Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices

Cai, Xiaoming; Lang, Li-Jun; Chen, Shu; Wang, Yupeng

doi:10.1103/physrevlett.110.176403

Cited by 151 publications

(172 citation statements)

References 36 publications

(44 reference statements)

Supporting

Mentioning

162

Contrasting

Order By: Relevance

“…The phase transition from the extended state to the localized state could also be expected according to previous works on the quasiperiodic 1D Kitaev chain [23,24]. In the following, we will discuss the properties of this generalized AAH model both in the incommensurate case and the commensurate case.…”

Section: Model Hamiltonianmentioning

confidence: 96%

“…If λ = 0, then the Hamiltonian is the same as the 1D Kitaev chain with on-site potential modulations which are investigated in detail in Refs. [23,24]. It has been predicted that if α is irrational, the Kitaev model (λ = 0, V = 0) or the diagonal AAH model (λ = 0, ∆ = 0, V = 0) will go through a localization transition where all extended states become localized as V is increased beyond some critical value.…”

Section: Model Hamiltonianmentioning

confidence: 99%

“…With the realization of the AAH model in photonic crystals [15][16][17] and ultracold atoms [18,19], this model has gained attention in recent years. The abundant phenomena revealed by the AAH model make it an ideal test field for topological phases and the transitions between them both in the incommensurate and commensurate cases [20][21][22][23][24][25][26][27][28][29][30]. When the lattice is incommensurate, the system will go through a transition from an extended phase to a localized phase due to the disordered on-site potential [23,24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Aubry-André-Harper model withp-wave superconducting pairing

2016

Self Cite

View full text Add to dashboard Cite

We investigate a generalized Aubry-André-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of 1/α. In the incommensurate case [α = ( √ 5 − 1)/2], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case (α = 1/2), we find that this model shows three different phases when we tune the system parameters: SuSchrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases.

show abstract

Section: Model Hamiltonianmentioning

confidence: 96%

Section: Model Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Aubry-André-Harper model withp-wave superconducting pairing

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…Most recently, the AAH model has attracted renewed attentions due to its experimental realization in photonic crystals [14][15][16] and ultracold atoms 17,18 . It has been found to play a non-trivial role to characterize emerging topological states of matter [19][20][21][22][23][24][25][26][27][28][29] and the intriguing phenomenon of quantum many-body localization 30,31 . The AAH model can be formally derived from the reduction of a two-dimensional (2D) quantum Hall system to a 1D chain 32 .…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of a non-Abelian Aubry-André-Harper model withp-wave superfluidity

Wang¹,

Liu²,

Xianlong³

et al. 2016

Phys. Rev. B

View full text Add to dashboard Cite

We theoretically study a one-dimensional quasi-periodic Fermi system with topological p-wave superfluidity, which can be deduced from a topologically non-trivial tight-binding model on the square lattice in a uniform magnetic field and subject to a non-Abelian gauge field. The system may be regarded a non-Abelian generalization of the well-known Aubry-André-Harper model. We investigate its phase diagram as functions of the strength of the quasi-disorder and the amplitude of the p-wave order parameter, through a number of numerical investigations, including a multifractal analysis. There are four distinct phases separated by three critical lines, i.e., two phases with all extended wave-functions (I and IV), a topologically trivial phase (II) with all localized wavefunctions and a critical phase (III) with all multifractal wave-functions. The phase I is related to the phase IV by duality. It also seems to be related to the phase II by duality. Our proposed phase diagram may be observable in current cold-atom experiments, in view of simulating non-Abelian gauge fields and topological insulators/superfluids with ultracold atoms.

show abstract

“…It is well known that the Aubry-André model or the Aubry-André-Harper (AAH) model will shows a phase transition from extended states to localized states (Anderson localization) when the lattice is incommensurate [35][36][37][38]. The normal Hermitian AAH model with or without p-wave superconducting pairing presents abundant physical phenomena both in the commensurate and incommensurate situations [39][40][41][42][43][44][45][46][47][48][49][50][51]. However, the influences of physical gain and loss on the AAH model have not been explored much.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

Self Cite

View full text Add to dashboard Cite

We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

show abstract

Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices

Cited by 151 publications

References 36 publications

Generalized Aubry-André-Harper model withp-wave superconducting pairing

Generalized Aubry-André-Harper model withp-wave superconducting pairing

Phase diagram of a non-Abelian Aubry-André-Harper model withp-wave superfluidity

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Contact Info

Product

Resources

About