arXiv subjects

Kwon Park

Publications and source records attributed to Kwon Park.

At least 37 records · Page 2Linked to original sources

arXiv2012

Correlation effects on 3D topological phases: from bulk to boundary

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit quantized electro-magnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean field theory, a method that incorporates quantum-many-body effects and allows us to evaluate the magneto-electric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

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arXiv2012

Self-similar occurrence of massless Dirac particles in graphene under magnetic field

Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron moving in lattice under magnetic field. Evolving from the $n=0$ Landau level, the central band of the Hofstadter butterfly is especially interesting since it may hold a key to the mysteries of the fractional quantum Hall effect observed in graphene. While the entire Hofstadter butterfly can be in principle obtained by solving Harper's equations numerically, the weak-field limit, most relevant for experiment, is intractable due to the fact that the size of the Hamiltonian matrix, that needs to be diagonalized, diverges. In this paper, we develop an effective Hamiltonian method that can be used to provide an accurate analytic description of the central Hofstadter band in the weak-field regime. One of the most important discoveries obtained in this work is that massless Dirac particles always exist inside the central Hofstadter band no matter how small the magnetic flux may become. In other words, with its bandwidth broadened by the lattice effect, the $n=0$ Landau level contains massless Dirac particles within itself. In fact, by carefully analyzing the self-similar recursive pattern of the central Hofstadter band, we conclude that massless Dirac particles should occur under arbitrary magnetic field. As a corollary, the central Hofstadter band also contains a self-similar structure of recursive Landau levels associated with such massless Dirac particles. To assess the experimental feasibility of observing massless Dirac particles inside the central Hofstadter band, we compute the width of the central Hofstadter band as a function of magnetic field in the weak-field regime.

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arXiv2012

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet

Motivated by the recent neutron scattering experiment on Rb2Cu3SnF12 [Nat. Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the Gamma point and cause a shift of the spin gap (the minimum triplon gap) position from the K to Gamma point in the first Brilloin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization and strong coupling expansion approaches. We find that the results of all above approaches are consistent with the experimental findings.

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arXiv2011

Spin cluster operator theory for the Kagome lattice antiferromagnet

The spin-1/2 quantum antiferromagnet on the Kagome lattice provides a quintessential example in the strongly correlated electron physics where both effects of geometric frustration and quantum fluctuation are pushed to their limit. Among possible non-magnetic ground states, the valence bond solid (VBS) with a 36-site unit cell is one of the most promising candidates. A natural theoretical framework for the analysis of such VBS order is to consider quantum states on a bond connecting the nearest-neighboring sites as fundamental quantum modes of the system and treat them as effectively independent "bond particles." While correctly describing the VBS order in the ground state, this approach, known as the bond operator theory, significantly overestimates the lowest spin excitation energy. To overcome this problem, we take a next logical step in this paper to improve the bond operator theory and consider extended spin clusters as fundamental building blocks of the system. Depending on two possible configurations of the VBS order, various spin clusters are considered: (i) in the VBS order with staggered hexagonal resonance, we consider one spin cluster for a David star and two spin clusters with each composed of a perfect hexagon and three attached dimers, and (ii) in the VBS order with uniform hexagonal resonance, one spin cluster composed of a David star and three attached dimers. It is shown that the majority of low-energy spin excitations are nearly or perfectly flat in energy. With most of its weight coming from the David star, the lowest spin excitation has a gap much lower than the previous value obtained by the bond operator theory, narrowing the difference against exact diagonalization results.

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arXiv2010

Superconducting Order Parameter for the Even-denominator Fractional Quantum Hall Effect

One of the most intriguing phenomena in nature is the fractional quantum Hall effect (FQHE) observed in the half-filled second Landau level which, arising in even-denominator filling factors, $ν=5/2$ and $7/2$, is completely different from other FQHEs in its origin, all of which, except for those two filling factors, occur in odd-denominator fractions. Usually formulated in terms of a trial wave function called the Moore-Read Pfaffian wave function, current leading theories attribute the origin of the 5/2 FQHE to the formation of Cooper pairs, not of electron, but of the true quasi-particle of the system known as composite fermion. The nature of superconductivity resulting from such Cooper pairing is particularly puzzling in the sense that it apparently coexists with strong magnetic fields, which poses an interesting dilemma since the Meissner effect is {\it the} most important defining property of superconductivity. This apparent dilemma is resolved by the fact that composite fermions do not respond to external magnetic field at even-denominator filling factors. To provide direct evidence that it is composite fermions that actually form the superconducting condensate, here, we develop a numerically exact method of creating a Cooper pair of composite fermions and explicitly compute the superconducting order parameter as a function of real space coordinates. As results, in addition to direct evidence for superconductivity, we obtain quantitative predictions for superconducting coherence length. Obtaining such theoretical predictions can serve as an important step toward fault-tolerant topological quantum computation.

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arXiv2008

Spontaneous Particle-Hole Symmetry Breaking in the $ν=5/2$ Fractional Quantum Hall Effect

The essence of the $ν=5/2$ fractional quantum Hall effect is believed to be well captured by the Moore-Read Pfaffian (or anti-Pfaffian) description. However, an important mystery regarding the formation of the Pfaffian state is the role of the three-body interaction Hamiltonian $H_3$ that produces the Pfaffian as an exact ground state and the concomitant particle-hole symmetry breaking. We show that a two-body interaction Hamiltonian $H_2$ constructed via particle-hole symmetrization of $H_3$ produces a ground state nearly exactly approximating the Pfaffian and anti-Pfaffian states, respectively, in the spherical geometry. More importantly, the ground state energy of $H_2$ is shown to exhibit a ``Mexican-hat'' structure as a function of particle number in the vicinity of half filling for a given flux indicating spontaneous particle-hole symmetry breaking. We do not find any such Mexican-hat signature in the second Landau level Coulomb interaction at 5/2.

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arXiv2008

Spin Triplet Excitations for a Valence Bond Solid on the Kagome Lattice

One of the most promising candidate ground states for the quantum antiferromagnetic Heisenberg model on the Kagome lattice is the valence bond solid (VBS) with a 36-site unit cell. We present a theory of triplet excitation spectra about this ground state using bond operator formalism. In particular we obtain dispersions of all 18 triplet modes in the reduced Brillouin zone. In the bond operator mean-field theory, it is found that a large number of triplet modes are non-dispersive. In particular, the lowest triplet excitation is non-dispersive and degenerate with a dispersive mode at the zone center. Away from the zone center, the lowest triplet is separated from two other flat modes by a small energy gap. Quantum fluctuations are considered by taking into account scattering processes of two triplets and their bound state formation, which leads to a downward renormalization of the lowest spin triplet gap. The dispersion of the lowest triplet excitation in the VBS state is compared with the dispersive lower bound of the triplet continuum expected in competing spin liquid phases. Implications to future neutron scattering experiments are discussed.

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arXiv2007

Dynamical Mean Field Theory of the Gutzwiller-projected BCS Hamiltonian: Phase Fluctuations and the Pseudogap

One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, $U$, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to $U$.

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arXiv2007

Doped Valence Bond Solid and Superconductivity on the Shastry-Sutherland Lattice

Motivated by recent experiments on SrCu$_2$(BO$_3$)$_2$, we investigate the ground states of the doped Mott insulator on the Shastry-Sutherland lattice. To provide a unified theoretical framework for both the valence-bond solid state found in undoped SrCu$_2$(BO$_3$)$_2$ and the doped counterpart being pursued in on-going experiments, we analyze the t-J-$V$ model via the bond operator formulation. It is found that novel superconducting states emerge upon doping with their properties crucially depending on the underlying valence bond order. Implications to future experiments are discussed.

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arXiv2004

Theory of Tunneling in the Exciton Condensate of Bilayer Quantum Hall Systems

We develop a theory of interlayer tunneling in the exciton condensate of bilayer quantum Hall systems, which predicts strongly enhanced, but finite, tunneling conductance peaks near zero bias even at zero temperature. It is emphasized that, though this strongly enhanced tunneling originates from spontaneous interlayer phase coherence, it is fundamentally not the Josephson effect. Because of strong interlayer correlation, the bilayer system behaves as a single system so that conventional tunneling theories treating two layers as independent systems are not applicable. Based on our theory, we compute the height of conductance peak as a function of interlayer distance, which is in good agreement with experiment.

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arXiv2002

Kondo effect of non-magnetic impurities and the co-existing charge order in the cuprate superconductors

We present a theory of Kondo effect caused by an induced magnetic moment near non-magnetic impurities such as Zn and Li in the cuprate superconductors. Based on the co-existence of charge order and superconductivity, a natural description of the induced moment and the resulting Kondo effect is obtained in the framework of bond-operator theory of microscopic t-J-V Hamiltonian. The local density of state near impurities is computed in a self-consistent Bogoliubov-de Gennes theory which shows a low-energy peak in the middle of superconducting gap. Our theory also suggests that the charge order can be enhanced near impuries.

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arXiv2001

Bond and Neel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions

We describe the zero temperature phases and phase boundaries of an effective lattice model for frustrated, easy-plane, spin S=1/2 quantum antiferromagnets. The model contains states with Neel and bond-centered charge order and fractionalization in different limiting regimes, and we describe how these orders compete at intermediate coupling. The complex Berry phase terms render this model unsuitable for direct simulation; however, a duality mapping leads to a model of interacting current loops with positive weights, which is then studied by Monte Carlo simulations.

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arXiv2001

Ground states of quantum antiferromagnets in two dimensions

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (Mod. Phys. Lett. B 4, 1043 (1990), http://onsager.physics.yale.edu/p32.pdf). The `minimal' model for square lattice antiferromagnets is a lattice discretization of the quantum non-linear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Neel order at weak coupling, and a confining paramagnetic ground state with bond charge (e.g. spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry group is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring non-collinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.

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arXiv2001

Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions

The ground states and excitations of two-dimensional insulating and doped Mott insulators are described by a bond operator formalism. While the method represents the degrees of freedom of an arbitrary antiferromagnet exactly, it is especially suited to systems in which there is a natural pairing of sites into bonds, as in states with spontaneous or explicit spin-Peierls order (or bond-centered charge order). In the undoped insulator, as discussed previously, we obtain both paramagnetic and magnetically-ordered states. We describe the evolution of superconducting order in the ground state with increasing doping--at low doping, the superconductivity is weak, can co-exist with magnetic order, and there are no gapless spin 1/2 fermionic excitations; at high doping, the magnetic order is absent and we obtain a BCS d-wave superconductor with gapless spin 1/2, nodal fermions. We present the critical theory describing the onset of these nodal fermionic excitations. We discuss the evolution of the spin spectrum, and obtain regimes where a spin 1 exciton contributes a sharp resonance in the dynamic spin susceptiblity. We also discuss the experimental consequences of low-energy, dynamically fluctuating, spin-Peierls order in an isotropic CuO_2 plane--we compute consequences for the damping and dispersion of an optical phonon involving primarily the O ions, and compare the results with recent neutron scattering measurements of phonon spectra.

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arXiv2001

Charged Excitons of Composite Fermions in the Fractional Quantum Hall Effect

Charged excitons of composite fermions (CFs) are considered in the fractional quantum Hall effect. Energies of the charged CF excitons are computed at $ν=1/3$ as a function of the size of exciton. We show that the charged CF exciton with size of roton is lower in energy than the unbound state of a neutral roton and a lone charge. Therefore we propose that the lowest-energy excitation of the fractional quantum Hall effect is in fact due to the charged excitons of composite fermions composed of two CF-particles and one CF-hole. We believe that charged excitons of composite fermions shed new light on interpreting the resonant inelastic light scattering experiments.

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arXiv2000

Cooper Instability of Composite Fermions

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particl es called `composite fermions'. The fractional quantum Hall effect occurs in such a system when the ratio (or `filling factor', $ν$) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling $ν=1/2$ corresponds to a metallic state in which the composite fermions form a gapless Fermi sea. But for $ν=5/2$, a fractional quantum Hall effect is observed instead; this unexpected result is the subject of considerable debate and controversy. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at $ν=5/2$, but not at $ν=1/2$. In effect, the repulsive Coulomb interaction between electrons is overscr eened in the $ν=5/2$ state by the formation of composite fermions, resulting in a weak, attractive interaction.

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arXiv2000

The excitonic collapse of higher Landau level fractional quantum Hall effect

The scarcity of the fractional quantum Hall effect in higher Landau levels is a most intriguing fact when contrasted with its great abundance in the lowest Landau level. This paper shows that a suppression of the hard core repulsion in going from the lowest Landau level to higher Landau levels leads to a collapse of the energy of the neutral excitation, destabilizing all fractional states in the third and higher Landau levels, and almost all in the second Landau level. The remaining fractions are in agreement with those observed experimentally.

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arXiv1999

Masses of composite fermions carrying two and four flux quanta: Differences and similarities

This study provides a theoretical rationalization for the intriguing experimental observation regarding the equality of the normalized masses of composite fermions carrying two and four flux quanta, and also demonstrates that the mass of the latter type of composite fermion has a substantial filling factor dependence in the filling factor range $4/17 > ν> 1/5$, in agreement with experiment, originating from the relatively strong inter-composite fermion interactions here.

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