Absence of a metallic phase in random-bond Ising models in two dimensions: Applications to disordered superconductors and paired quantum Hall states

Read, N.; Ludwig, Andreas

doi:10.1103/physrevb.63.024404

Cited by 82 publications

(34 citation statements)

References 31 publications

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“…Without Majorana bound states, the chiral p-wave superconductor would be in the thermal insulator phase, with an exponentially small thermal conductivity at any nonzero " U [3,32,35,36]. Our findings imply that electrostatic disorder can convert the thermal insulator into a thermal metal, thereby destroying the thermal quantum Hall effect.…”

Section: Prl 105 046803 (2010) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 78%

Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

et al. 2010

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Vortices in two-dimensional superconductors with broken time-reversal and spin-rotation symmetry can bind states at zero excitation energy. These so-called Majorana bound states transform a thermal insulator into a thermal metal and may be used to encode topologically protected qubits. We identify an alternative mechanism for the formation of Majorana bound states, akin to the way in which Shockley states are formed on metal surfaces: An electrostatic line defect can have a pair of Majorana bound states at the end points. The Shockley mechanism explains the appearance of a thermal metal in vortex-free lattice models of chiral p-wave superconductors and (unlike the vortex mechanism) is also operative in the topologically trivial phase. DOI: 10.1103/PhysRevLett.105.046803 PACS numbers: 73.20.At, 73.20.Hb, 74.20.Àz, 74.25.fc Two-dimensional superconductors with spin-polarizedtriplet, p-wave pairing symmetry have the unusual property that vortices in the order parameter can bind a nondegenerate state with zero excitation energy [1][2][3][4]. Such a midgap state is called a Majorana bound state, because the corresponding quasiparticle excitation is a Majorana fermion-equal to its own antiparticle. A pair of spatially separated Majorana bound states encodes a qubit, in a way which is protected from local sources of decoherence [5]. Since such a qubit might form the building block of a topological quantum computer [6], there is an intensive search [7][8][9][10][11][12] for two-dimensional superconductors with the required combination of broken time-reversal and spinrotation symmetries (symmetry class D [13]).The generic Bogoliubov-de Gennes Hamiltonian H of a chiral p-wave superconductor is only constrained by particle-hole symmetry, x H Ã x ¼ ÀH. At low excitation energies E (to second order in momentum p ¼ Ài@@=@r) it has the form H ¼ Áðp x x þ p y y Þ þ ½UðrÞ þ p 2 =2m z ; (1) for a uniform (vortex-free) pair potential Á. The electrostatic potential U (measured relative to the Fermi energy) opens up a band gap in the excitation spectrum. At U ¼ 0 the superconductor has a topological phase transition (known as the thermal quantum Hall effect) between two localized phases, one with and one without chiral edge states [14][15][16][17].Our key observation is that the Hamiltonian (1) on a lattice has Majorana bound states at the two end points of a linear electrostatic defect. The mechanism for the production of these bound states goes back to Shockley [18]: The band gap closes and then reopens upon formation of the defect, and as it reopens a pair of states splits off from the band edges to form localized states at the end points of the defect [see Fig. 1]. Such Shockley states appear in systems as varied as metals and narrow-band semiconductors [19], carbon nanotubes [20], and photonic crystals [21]. In these systems they are unprotected and can be pushed out of the band gap by local perturbations. In a superconductor, particle-hole symmetry requires the spectrum to be AEE symmetric, so an isolated bound state is co...

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Section: Prl 105 046803 (2010) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 78%

Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

et al. 2010

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“…27 In principle, it is possible to study also the class D phase diagram ͑without Majorana bound states͒, by choosing a random mass landscape that is smooth on the scale of a. Such a study was recently performed, 28 using a different model, 29 to demonstrate the absence of the M-I transition in class D. 2,5,6 Since here we wish to study both the I-I and M-I transitions, we do not take a smooth mass landscape.…”

Section: Staggered Fermion Modelmentioning

confidence: 99%

“…A further difference between these two problems appear if the superconducting order parameter contains vortices. 2,5,6 A vortex contains a Majorana bound state at zero excitation energy in the weak-pairing regime. 7,8 A sufficiently large density of Majorana bound states allows for extended states at the Fermi level, with a thermal conductivity increasing ϰln L with increasing system size L. 3 This so-called thermal metal has no counterpart in the electronic quantum Hall effect.…”

Section: Introductionmentioning

confidence: 99%

Effective mass and tricritical point for lattice fermions localized by a random mass

2010

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This is a numerical study of quasiparticle localization in symmetry class BD ͑realized, for example, in chiral p-wave superconductors͒, by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average ͑thermal͒ conductivity is well described by an effective mass M eff , dependent on the first two moments of the random mass M͑r͒. The effective mass vanishes linearly when the average mass M → 0, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity c =1/ and critical exponent = 1. For strong disorder a transition to a metallic phase appears, with larger c but the same . The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a repulsive tricritical point.

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“…For weak disorder, the electronic density, as expressed by the filling factor ν, functions as a tuning parameter that drives the system across the four continuous quantum phase transitions. For fixed ν but increasing strength of disorder, the system may eventually transition into a thermal metal phase where the thermal Hall conductance is no longer quantized [31][32][33][34][35]. Pfaffianology.…”

mentioning

confidence: 99%

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance

et al. 2018

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The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κ_{xy}=5/2 (in units of temperature times π^{2}k_{B}^{2}/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κ_{xy}=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κ_{xy}=3/2 or 7/2. Interactions between these puddles generate a coherent macroscopic state that exhibits a plateau with quantized κ_{xy}=5/2. The non-Abelian quasiparticles characterizing this phase are distinct from those of the microscopic puddles and, by the same mechanism, could even emerge from a system comprised of microscopic Abelian puddles.

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Absence of a metallic phase in random-bond Ising models in two dimensions: Applications to disordered superconductors and paired quantum Hall states

Cited by 82 publications

References 31 publications

Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

Effective mass and tricritical point for lattice fermions localized by a random mass

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance

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