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

Medvedyeva, M. V.; Tworzydło, J.; Beenakker, C. W. J.

doi:10.1103/physrevb.81.214203

Cited by 53 publications

(52 citation statements)

References 37 publications

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“…[28], where it was found that for large N a spinless superconducting wire enters a quasi-critical region with algebraic instead of exponentially decaying transmission [29], which persists up to wire lengths L much larger than the normal-state localization length and out of range of our numerical simulations. It is also consis- tent with the approach of the two-dimensional limit, in which the one-dimensional thermal insulator transitions into a twodimensional thermal metal [30].…”

Section: Inanç Adagidelimentioning

confidence: 90%

Reentrant topological phase transitions in a disordered spinless superconducting wire

2013

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In a one-dimensional spinless p-wave superconductor with coherence length ξ, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean free path l = ξ/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean free path l = ξ/(N + 1), parametrically smaller than the critical mean free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length ξ.

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Section: Inanç Adagidelimentioning

confidence: 90%

Reentrant topological phase transitions in a disordered spinless superconducting wire

2013

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“…Our findings imply that electrostatic disorder can convert the thermal insulator into a thermal metal, thereby destroying the thermal quantum Hall effect. Numerical results for this insulator-metal transition will be reported elsewhere [37].…”

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: 99%

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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“…For strong disorder, both chiral and helical superconductors have a thermal metal-insulator transition, but the critical behavior is different: We find a localization length exponent ν ≈ 2.0, about twice as large as the known value for chiral p-wave superconductors. 13 The outline of this paper is as follows. To put our results for helical superconductors in the proper context, in the next section, we first summarize known results for chiral p-wave superconductors.…”

Section: Introductionmentioning

confidence: 99%

Thermal metal-insulator transition in a helical topological superconductor

et al. 2012

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Two-dimensional superconductors with time-reversal symmetry have a Z 2 topological invariant, which distinguishes phases with and without helical Majorana edge states. We study the topological phase transition in a class-DIII network model and show that it is associated with a metal-insulator transition for the thermal conductance of the helical superconductor. The localization length diverges at the transition with critical exponent ν ≈ 2.0, about twice the known value in a chiral superconductor.

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

Cited by 53 publications

References 37 publications

Reentrant topological phase transitions in a disordered spinless superconducting wire

Reentrant topological phase transitions in a disordered spinless superconducting wire

Majorana Bound States without Vortices in Topological Superconductors with Electrostatic Defects

Thermal metal-insulator transition in a helical topological superconductor

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