研究委员会光学研究所）；Università di Trento（特伦托大学）；Ecole Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学材料科学研究高等研究院）；Institut Courtois（库尔瓦研究所）
We show that a weak hexagonal periodic potential could transform a two-dimensional electron gas with an even-denominator magnetic filling factor to a quantum anomalous Hall insulator of composite fermions, giving rise to fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.
The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Cher…
We introduce a "second-quantized" representation of the ring of symmetric functions to further develop a purely second-quantized -- or "lattice" -- approach to the study of zero modes of frustration free Haldane-pseudo-potential-type Hamiltonians, which in particular stabilize Laughlin ground states. We present three applications of this formalism. We start demonstrating how to systematically construct all zero-modes of Laughlin-type parent Hamiltonians in a framework that is free of first-quantized polynomial wave functions, and show that they are in one-to-one correspondence with dominance p…
Quantized Photocurrents in Gapless Topological Matter
Princeton University（普林斯顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Nanyang Technological University（南洋理工大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Indian Institute of Technology Delhi（德里印度理工学院）；Stanford University（斯坦福大学）；Paul Scherrer Institute（保罗谢尔研究所）；Bruker Scientific, LLC（布鲁克科学有限责任公司）；University of California, Los Angeles（加州大学洛杉矶分校）
We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the onsite orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy level splitting between the onsite $p_x+ip_y$ and $p_x-ip_y$ orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model without Landau levels. The distribution of Berry curvature in the momentum space and the quantized Ch…
Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a TFB, we find convincing numerical evidence of a stable $ν=1$ bosonic NA-QHE, with the characteristic three-fold quasi-degeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a fini…
We present a simple prescription to flatten isolated Bloch bands with non-zero Chern number. We first show that approximate flattening of bands with non-zero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest neighbor hoppings in the Haldane model and, similarly, in the chiral-pi-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the e…
Parity-Anomalous Hall Response of Chiral Lifshitz Fermions
School of Physics, Beihang University（北京航空航天大学物理学院）；International Center for Quantum Materials and School of Physics, Peking University（北京大学量子材料科学中心及物理学院）
The understanding of the Chern insulator and anomalous quantum Hall effect (AQHE) in terms of chiral edge states in confined systems is the first aim of the paper. The model we use consists in a diatomic square lattice with hopping to the next-nearest-neighbors and broken time-reversal symmetry, which exhibits edge states in the absence of an external magnetic field. The question of chiral edge states is approached in the ribbon and plaquette geometries with different atomic connectivities at the boundaries. Insulating and semi-metallic phases are revealed, the resulting phase diagram being ri…
