Proposal for observing non-Abelian statistics of Majorana-Shockley fermions in an optical lattice

Deng, Dong Ling; Wang, Sheng Tao; Sun, Kai; Duan, Liwei

doi:10.1103/physrevb.91.094513

Cited by 14 publications

(10 citation statements)

References 49 publications

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“…The flat nature of these bands and the fact that they are separated by a finite gap from the other bands suggest that they are due to surface effects. Moreover, since these states emerge at crossing band points, they have a similar origin as the edge states that appear in the Shockley model 38,[53][54][55] , which always come in pairs and can have an exotic Majorana-like nature. Actually, these kind of edge states have been predicted to appear in a 1D s-wave superconductor wire 36 .…”

Section: Quasienergy Spectrum: Numerical Resultsmentioning

confidence: 99%

“…Hence many theoretical condensed matter systems that exhibit topological edge modes have been proposed, among them, the most promising ones seem to be periodically driven systems, studied under the Floquet approach 28,[33][34][35][36][37][38][39][40][41][42][43][44] . Actually, these system are able to host not only zero energy flat bands but also ±π-energy flat bands 40,45 .…”

Section: Introductionmentioning

confidence: 99%

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Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

Roman‐Taboada

Naumis

2017

Phys. Rev. B

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We study the emergence of electronic non-trivial topological flat bands in time-periodically driven strained graphene within a tight binding approach based on the Floquet formalism. In particular, we focus on uniaxial spatially periodic strain since it can be mapped onto an effective one-dimensional system. Also, two kinds of time-periodic driving are considered: a short pulse (delta kicking) and a sinusoidal variation (harmonic driving). We prove that for special strain wavelengths, the system is described by a two level Dirac Hamiltonian. Even though the study case is gapless, we find that topologically non-trivial flat bands emerge not only at zero-quasienergy but also at ±π quasienergy, the latter being a direct consequence of the periodicity of the Floquet space. Both kind of flat bands are thus understood as dispersionless bands joining two inequivalent touching band points with opposite Berry phase. This is confirmed by explicit evaluation of the Berry phase in the touching band points' neighborhood. Using that information, the topological phase diagram of the system is built. Additionally, the experimental feasibility of the model is discussed and two methods for the experimental realization of our model are proposed.

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Section: Quasienergy Spectrum: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

Roman‐Taboada

Naumis

2017

Phys. Rev. B

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“…According to the results of section IV, the band touching condition reduces to the vanishing of the discriminant given in Eq. (10). We now show the steps of deriving the inequality (11).…”

Section: Appendix A: Hamiltonian In Majorana Representationmentioning

confidence: 99%

“…Majorana fermions (MF) have attracted much attention in recent years due to their implications for particle physics and potential applications to fault-tolerant topological quantum computation [1][2][3]. Many protocols for the realization of MFs and implementing nonabelian statistics have been proposed, yet no single platform has been identified to be ideal for studies in all aspects [4][5][6][7][8][9][10][11][12]. In versatile platforms, such as condensed matter and quantum gas systems, MFs arise as Bogoliubov quasiparticle excitations at the defect sites (vortices, interfaces, system edges, etc.).…”

Section: Introductionmentioning

confidence: 99%

Implementing Majorana Fermions in a Cold-Atom Honeycomb Lattice with Textured Pairings

Pan

Clark

2018

Frontiers in Optics / Laser Science

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Recent studies in the realization of Majorana fermion (MF) quasiparticles have focused on engineering topological superconductivity that derives from proximity effects of conventional superconductors and spin textures. We propose an effective model to create unpaired MFs at a honeycomb lattice edge by generalizing a 2-dimensional topologically nontrivial Haldane model and introducing textured pairings. The core idea is to add both the spin-singlet and textured spin-triplet pairings to a pseudospin-state dependent, time-reversal symmetry (TRS) noninvariant honeycomb lattice, and to satisfy generalized "sweet spot" conditions as in the Kitaev chain model. Our model has a gapped superconducting phase and a gapless phase; either phase may have zero or nonzero topological winding numbers. The discriminant that distinguishes those two phases gives a measure of TRS breaking and may have more general implications. Effective Majorana zero modes arise at edges in distinct phases with different degrees of degeneracy. Our theoretical model motivates concepts, such as "textured pairings" and the "strength" of TRS breaking, that may play important roles in future implementation of MFs with cold atoms in optical lattices. arXiv:1802.08804v3 [cond-mat.mes-hall]

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“…There have been a great variety of proposals for topological superconductors, including 2D semiconductor heterostructures [30,31], topological insulatorsuperconductor proximity [32][33][34][35][36], 1D spin-orbit-coupled quantum wires [37][38][39][40][41][42][43][44][45], spiral magnetic chains on superconductors [46][47][48][49][50], Shockley mechanism [51,52], and cold atom systems in 2D [53][54][55][56] and 1D [57,58], etc. Experimentally, suggestive signatures of MZMs in both 1D [59][60][61][62][63][64][65][66][67][68][69] and 2D [70][71][72][73][74][75] topological superconductors have been found.…”

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confidence: 99%

Majorana Zero Modes Protected by a Hopf Invariant in Topologically Trivial Superconductors

Yan

Wang

2017

Phys. Rev. Lett.

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Majorana zero modes are usually attributed to topological superconductors. We study a class of twodimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.Majorana zero modes (MZMs) or Majorana bound states are exotic excitations predicted to exist in the vortex cores [1, 2] of two-dimensional (2D) topological superconductors [3][4][5][6][7] and at the ends of 1D topological superconductors [8]. Spatially separated MZMs give rise to degenerate ground states, which encode qubits immune to local dechoerence [8, 9]. Furthermore, unitary transformations among the ground states can be implemented by braiding [10][11][12][13][14] or measurements [15, 16] of these modes, indicating that such qubits may become building blocks in topological quantum computation and information [17][18][19][20][21][22]. Therefore, MZMs have been vigorously pursued in condensed matter physics [23][24][25][26][27][28][29].There have been a great variety of proposals for topological superconductors, including 2D semiconductor heterostructures [30,31], topological insulatorsuperconductor proximity [32][33][34][35][36], 1D spin-orbit-coupled quantum wires [37][38][39][40][41][42][43][44][45], spiral magnetic chains on superconductors [46][47][48][49][50], Shockley mechanism [51, 52], and cold atom systems in 2D [53][54][55][56] and 1D [57,58] It is often implicitly assumed that topological superconductivity is a prerequisite for MZMs, accordingly, the chiral edge states go hand in hand with the vortex zero modes in 2D superconductors. In this Letter we show that certain topological defects [76][77][78][79][80][81] in 2D topologically trivial superconductors can support robust MZMs. Somewhat surprisingly, single-band superconductors suffice this purpose. The model Hamiltonian is related to the Hopf maps, which originally refer to nontrivial mappings from a 3D sphere S 3 to a 2D sphere S 2 , characterized by the integer Hopf invariant [82,83]. Mappings from a 3D torus T 3 to S 2 inherit the nontrivial topology from the mappings S 3 → S 2 . The Hopf invariant has found interesting applications in nonlinear σ models and spin systems [82,84], Hopf insulators [85][86][87][88][89][90], liquid crystals [91], and quench dynamics of Chern insulators [92,93].Our model describes topologically trivial superconductors with zero Chern number and no chiral edge state. Nevertheless, a topological point defect is characterized by a Hopf invariant defined in the (k x , k y , θ) space, where k x , k y are crystal momenta and θ is the polar angle [94] (Fig.1a). The parity (even/odd) of Hopf invariant determines the presence (absence) of robust MZMs, though the superconductor for ev- ery fixed θ is topologically trivial. Stimulated by this mechanis...

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Proposal for observing non-Abelian statistics of Majorana-Shockley fermions in an optical lattice

Cited by 14 publications

References 49 publications

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

Implementing Majorana Fermions in a Cold-Atom Honeycomb Lattice with Textured Pairings

Majorana Zero Modes Protected by a Hopf Invariant in Topologically Trivial Superconductors

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