Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.

doi:10.1103/physrevx.4.011036

Cited by 339 publications

(470 citation statements)

References 147 publications

(238 reference statements)

Supporting

Mentioning

463

Contrasting

Order By: Relevance

“…Recently, the CWC of two-dimensional systems has been employed in various contexts [34][35][36][37][38][39][40] including a derivation of the periodic table of integer and fractional fermionic topological phases [41]. In a way, the CWC of Abelian and nonAbelian CSLs reported in this paper completes the program previously pursued for the CWC of Read-Rezayi states in the FQHE [42,43] and their superconducting analogues [44,45]. As such, the CWC provides a fruitful perspective on a broad range of non-Abelian topological quantum states of matter.…”

mentioning

confidence: 52%

Coupled-wire construction of chiral spin liquids

et al. 2015

View full text Add to dashboard Cite

We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.PACS numbers: 71.10. Pm, 75.10.Kt, Introduction.-The experimental discovery [1] and conceptual understanding [2] of the fractional quantum Hall effect (FQHE) had a tremendous impact on contemporary research of strongly correlated electron systems. In particular, it triggered interest in topologically ordered quantum states of matter, which since then have persisted as a predominant focus. Following up on an idea by D. H. Lee, Kalmeyer and Laughlin [3,4] proposed the chiral spin liquid [5,6] (CSL) as a fractionally quantized Hall liquid for bosonic spin flip operators acting on a spin-polarized reference state. Fractionalization of charge for FQHE relates to fractionalization of spin for the CSL, which supports S = 1/2 spinons obeying halfFermi statistics [7]. The CSL has been an invaluable seed for new concepts such as topological order [8], providing a direct perspective on the fundamental relations between FQHE, spin liquids, and superconductivity [5,9]. Despite its high relevance as a paradigm formulated via wave functions, the first Hamiltonian for which the CSL is the (aside from topological degeneracies) unique ground state was only identified two decades after the liquid had been proposed [10]. The approach was subsequently expanded to yield different classes of such trial Hamiltonians [11], where the latest and more generic versions are more short-ranged than the initial microscopic models: they involve 2-body and 3-body spin interactions which can be deduced from the explicit construction of appropriate annihilation operators [12] or null operators in conformal field theory [13]. In particular, non-Abelian chiral spin liquids with level k parafermionic spin excitations have been proposed [12,14], which nurture the hope for alternative scenarios of topological quantum computation in frustrated magnets and Mott regimes of alkaline earth atoms deposited in optical lattices [15,16].Since their discovery, CSLs have been appreciated as a realisation of a bosonic Laughlin state at Landau level filling fraction ν = 1/2 on a spin lattice. Naturally, the CSL of Refs. 3 and 4 can be defined on any lattice [17,18], which becomes mathematically transparent via the generalized Perelomov identity [19] for lattices with a primitive unit cell. Some of these motifs have later reappeared in the field of fractional Chern insulators [20][21][22]. As

show abstract

mentioning

confidence: 52%

Coupled-wire construction of chiral spin liquids

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Interestingly, the addition of interaction can often modify the topological classification qualitatively 16,17 . In fact, some of the states such as parafermion states in superconductors 18 are already known to be characterized by exotic Josephson effects.…”

Section: Introductionmentioning

confidence: 99%

“…While several topological superconducting phases involving interactions have been proposed [18][19][20] , not many of them are within experimental reach. On the other hand, an interesting 8π-periodic Josephson effect, which relies on the combination of interaction and topology that has recently been proposed 21 certainly appears to be within the realm of experimental possibility.…”

Section: Introductionmentioning

confidence: 99%

8π -periodic dissipationless ac Josephson effect on a quantum spin Hall edge via a quantum magnetic impurity

Hui

2017

Phys. Rev. B

View full text Add to dashboard Cite

Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence of interaction. Interactions and spinconservation breaking are key ingredients for the realization of dissipationless ac Josephson effect on such quantum spin Hall edges. We present a simple quantum impurity model that allows to create a dissipationless fractional Josephson effect on a quantum spin Hall edge. We then use this model to substantiate a general argument that shows that any such non-dissipative Josephson effect must necessarily be 8π-periodic.

show abstract

“…Furthermore, the superconducting regions in our setup should have a diameter w > ξ sc . In contrast, the proposal of [33] requires superconducting trenches that have a width w < ξ sc , which can be potentially challenging to fabricate.…”

mentioning

confidence: 99%

“…They were then also shown to arise in FQH systems coupled to superconductors, at domain walls between regions of normal and Andreev backscattering at the edge [19][20][21], where they were referred to as parafermion [22], or fractionalized Majorana, zero modes. The general theory of these defects [23][24][25][26][27], a number of experimental proposals in FQH systems [28][29][30], other exotic phenomena at the boundary of FQH states and superconductivity [31], and theoretical suggestions for more exotic non-Abelian states of matter [32][33][34][35][36], have since been developed.In this paper, we propose a path to realizing topological degeneracies in bilayer FQH systems in contact with superconductivity without the existence of a localized parafermion zero mode. We consider an electron-hole bilayer FQH system, with a 1/3 Laughlin FQH state in each layer.…”

mentioning

confidence: 99%

Charge2e/3Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States

Barkeshli

2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1/3 Laughlin FQH state in each layer, with boundaries that are proximity-coupled to a superconductor. We show that the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (1) topologically protected degeneracies that can be measured through charge sensing experiments and (2) a fractional charge 2e/3 AC Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also extensions to electron-electron bilayers at ν = 2/3 + 1/3 coupled to superconductivity, and to electron-hole bilayers with only interlayer tunneling.A profound feature of topologically ordered states of matter is the existence of topologically protected degeneracies [1]. These are degeneracies in the ground state spectrum of a given Hamiltonian for which no local operator can distinguish the topologically distinct states, thus rendering them robust to local perturbations. Topological degeneracies are predicted to occur when a topological phase is defined on a space with nontrivial topology, such as a torus [2,3], when the system hosts non-Abelian quasiparticle excitations [4][5][6][7], and in topological superconductors when Majorana zero modes are bound to cores of vortices or the ends of one-dimensional wires [8][9][10][11][12][13][14][15].It has recently been shown theoretically that a wide class of non-Abelian defects can be realized in conventional Abelian fractional quantum Hall (FQH) states, such as the Laughlin FQH states, by suitably controlling the tunneling processes along the edge modes. In particular, it was shown that in bilayer FQH states, domain walls between regions of interlayer and intra-layer tunneling can give rise to a novel type of non-Abelian defect that generalizes Majorana zero modes by yielding m states per pair of defects, where the integer m depends on the filling fraction ν of the FQH state [16]. These non-Abelian defects were subsequently shown to also arise as lattice defects in certain lattice spin models [17], extending [18]. They were then also shown to arise in FQH systems coupled to superconductors, at domain walls between regions of normal and Andreev backscattering at the edge [19][20][21], where they were referred to as parafermion [22], or fractionalized Majorana, zero modes. The general theory of these defects [23][24][25][26][27], a number of experimental proposals in FQH systems [28][29][30], other exotic phenomena at the boundary of FQH states and superconduct...

show abstract

Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

Cited by 339 publications

References 147 publications

Coupled-wire construction of chiral spin liquids

Coupled-wire construction of chiral spin liquids

8π -periodic dissipationless ac Josephson effect on a quantum spin Hall edge via a quantum magnetic impurity

Charge2e/3Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States

Contact Info

Product

Resources

About