Chiral solitons in a coupled double Peierls chain

Cheon, Sangmo; Kim, Tae-Hwan; Lee, Sung Hoon; Yeom, Han Woong

doi:10.1126/science.aaa7055

Cited by 119 publications

(146 citation statements)

References 31 publications

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“…The prototype of its realization is the one based on the Su-SchriefferHeeger/Rice-Mele (SSH/RM) model [22,23] for polyacetylene. It has generated renewed interests thanks to various recent experimental realizations in ultracold atoms and condensed matter systems, where the Zak phase [24], quantum pumping phenomena [25][26][27], and chiral solitonic edge states [28] are directly measured. In this Letter, we present a generalized Creutz scheme [29] as a distinct microscopic two-band quantum pump model utilizing quantum interference effect.…”

Section: Pacs Numbersmentioning

confidence: 99%

Quantum charge pumps with topological phases in a Creutz ladder

Sun

Lim

2017

Phys. Rev. B

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Quantum charge pumping phenomenon connects band topology through the dynamics of a onedimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zakphase-difference of π and 2π, respectively, various charge pumping schemes are studied by applying an elaborate Peierl's phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This puts cold atoms with artificial gauge fields as an unique system where this kind of phenomena can be realized. PACS numbers:Introduction -Quantum charge pumping was one of the early example of a counterintuitive one-dimensional (1D) transport phenomenon as a result of the subtle interplay between nontrivial band topology and quantum adiabatic transport [1]. It underpins the many facets of understanding topological physics ranging from the integer quantum Hall effect [2, 3] to modern studies of electric polarization [4,5], and most recently, topological Floquet physics [6][7][8][9][10][11][12][13][14][15][16]. Explicit models of a quantum pump, however, are surprisingly rare [17][18][19][20][21]. The prototype of its realization is the one based on the Su-SchriefferHeeger/Rice-Mele (SSH/RM) model [22,23] for polyacetylene. It has generated renewed interests thanks to various recent experimental realizations in ultracold atoms and condensed matter systems, where the Zak phase [24], quantum pumping phenomena [25][26][27], and chiral solitonic edge states [28] are directly measured. In this Letter, we present a generalized Creutz scheme [29] as a distinct microscopic two-band quantum pump model utilizing quantum interference effect. The model points to a new quasi-one-dimensional tight-binding quantum pump displaying rich topological physics, and realizable with artificial gauge fields in a cold atomic setting.In the SSH/RM quantum pump, the physical picture is one based on confining quantum particle in a periodic potential that 'slides' slowly in time [17,30]. Specifically, the sliding potential interpolates the two possible alternations of bond strength, such that two dimerization phases of the SSH are realized in a time periodic manner.In the quasi-1D Creutz model (Fig. 1a with φ = 0) [29,31], there actually exists three distinct phases, a feature not apparent by inspection of the tight-binding model. An intuition is provided as follows. First, notice that cross-link hoppings and external flux in the two-leg ladder lattice enhance quantum interference effect. As a result, a complete basis in the topological regime, as found by Creutz [29], takes the form of pla...

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Section: Pacs Numbersmentioning

confidence: 99%

Quantum charge pumps with topological phases in a Creutz ladder

Sun

Lim

2017

Phys. Rev. B

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“…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.…”

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confidence: 97%

“…The electronic states of RC (LC) solitons emerge below (above) the Fermi level within the bandgap, whereas AC solitons have their states both above and below the Fermi level ( Supplementary Fig. 2a) 23,24 . The electronic difference results in the fact that RC solitons always looks brighter in STM images than LC solitons due to their enhanced density of states in filled states ( Supplementary Fig.…”

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confidence: 99%

Switching chiral solitons for algebraic operation of topological quaternary digits

2017

Self Cite

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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...

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“…A 1D CDW is a macroscopic quantum state, where atoms in a 1D metallic system relax and break translational symmetry to reduce total energy by opening a small bandgap at the Fermi energy (E F ) and modulating the charge density at the periodicity of the lattice distortion 30,31 . Although CDW order has been observed in 2D TMD metals such as NbSe 2 and TiSe 2 at low temperature 32,33 , CDWs have not previously been associated with 2D TMD semiconductors.Most studies of 1D CDWs have been performed on ensembles of CDWs in conducting polymers, quasi-one-dimensional metals or self-assembled atomic chains adsorbed on semiconducting surfaces, where inter-CDW coupling can significantly impact CDW properties [34][35][36][37][38] . The CDWs observed here are electronically isolated from one another, and have truly one-dimensional character, forming an atomically precise model system to explore intrinsic CDW phenomena.…”

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confidence: 99%

Charge density wave order in 1D mirror twin boundaries of single-layer MoSe2

et al. 2016

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We provide direct evidence for the existence of isolated, one-dimensional charge density waves at mirror twin boundaries (MTBs) of single-layer semiconducting MoSe 2 . Such MTBs have been previously observed by transmission electron microscopy and have been predicted to be metallic in MoSe 2 and MoS 2 1-7. Our low-temperature scanning tunnelling microscopy/spectroscopy measurements revealed a substantial bandgap of 100 meV opening at the Fermi energy in the otherwise metallic one-dimensional structures. We found a periodic modulation in the density of states along the MTB, with a wavelength of approximately three lattice constants. In addition to mapping the energy-dependent density of states, we determined the atomic structure and bonding of the MTB through simultaneous high-resolution non-contact atomic force microscopy. Density functional theory calculations based on the observed structure reproduced both the gap opening and the spatially resolved density of states.Properties of two-dimensional (2D) transition metal dichalcogenides (TMDs) are highly sensitive to the presence of defects, and a detailed understanding of their structure may lead to tailoring of material properties through 'defect engineering' . Intrinsic defects have been studied extensively in graphene [8][9][10][11][12] . Defects in 2D semiconductors have been explored to a lesser extent, but are expected to substantially modify material properties. 2D TMD semiconductors are particularly interesting because they exhibit direct bandgaps in the visible range [13][14][15] , high charge-carrier mobility 16,17 , extraordinarily enhanced light-matter interactions [18][19][20][21] and potential applications in novel optoelectronic devices 22,23 . Individual atomic-scale defects in 2D TMDs are expected to modify charge transport 24 or introduce ferromagnetism 25 , whereas one-dimensional defects such as grain boundaries and edges may alter electronic 1 and optical properties 1,26 , and introduce magnetic 27 or catalytic 28,29 functionality. Here we report the direct observation of one-dimensional (1D) charge density waves (CDWs) intrinsic to the conducting MTBs of monolayer MoSe 2 . A 1D CDW is a macroscopic quantum state, where atoms in a 1D metallic system relax and break translational symmetry to reduce total energy by opening a small bandgap at the Fermi energy (E F ) and modulating the charge density at the periodicity of the lattice distortion 30,31 . Although CDW order has been observed in 2D TMD metals such as NbSe 2 and TiSe 2 at low temperature 32,33 , CDWs have not previously been associated with 2D TMD semiconductors.Most studies of 1D CDWs have been performed on ensembles of CDWs in conducting polymers, quasi-one-dimensional metals or self-assembled atomic chains adsorbed on semiconducting surfaces, where inter-CDW coupling can significantly impact CDW properties [34][35][36][37][38] . The CDWs observed here are electronically isolated from one another, and have truly one-dimensional character, forming an atomically precise model system t...

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Chiral solitons in a coupled double Peierls chain

Cited by 119 publications

References 31 publications

Quantum charge pumps with topological phases in a Creutz ladder

Quantum charge pumps with topological phases in a Creutz ladder

Switching chiral solitons for algebraic operation of topological quaternary digits

Charge density wave order in 1D mirror twin boundaries of single-layer MoSe2

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