Switching chiral solitons for algebraic operation of topological quaternary digits

Abstract

Chiral objects can be found throughout nature [1][2][3][4] ; in condensed matter chiral objects are often excited states protected by a system's topology. The use of chiral topological excitations to carry information has been demonstrated, where the information is robust against external perturbations 5,6 . For instance, reading, writing, and transfer of binary information have been demonstrated with chiral topological excitations in magnetic systems, skyrmions [7][8][9][10][11][12][13][14] , for spintronic devices [13][14][15][16][17][18][19] . The next step is logic or algebraic operations of such topological bits [20][21][22] . Here, we show experimentally the switching between chiral topological excitations or chiral solitons of di erent chirality in a one-dimensional electronic system with Z 4 topological symmetry 23,24 . We found that a fast-moving achiral soliton merges with chiral solitons to switch their handedness. This can lead to the realization of algebraic operation of Z 4 topological charges 25 . Chiral solitons could be a platform for storage and operation of robust topological multi-digit information.Topological particle-like excitations can be used as information carriers in next-generation non-volatile memory and logic devices on the basis of their non-perturbative topological robustness. Promising candidates for topological information carriers using such topological excitations have been discussed actively in magnetic systems-for example, domain walls for racetrack memory devices 5,6 and skyrmions 7-14 , two-dimensional chiral spin configurations protected topologically [13][14][15][16][17][18][19] . However, neighbouring domain walls with opposite chirality would annihilate each other under the influence of an applied field in the former case. On the other hand, ironically, the chirality of skyrmions is very difficult to switch due to the intrinsic parity-breaking chiral interaction 6,26 . For these reasons, although binary-digit memory devices based on skyrmions have been successful demonstrated, the realization of logic operations with magnetic topological excitations faces huge obstacles requiring sophisticated nanoscale fabrication and precise material engineering [20][21][22] . On the other hand, topological excitations have been known for a long time in one-dimensional electronic systems; a Peierlsdistorted atomic chain such as polyacetylene has two topologically distinct ground states, which are connected by a unique topological soliton [27][28][29][30][31] . This topological excitation does not have such chirality 24 as magnetic solitons 32-34 and skyrmions 7-14 . However, our team recently discovered new kinds of topological solitons having chirality in double Peierls chains of indium atomic wires 23,24 . Double Peierls chains uniquely have topologically distinct four-fold degenerate ground states: the topology of the energetically degenerate ground states is distinguished in the topological order-parameter space using the order parameters m x and m z , representing sublattice dim...

Tuneable topological domain wall states in engineered atomic chains

“…Topological modes in one-and two-dimensional systems have been proposed for numerous applications utilizing their exotic electronic responses [16][17][18][19][20][21][22][23][24] . Atomic manipulation can naturally also be applied to topological materials and systems with interface and edge states can be constructed 8 .…”

“…The existence of a domain wall state at exactly mid-gap energy does not necessarily occur for 1D chains consisting of sites with different on-site energies or more complicated unit cells with three or more atoms 21,22,[31][32][33][34][35] . While the states still necessarily occur at the domain wall, their energies within the gap can be tuned.…”

Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons

“…The SSH model describes the physics of a dimerized one-dimensional chain within the tight-binding model and here we will explain how it can be implemented in artificial lattices and later, in graphene nanoribbons [86,87]. The ideas related to dimer chains can be extended to topological domain wall states in trimers and coupled dimer chains that have also been characterized experimentally and theoretically [88][89][90][91].…”

Formation of Sn‐Induced Nanowires on Si(557)

“…Nanowires grown by self‐assembly on surfaces were shown to provide a perfect template to study fundamental ground state properties of one‐dimensional systems. Moreover, they also appear to be interesting candidates for getting a deep insight into the transient of a phase transition or dynamics of solitons, as impressively demonstrated for In/Si(111) …”