arXiv subjects

S. -R. Eric Yang

Publications and source records attributed to S. -R. Eric Yang.

At least 19 recordsLinked to original sources

arXiv2025

Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry

Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of fractionalized anyons using mutual information and interpret the results within this emergent geometric framework. As a concrete example, we consider pairs of $e/2$-charged semions that arise from instanton configurations in a disordered zigzag graphene nanoribbon. These fractional charges, located on opposite zigzag edges, show long-range quantum entanglement despite being spatially separated. We analyze the scale dependence of their entanglement and embed the ribbon into an AdS-like bulk geometry. In this setup, the entanglement structure defines minimal surfaces in the bulk, providing a geometric view of the edge correlations. This gives a holographic picture of fractionalized degrees of freedom in quasi-one-dimensional systems and shows how quantum entanglement can generate emergent geometry even without conformal symmetry.

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arXiv2025

Instantons and topological order in two-leg electron ladders: A universality class

Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially decaying gap. The value of the topological entanglement entropy suggests that two-leg ladders belong to the same universality class as graphene zigzag nanoribbons, despite several structural differences. A Shankar-Witten-type bosonization Lagrangian with disorder captures several features of the numerically obtained results for disordered two-leg ladders. Additionally, we propose a Lagrangian in which the fusion of two semions residing on different chains generates a fermion (instanton). We apply this Lagrangian within the framework of the pinned charge-density-wave model and compute the relevant Green's function using the bosonization method. This approach predicts a linear density of states at a critical disorder strength. Below this threshold, a soft gap emerges, which is in qualitative agreement with our numerical results.

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arXiv2024

Anomalous Induced Density of Supercritical Coulomb Impurities in Graphene Under Strong Magnetic Fields

The Coulomb impurity problem of graphene, in the absence of a magnetic field, displays discrete scale invariance. Applying a magnetic field introduces a new magnetic length scale $\ell$ and breaks discrete scale invariance. Moreover, a magnetic field is a singular perturbation as it turns complex energies into real energies. Nonetheless, the Coulomb potential must be regularized with a length $R$ at short distances for supercritical impurities. We investigate the structure of the induced density of a filled Landau impurity band in the supercritical regime. The coupling between Landau level states by the impurity potential is nontrivial and can lead to several anomalous effects. First, we find that the peak in the induced density can be located away from the center of the impurity, depending on the characteristics of the Landau impurity bands. Second, the impurity charge is screened, despite the Landau impurity band being filled. Third, anticrossing impurity states lead to additional impurity cyclotron resonances.

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arXiv2023

Chiral symmetry breaking and topological charge of graphene nanoribbons

We explore the edge properties of rectangular graphene nanoribbons featuring two zigzag edges and two armchair edges. Although the self-consistent Hartree-Fock fields break chiral symmetry, our work demonstrates that graphene nanoribbons maintain their status as short-range entangled symmetry-protected topological insulators. The relevant symmetry involves combined mirror and time-reversal operations. In undoped ribbons displaying edge ferromagnetism, the band gap edge states with a topological charge form on the zigzag edges. An analysis of the anomalous continuity equation elucidates that this topological charge is induced by the gap term. In low-doped zigzag ribbons, where the ground state exhibits edge spin density waves, this topological charge appears as a nearly zero-energy edge mode. Our system is outside the conventional calssification for topological insulators.

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arXiv2023

Mutual information and correlations across topological phase transitions in topologically ordered graphene zigzag nanoribbons

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines' chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.

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arXiv2023

Phase Diagram and Crossover Phases of Topologically Ordered Graphene Zigzag Nanoribbons: Role of Localization Effects

We computed the phase diagram of the zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with a nonuniversal topological entanglement entropy with significant variance. The topological order is destroyed by competition between localization effects and on-site repulsion. We found that strong on-site repulsion and/or doping weakens the nonlocal correlations between the opposite zigzag edges. In one of the crossover phases, both $\frac{e^-}{2}$ fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains $\frac{e^-}{2}$ fractional charges, but no charge transfer correlations. In low-doped zigzag ribbons the interplay between electron localization and on-site repulsion contributes to the spatial separation of quasi-degenerate gap-edge states and protects the charge fractionalization against quantum fluctuations. In all these effects, mixed chiral gap-edge states play an important role. The properties of nontopological strongly disordered and strongly repulsive phases are also observed. Each phase of the phase diagram has a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.

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arXiv2022

New disordered anyon phase of doped graphene zigzag nanoribbon

We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges. We make the following new predictions, which can be experimentally tested: (1) In the low doping case and weak disorder regime, the soft gap in the tunneling density of states is replaced by a sharp peak at the midgap energy with two accompanying peaks. The $e^-/2$ fractional charges that reside on the boundary of the zigzag edges are responsible for these peaks. (2) We find that the midgap peak disappears as the doping concentration increases. The presence of $e-/2$ fractional charges will be strongly supported by the detection of these peaks. Doped zigzag ribbons may also exhibit unusual transport, magnetic, and inter-edge tunneling properties.

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arXiv2020

Topological entanglement entropy of interacting disordered zigzag graphene ribbons

Interacting disordered zigzag graphene nanoribbons have fractional charges, are quasi-one-dimensional, and display an exponentially small gap. Our numerical computations showed that the topological entanglement entropy of these systems has a small finite but universal value, independent of the strength of the interaction and the disorder. The result that was obtained for the topological entanglement entropy shows that the disorder-free phase is critical and becomes unstable in the presence of disorder.

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arXiv2020

Topologically ordered zigzag nanoribbon: $e/2$ fractional edge charge, spin-charge separation, and ground state degeneracy

We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of $I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of fractional charges in interacting disordered ZGNR. We show that even a weak disorder potential acts as a singular perturbation on zigzag edge electronic states, producing drastic changes in the energy spectrum. Spin-charge separation and fractional charges play a key role in the reconstruction of edge antiferromagnetism. Our results show that an interacting disordered ZGNR is a topologically ordered Mott-Anderson insulator.

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arXiv2019

Soliton fractional charges in graphene nanoribbon and polyacetylene: similarities and differences

An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e/2, with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

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arXiv2018

Soliton fractional charge of disordered graphene nanoribbon

We investigate the properties of the gap-edge states of half-filled interacting disordered zigzag graphene nanoribbons. We find that the midgap states can display the quantized fractional charge of 1/2. These gap-edge states can be represented by topological kinks with their site probability distribution divided between the opposite zigzag edges with different chiralities. In addition, there are numerous spin-split gap-edge states, similar to those in a Mott-Anderson insulator.

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arXiv2017

Gap states and edge properties of rectangular graphene quantum dot in staggered potential

We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag edge. We find that, although the bulk states outside the energy gap are nearly unaffected, spin degeneracy of each gap state is lifted by the staggered potential. We have computed the occupation numbers of spin-up and -down gap states at various values of the strength of the staggered potential. The electronic and magnetic properties of the zigzag edges depend sensitively on these numbers. We discuss the possibility of applying this system as a single electron spintronic device.

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arXiv2017

Topological end states and Zak phase of rectangular armchair ribbon

We consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron-electron interactions into account we find that, as the strength of the staggered potential varies, three types of couplings between the end states can occur: antiferromagnetic without or with spin splitting, and paramagnetic without spin-splitting. We find that a spin-splitting is present only in the staggered potential region $0<Δ<Δ_c$. The transition from the antiferromagnetic state at $Δ=0$ to the paramagnetic state goes through an intermediate spin-split antiferromagnetic state, and this spin-splitting disappears suddenly at $Δ_c$. For small and large values of $Δ$ the end charge of a RAGR can be connected to the Zak phase of the periodic armchair graphene ribbon (PARG) with the same width, and it varies continuously as the strength of the potential changes.

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arXiv2015

Graphene nanosystems and low-dimensional Chern-Simons topological insulators

A graphene nanoribbon is a good candidate for a $(1+1)$ Chern-Simons topological insulator since it obeys particle-hole symmetry. We show that in a finite semiconducting armchair ribbon, which has two zigzag edges and two armchair edges, a $(1+1)$ Chern-Simons topological insulator is indeed realized as the length of the armchair edges becomes large in comparison to that of the zigzag edges. But only a quasi-topological insulator is formed in a metallic armchair ribbon with a pseudogap. In such systems a zigzag edge acts like a domain wall, through which the polarization changes from $0$ to $e/2$, forming a fractional charge of one-half. When the lengths of the zigzag edges and the armchair edges are comparable a rectangular graphene sheet (RGS) is realized, which also possess particle-hole symmetry. We show that it is a $(0+1)$ Chern-Simons topological insulator. We find that the cyclic Berry phase of states of a RGS is quantized as $π$ or $0$ (mod $2π$), and that the Berry phases of the particle-hole conjugate states are equal each other. By applying the Atiyah-Singer index theorem to a rectangular ribbon and a RGS we find that the lower bound on the number of nearly zero energy end states is approximately proportional to the length of the zigzag edges. However, there is a correction to this index theorem due to the effects beyond the effective mass approximation.

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arXiv2015

Topological gap states of semiconducting armchair graphene ribbons

In semiconducting armchair graphene ribbons a chiral lattice deformation can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost degenerate with zero energy and have a fractional charge one-half. Such a semiconducting armchair ribbon represents a one-dimensional topological insulator with nearly zero energy end states. Using data collapse of numerical results we find that the shape of the kink displays an anomalous power-law dependence on the width of the local lattice deformation. We suggest that these gap states may be probed in optical measurements. However, "metallic" armchair graphene ribbons with a gap induced by many-electron interactions have no gap states and are not topological insulators.

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arXiv2014

Impurity cyclotron resonance of anomalous Dirac electrons in graphene

We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of anomalous boundstates that have a sharp peak with a width $R$ in the probability density inside the potential and a broad peak of size magnetic length $\ell$ outside the potential. We investigate optical matrix elements of anomalous states, and find that they are unusually small and depend sensitively on magnetic field. The effect of many-body interactions on their optical conductivity is investigated using a self-consistent time-dependent Hartree-Fock approach (TDHFA). For a completely filled Landau level we find that an excited electron-hole pair, originating from the optical transition between two anomalous impurity states, is nearly uncorrelated with other electron-hole pairs, although it displays a substantial exchange self-energy effects. This absence of correlation is a consequence of a small vertex correction in comparison to the difference between renormalized transition energies computed within the one electron-hole pair approximation. However, an excited electron-hole pair originating from the optical transition between a normal and an anomalous impurity states can be substantially correlated with other electron-hole states with a significant optical strength.

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arXiv2014

Coulomb impurity problem of graphene in magnetic fields

Analytical solutions of the Coulomb impurity problem of graphene in the absence of a magnetic field show that when the dimensionless strength of the Coulomb potential $g$ reaches a critical value the solutions become supercritical with imaginary eigenenergies. Application of a magnetic field is a singular perturbation, and no analytical solutions are known except at a denumerably infinite set of magnetic fields. We find solutions of this problem by numerical diagonalization of large Hamiltonian matrices. Solutions are qualitatively different from those of zero magnetic field. All energies are discrete and no complex energies allowed. We have computed the finite-size scaling function of the probability density containing s-wave component of Dirac wavefunctions. This function depends on the coupling constant, regularization parameter, and the gap. In the limit of vanishing regularization parameter our findings are consistent with the expected values exponent $ν$ which determines of the asymptotic behavior of the wavefunction near $r=0$.

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arXiv2012

Resonant, non-resonant, and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields

We report on several new basic properties of a parabolic dot in the presence of a magnetic field. The ratio between the potential strength and the Landau level (LL) energy spacing serves as the coupling constant of this problem. In the weak coupling limit the energy spectrum in each Hilbert subspace of an angular momentum consists of discrete LLs of graphene. In the intermediate coupling regime non-resonant states form a closely spaced energy spectrum. We find, counter-intuitively, that resonant quasi-boundstates of both positive and negative energies exist in the spectrum. The presence of resonant quasi-boundstates of negative energies are a unique property of massless Dirac fermions. As the strong coupling limit is approached resonant and non-resonant states transform into anomalous states, whose probability densities develop a narrow peak inside the well and another broad peak under the potential barrier. These properties may investigated experimentally by measuring optical transition energies that can be described by a scaling function of the coupling constant.

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