From topological superconductivity to quantum Hall states in coupled wires

Yang, Fan; Perrin, Vivien; Petrescu, Alexandru; Garate, Ion; Hur, Karyn Le

doi:10.1103/physrevb.101.085116

Cited by 20 publications

(13 citation statements)

References 97 publications

(190 reference statements)

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“…Two-dimensional systems of coupled, parallel quantum layers (electron-electron or electron-hole bilayers) show many unique phenomena [26][27][28][29][30][31][32]. Similarly, in 1D systems the additional interaction between charge carriers residing in different wires yields quantum properties such * sharmarajesh0387@gmail.com as non-Abelian topological phases (edge properties) [33][34][35][36][37], Coulomb drag between wires [38][39][40], nonadditive dispersion [41][42][43][44], enhancement in the onset of Wigner crystallization [45], and formation of biexcitons [46][47][48]. Because of these interesting properties, coupled parallel quantum wires have gained significant attention in the research community.…”

Section: Introductionmentioning

confidence: 99%

Ground-state properties of electron-electron biwire systems

et al. 2021

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The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities (rs) and interwire separations (d). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as ln(d) for d → 0 and it decreases as d −2 when d → ∞. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter rs to a single monowire of density parameter rs/2 as d is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near kF even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when d is reduced the MD decreases for k < kF and increases for k > kF, similar to its behavior with increasing rs. The TL liquid exponent is extracted by fitting the MD data near kF, from which the TL liquid interaction parameter Kρ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.

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Section: Introductionmentioning

confidence: 99%

Ground-state properties of electron-electron biwire systems

et al. 2021

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“…Although more general scenarios may be considered, we focus here on the coupled wire formalism which is obtained by setting g = 0. In particular, this adresses the one-dimensional limit of the Harper-Hofstadter model [72,73], understood as a coupled-wire system [55] and studied recently also in the context of superconductivity [74]. We require a central charge c = 1 such that one has a single pair of left and right moving species defined on the lowest band ε 1 (±k F ).…”

Section: Discussionmentioning

confidence: 99%

Drude weight increase by orbital and repulsive interactions in fermionic ladders

Haller

Rizzi

Filippone

2020

Phys. Rev. Research

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In strictly one-dimensional systems, repulsive interactions tend to reduce particle mobility on a lattice. Therefore, the Drude weight, controlling the divergence at zero-frequency of optical conductivities in perfect conductors, is lower than in non-interacting cases. We show that this is not the case when extending to quasi one-dimensional ladder systems. Relying on bosonization, perturbative and matrix product states (MPS) calculations, we show that nearest-neighbor interactions and magnetic fluxes provide a bias between back-and forward-scattering processes, leading to linear corrections to the Drude weight in the interaction strength. As a consequence, Drude weights counter-intuitively increase (decrease) with repulsive (attractive) interactions. Our findings are relevant for the efficient tuning of Drude weights in the framework of ultracold atoms trapped in optical lattices and equally affect topological edge states in condensed matter systems. arXiv:1911.11160v1 [cond-mat.quant-gas]

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“…4 produces a chiral edge mode as in the quantum Hall effect [28][29][30] and in the Haldane model [7]. The interpretation of the fractional one-half Chern number in the presence of the second band for M 1 = M 2 needs to be further studied in the layer basis, in relation with the classification table [13] including Z 2 helical edge states [31, Ising or Majorana fermion models [33,34], and ladder models [35][36][37][38].…”

Section: Lattice Modelmentioning

confidence: 99%

Quantum entangled fractional topology and curvatures

Hutchinson

Hur

2021

Commun Phys

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Topological spaces have numerous applications for quantum matter with protected chiral edge modes related to an integer-valued Chern number, which also characterizes the global response of a spin-1/2 particle to a magnetic field. Such spin-1/2 models can also describe topological Bloch bands in lattice Hamiltonians. Here we introduce interactions in a system of spin-1/2s to reveal a class of topological states with rational-valued Chern numbers for each spin providing a geometrical and physical interpretation related to curvatures and quantum entanglement. We study a driving protocol in time to reveal the stability of the fractional topological numbers towards various forms of interactions in the adiabatic limit. We elucidate a correspondence of a one-half topological spin response in bilayer semimetals on a honeycomb lattice with a nodal ring at one Dirac point and a robust π Berry phase at the other Dirac point.

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From topological superconductivity to quantum Hall states in coupled wires

Cited by 20 publications

References 97 publications

Ground-state properties of electron-electron biwire systems

Ground-state properties of electron-electron biwire systems

Drude weight increase by orbital and repulsive interactions in fermionic ladders

Quantum entangled fractional topology and curvatures

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