Helical nuclear spin order in a strip of stripes in the quantum Hall regime

Meng, Tobias; Stano, Peter; Klinovaja, Jelena; Loss, Daniel

doi:10.1140/epjb/e2014-50445-1

Cited by 47 publications

(77 citation statements)

References 71 publications

(121 reference statements)

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“…1), where each of them can be treated as a one-dimensional Luttinger liquid by bosonization [75][76][77][78][79][80][81][82][83][84][85][86]. This will allow us to introduce the Floquet version not only of TIs but also of Weyl semimetals in driven 2D systems.…”

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confidence: 99%

Topological Floquet Phases in Driven Coupled Rashba Nanowires

2016

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We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e=m with m being an odd integer. DOI: 10.1103/PhysRevLett.116.176401 Introduction.-Topological effects in condensed matter systems have attracted attention for many years. From the quantum Hall effect over topological insulators (TIs) [1][2][3][4][5][6][7][8][9][10][11][12] and Weyl semimetals [13][14][15][16][17], to Majorana fermions and parafermions [39][40][41][42][43][44][45][46][47][48][49], the interest is driven both by fundamental physics and the promise for topological quantum computation. Despite the many proposals for topological systems, the search for the most optimal material still continues unabated.While most studies were focused on static structures, it has recently been proposed to extend topological phases to nonequilibrium systems, described by Floquet states . Remarkably, this approach no longer relies on given material properties, such as strong spin orbit interactions (SOIs), typically necessary for reaching topological regimes, but instead allows one to turn initially nontopological materials such as graphene [50] and non-bandinverted semiconducting wells into TIs [52] by applying an external driving field.An even bigger challenge is to describe topological effects that involve fractional excitations. This requires the presence of strong electron-electron interactions. However, given the difficulties in the search for conventional TIs, it would be even more surprising to expect such phases to occur naturally. Moreover, even if they existed, twodimensional (2D) systems with electron-electron interactions are difficult to describe analytically and often progress can come only from numerics [61].Here, we circumvent this difficulty by considering strongly anisotropic 2D systems [71][72][73][74] formed by weakly coupled Rashba wires (see Fig. 1), where each of them can be treated as a one-dimensional Luttinger liquid by bosonization [75][76][77][78][79][80][81][82][83][84][85][86]. This will allow us to introduce the Floquet version not only of TIs but also of Weyl semimetals in driven 2D systems. Importantly, in this way we can also address fractional regimes and are able to obtain the Floquet version of fractional TIs and Weyl semimetals.

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confidence: 99%

Topological Floquet Phases in Driven Coupled Rashba Nanowires

2016

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“…The latter is especially important for the fractional regime [53][54][55][56][57][58][59][60][61][62][63] as it allows one to design fractional TIs for an array of coupled The constriction could be either doped with magnetic impurities or subjected to a magnetic field. The pairs of helical edge states are coupled by tunneling which results in the opening of an energy gap at zero momentum.…”

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confidence: 99%

“…For example, gaps can be opened by magnetic fields, tunneling between edges, charge density waves, or solely by interactions. We finally note that the proposed coupled edge states could be realized not only in TIs but also in systems of coupled wires [53] in the framework of strip of stripes [53][54][55][56][57][58][59][60][61][62][63], which is especially relevant for the fractional TI regime.…”

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Fractional charge and spin states in topological insulator constrictions

Klinovaja

Loss

2015

Phys. Rev. B

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We investigate theoretically properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpedicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interactions dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8π-peridiodicity.

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“…29 Similar behavior was recently predicted to occur in coupled-wire models. 30 Establishing such nuclear order would suppress spin noise, 31 stabilize fractional fermions, 21 and provide a tune-free platform for Majorana fermions.…”

Section: -24mentioning

confidence: 99%

“…This one-dimensional model of effective spins of length I = N ⊥ I 3/2 is discussed in detail elsewhere. 29,30 Finally, S ni = σ n δ(x n − x i )/2πR 2 ρ is the electron spin density operator at the ith transverse plane at x i = ia, and L = N a is the wire length.…”

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confidence: 99%

NMR response of nuclear-spin helix in quantum wires with hyperfine and spin-orbit interaction

Stano¹,

Loss²

2014

Phys. Rev. B

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We calculate the nuclear magnetic resonance (NMR) response of a quantum wire where at low temperature a self-sustained electron-nuclear spin order is created. Our model includes the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange, electron spin-orbit interactions, nuclear dipolar interactions, and the static and oscillating NMR fields, all of which play an essential role. The paramagnet to helimagnet transition in the nuclear system is reflected in an unusual response: it absorbs at a frequency given by the internal RKKY exchange field, rather than the external static field, whereas the latter leads to a splitting of the resonance peak.

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Helical nuclear spin order in a strip of stripes in the quantum Hall regime

Cited by 47 publications

References 71 publications

Topological Floquet Phases in Driven Coupled Rashba Nanowires

Topological Floquet Phases in Driven Coupled Rashba Nanowires

Fractional charge and spin states in topological insulator constrictions

NMR response of nuclear-spin helix in quantum wires with hyperfine and spin-orbit interaction

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