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Register a new userObservation of non-Abelian topological semimetals and their phase transitions
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Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have almost exclusively been restricted to single-gap band topology because of the Fermi-Dirac filling effect. Here, we theoretically analyze and experimentally confirm a novel class of multi-gap topological phases, which we will refer to as non-Abelian topological semimetals, on kagome geometries. These unprecedented forms of matter depend on the notion of Euler class and frame charges which arise due to non-Abelian charge conversion processes when band nodes of different gaps are braided along each other in momentum space. We identify such exotic phenomena in acoustic metamaterials and uncover a rich topological phase diagram induced by the creation, braiding and recombination of band nodes. Using pump-probe measurements, we verify the non-Abelian charge conversion processes where topological charges of nodes are transferred from one gap to another. Moreover, in such processes, we discover symmetry-enforced intermediate phases featuring triply-degenerate band nodes with unique dispersions that are directly linked to the multi-gap topological invariants. Furthermore, we confirm that edge states can faithfully characterize the multi-gap topological phase diagram. Our study unveils a new regime of topological phases where multi-gap topology and non-Abelian charges of band nodes play a crucial role in understanding semimetals with inter-connected multiple bands.
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We report two theoretical discoveries for $mathbb{Z}_2$-topological metals and semimetals. It is shown first that any dimensional $mathbb{Z}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for $mathbb{Z}$ Fermi points in a periodic system without any discrete symmetry, is generalized to that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all $mathbb{Z}_2$ Fermi points have the same topological charge $ u_{mathbb{Z}_2} =1$ or $0$ for periodic systems. Moreover, we also establish all six topological types of $mathbb{Z}_2$ models for realistic physical dimensions.
Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics can be tested. Here, we generalize this system to non-Abelian quantum electrodynamics, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly-interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.
Weyl semimetals are arguably the most paradigmatic form of a gapless topological phase. While the stability of Weyl nodes, as quantified by their topological charge, has been extensively investigated, recent interest has shifted to the manipulation of the location of these Weyl nodes for non-Abelian braiding. To accomplish this braiding it is necessary to drive significant Weyl node motion using realistic experimental parameter changes. We show that a family of phase transitions characterized by certain symmetry constraints impose that the Weyl nodes have to reorganise by a large amount, shifting from one high symmetry plane to another. Additionally, for a subset of pairs of nodes with nontrivial Euler class topology, this reorganization can only occur through a braiding process with adjacent nodes. As a result, the Weyl nodes are forced to move a large distance across the Brillouin zone and to braid, all driven by small temperature changes, a process we illustrate with Cd$_2$Re$_2$O$_7$. Our work opens up routes to readily manipulate Weyl nodes using only slight external parameter changes, paving the way for the practical realization of reciprocal space braiding.
Braiding operations are challenging to create topological quantum computers. It is unclear whether braiding operations can be executed with any materials. Although various calculations based on Majorana fermions show braiding possibilities, a braiding operation with a Majorana fermion has not yet been experimentally proven. Herein, braiding operations are demonstrated using a molecular topological superconductor (MTSC) that utilizes the topological properties intrinsic in molecules. The braiding operations were implemented by controlling two MTSC modules made by pelletizing crystals of 4,5,9,10-tetrakis(dodecyloxy)pyrene, which is proposed as the first MTSC material through n-MOSFETs. It shows the elements of topological quantum computers that can be demonstrated without an external magnetic field at room temperature.
In magnetic topological phases of matter, the quantum anomalous Hall (QAH) effect is an emergent phenomenon driven by ferromagnetic doping, magnetic proximity effects and strain engineering. The realization of QAH states with multiple dissipationless edge and surface conduction channels defined by a Chern number $mathcal{C}geq1$ was foreseen for the ferromagnetically ordered SnTe class of topological crystalline insulators (TCIs). From magnetotransport measurements on Sn$_{1-x}$Mn$_{x}$Te ($0.00leq{x}leq{0.08}$)(111) epitaxial thin films grown by molecular beam epitaxy on BaF$_{2}$ substrates, hole mediated ferromagnetism is observed in samples with $xgeq0.06$ and the highest $T_mathrm{c}sim7.5,mathrm{K}$ is inferred from an anomalous Hall behavior in Sn$_{0.92}$Mn$_{0.08}$Te. The sizable anomalous Hall angle $sim$0.3 obtained for Sn$_{0.92}$Mn$_{0.08}$Te is one of the greatest reported for magnetic topological materials. The ferromagnetic ordering with perpendicular magnetic anisotropy, complemented by the inception of anomalous Hall effect in the Sn$_{1-x}$Mn$_{x}$Te layers for a thickness commensurate with the decay length of the top and bottom surface states, points at Sn$_{1-x}$Mn$_{x}$Te as a preferential platform for the realization of QAH states in ferromagnetic TCIs.
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