arXiv subjects

Hsiang-Hsuan Hung

Publications and source records attributed to Hsiang-Hsuan Hung.

At least 19 recordsLinked to original sources

arXiv2017

Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure

We study a vortex chain in a thin film of a topological insulator with proximity-induced superconductivity---a promising platform to realize Majorana zero modes (MZMs)---by modeling it as a two-leg Majorana ladder. While each pair of MZMs hybridizes through vortex tunneling, we hereby show that MZMs can be stabilized on the ends of the ladder with the presence of tilted external magnetic field and four-Majorana interaction. Furthermore, a fruitful phase diagram is obtained by controlling the direction of magnetic field and the thickness of the sample. We reveal many-body Majorana states and interaction-induced topological phase transitions and also identify trivial-superconducting and commensurate/incommensurate charge-density-wave states in the phase diagram.

cond-mat.supr-con↗

arXiv2016

Phase diagram of a frustrated asymmetric ferromagnetic spin ladder

We perform a systematic investigation on the ground state of an asymmetric two-leg spin ladder (where exchange couplings of the legs are unequal) with ferromagnetic (FM) nearest-neighbor interaction and diagonal anti-ferromagnetic frustration using the Density Matrix Renormalization Group (DMRG) method. When the ladder is strongly asymmetric with moderate frustration, a magnetic canted state is observed between a FM state and a singlet dimerized state. The phase boundaries are dependent on the asymmetric strength $α_{a}$. On the other hand, when the asymmetric strength is intermediate, a so-called spin-stripe state (spins align parallel on same legs, but antiparallel on rungs) is discovered, and the system experiences a first-order phase transition from the FM state to the spin-stripe state upon increasing frustration. We present numerical evidence to interpret the phase diagram in terms of frustration and the asymmetric strength.

cond-mat.str-el↗

arXiv2016

A correlated Anderson insulator on the honeycomb lattice

We study the effect of disorder on the semimetal -- Mott insulator transition in the half-filled repulsive Hubbard model on a honeycomb lattice, a system that features vanishing density of states at the Fermi level. Using the determinant quantum Monte Carlo method, we characterize various phases in terms of the bulk-limit antiferromagnetic (AF) order parameter, compressibility, and temperature-dependent DC conductivity. In the clean limit, our data are consistent with previous results showing a single quantum critical point separating the semi-metallic and AF Mott insulating phases. With the presence of randomness, a non-magnetic disordered insulating phase emerges. Inside this disordered insulator phase, there is a crossover from a gapless Anderson-like insulator to a gapped Mott-like insulator.

cond-mat.str-el↗

arXiv2016

Disorder effects in correlated topological insulators

Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both non-interacting and interacting models of two-dimensional topological insulators. In the fermion sign problem-free interacting models we study, electron-electron interactions are described by an on-site repulsive Hubbard interaction and disorder is included via the one-body hopping operators. In both the non-interacting and interacting models we make use of recent advances in highly accurate real-space numerical evaluation of topological invariants to compute phase boundaries, and in the non-interacting models determine critical exponents of the transitions. We find different models exhibit distinct stability conditions of the topological phase with respect to interactions and disorder. We provide a general analytical theory that accurately predicts these trends.

cond-mat.str-el↗

arXiv2015

Correlation effects in pyrochlore iridate thin films grown along the $[111]$ direction

Over the past few years bulk pyrochlore iridates of the form $A_2$Ir$_2$O$_7$ (where $A$ is a rare earth element, Ir is iridium, and O is oxygen) have been studied as model systems for investigating the interplay of electronic correlations and strong spin-orbit coupling, particularly with the aim of finding correlation-driven topological phases. In this work, we use cellular dynamical mean field theory (CDMFT) to study effects of electronic correlations beyond Hartree-Fock theory in thin films of pyrochlore irradiates grown along the $[111]$ direction. We focus on the bilayer and trilayer systems, and compute the phase diagrams of these systems as a function of electron-electron interaction strength, which is modeled by an on-site Hubbard interaction. By evaluating the $Z_2$ invariant and Chern number using formulas based on the single-particle Green's function and the quasi-particle effective Hamiltonian, we show that on-site correlations can drive an interaction-induced topological phase transition, turning a time-reversal invariant topological insulator and a nearly flat band metal to a correlated Chern insulator (CI) in bilayer and trilayer systems, respectively. By comparing with the Hartree-Fock results, the CDMFT results show that quantum fluctuations enhance the robustness of the interaction-driven CI phase in the thin films. Furthermore, our numerical analysis of the quasiparticle spectrum reveals that the topological phases we find in our many-body calculations are adiabatically connected to those in the single-particle picture.

cond-mat.str-el↗

arXiv2015

Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method

Time-reversal symmetric topological insulator is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the $Z_2$ topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg,Cd)Te quantum wells. Yet an interacting topological insulator is still an elusive subject, and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this review, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in three generalized versions of the Kane-Mele model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo calculations on the same model, and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

cond-mat.str-el↗

arXiv2014

Effects of short-ranged interactions on the Kane-Mele model without discrete particle-hole symmetry

We study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in the Kane-Mele model at half-filling with staggered potentials which explicitly breaks the discrete particle-hole symmetry. Within Hartree-Fock mean-field analysis, we conclude that the on-site repulsive interactions help stabilize the topological phase (quantum spin Hall) against the staggered potentials by enlarging the regime of the topological phase along the axis of the ratio of the staggered potential strength and the spin-orbit coupling. In sharp contrast, the on-site attractive interactions destabilize the topological phase. We also examine the attractive interaction case by means of the unbiased determinant projector quantum Monte Carlo and the results are qualitatively consistent with the Hartree-Fock picture.

cond-mat.str-el↗

arXiv2014

Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature

Topological phases originating from spin-orbit coupling have attracted great attention recently. In this work, we use cellular dynamical mean field theory with the continuous-time quantum Monte Carlo solver to study the Kane-Mele-Hubbard model supplemented with an additional third-neighbor hopping term. For weak interactions, the third-neighbor hopping term drives a topological phase transition between a topological insulator and a trivial insulator, consistent with previous fermion sign-free quantum Monte Carlo results [H.-Hung et al., Phys. Rev. B 89, 235104 (2014)]. At finite temperatures, the Dirac cones of the zero temperature topological phase boundary give rise to a metallic regime of finite width in the third-neighbor hopping. Furthermore, we extend the range of interactions into the strong coupling regime and find an easy-plane anti-ferromagnetic insulating state across a wide range of third-neighbor hopping. In contrast to the weak coupling regime, no topological phase transition occurs at strong coupling, and the ground state is a trivial anti-ferromagnetic insulating state. A comprehensive finite temperature phase diagram in the interaction-third-neighbor hopping plane is provided.

cond-mat.str-el↗

arXiv2014

Short-ranged interaction effects on $Z_2$ topological phase transitions

Using a combined perturbative and self-consistent mean-field approach that we directly compare with quantum Monte Carlo calculations, we study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in two generalized versions of the Kane-Mele model at half-filling on the honeycomb lattice. For interactions weaker than the critical value for magnetic instability, we find that the interactions can stabilize the quantum spin Hall phase against third neighbor hoppings, which preserve $C_3$ lattice rotation symmetry, but destabilize it for a dimerization that explicitly breaks the $C_3$ symmetry. Consistent with quantum Monte Carlo calculations, we show the phase boundary shifts are linearly proportional to the square of the interaction strength, but with opposite sign--a result that cannot be reproduced with a perturbative treatment that does not also include a self-consistent treatment of the perturbed Hamiltonian. Our results emphasize that short-range interactions can have subtle effects on the stability of topological phases, and may need to be treated by methods analogous to those we use here.

cond-mat.str-el↗

arXiv2014

Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations

We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\times 18^2$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the $\mathbb{Z}_2$ invariant and spin Chern number $C_σ$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The $\mathbb{Z}_2$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the non-interacting limit, without any spontaneously symmetry breaking. The interaction-induced shift is non-perturbative in the interactions and cannot be captured within a "simple" self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the $D_3$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the $D_3$ symmetry.

cond-mat.str-el↗

arXiv2014

Tuning between singlet, triplet, and mixed pairing states in an extended Hubbard chain

We study spin-half fermions in a one-dimensional extended Hubbard chain at low filling. We identify three triplet and one singlet pairing channels in the system, which are independently tunable as a function of nearest-neighbor charge and spin interactions. In a large-size system with translational invariance, we derive gap equations for the corresponding pairing gaps and obtain a Bogoliubov-de Gennes Hamiltonian with its non-trivial topology determined by the interplay of these gaps. In an open-end system with a fixed number of particles, we compute the exact many-body ground state and identify the dominant pairing revealed by the pair density matrix. Both cases show competition between the four pairing states, resulting in broad regions for each of them and relatively narrow regions for mixed-pairing states in the parameter space. Our results enable the possibility of tuning a nanowire between singlet and triplet pairing states without breaking time-reversal or SU(2) symmetry, accompanied by a change in the system's topology.

cond-mat.supr-con↗

arXiv2014

Topological Phase Transition in the Hofstadter-Hubbard Model

We study the interplay between topological and conventional long range order of attractive fermions in a time reversal symmetric Hofstadter lattice using quantum Monte Carlo simulations, focussing on the case of one-third flux quantum per plaquette. At half-filling, the system is unstable towards s-wave pairing and charge-density-wave order at infinitesimally small interactions. At one-third-filling, the noninteracting system is a topological insulator, and a nonzero critical interaction strength is needed to drive a transition from the quantum spin Hall insulator to a superfluid. We probe the topological signature of the phase transition by threading a magnetic flux through a cylinder and observe quantized topological charge pumping.

cond-mat.str-el↗

arXiv2014

A comparative DMFT study of the eg-orbital Hubbard model in thin films

Heterostructures of transition-metal oxides emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

cond-mat.str-el↗

arXiv2013

The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model

Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the $Z_2$ topological invariant and are protected by time-reversal symmetry. The Kane-Mele model is one model to realize this topological class in two dimensions, also called the quantum spin Hall state. In this review, we provide a pedagogical introduction to the influence of correlation effects in the quantum spin Hall states, with special focus on the half-filled Kane-Mele-Hubbard model, solved by means of unbiased determinant quantum Monte Carlo (QMC) simulations. We explain the idea of identifying the topological insulator via $π$-flux insertion, the $Z_2$ invariant and the associated behavior of the zero-frequency Green's function, as well as the spin Chern number in parameter-driven topological phase transitions. The examples considered are two descendants of the Kane-Mele-Hubbard model, the generalized and dimerized Kane-Mele-Hubbard model. From the $Z_2$ index, spin Chern numbers and the Green's function behavior, one can observe that correlation effects induce shifts of the topological phase boundaries. Although the implementation of these topological quantities has been successfully employed in QMC simulations to describe the topological phase transition, we also point out their limitations as well as suggest possible future directions in using numerical methods to characterize topological properties of strongly correlated condensed matter systems.

cond-mat.str-el↗

arXiv2013

Quantum magnetic properties of the SU(2N) Hubbard model in the square lattice: a quantum Monte Carlo study

We employ the determinant projector quantum Monte-Carlo method to investigate the ground state magnetic properties in the Mott insulating states of the half-filled SU(4) and SU(6) Fermi-Hubbard model in the 2D square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the SU(4) case with a small residual Neel moment. Quantum fluctuations are even stronger in the SU(6) case. Numeric results are consistent with either a vanishing or even weaker Neel ordering than that of SU(4).

cond-mat.str-el↗

arXiv2013

Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector Quantum Monte Carlo (QMC) method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction-dependence of the Z2 topological insulator/trivial insulator phase boundary by calculating the Z2 invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum °uctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.

cond-mat.str-el↗

arXiv2012

Vortex Lattices in the Superconducting Phases of Doped Topological Insulators and Heterostructures

Majorana fermions are predicted to play a crucial role in condensed matter realizations of topological quantum computation. These heretofore undiscovered quasiparticles have been predicted to exist at the cores of vortex excitations in topological superconductors and in heterostructures of superconductors and materials with strong spin-orbit coupling. In this work we examine topological insulators with bulk s-wave superconductivity in the presence of a vortex-lattice generated by a perpendicular magnetic field. Using self-consistent Bogoliubov-de Gennes, calculations we confirm that beyond the semi-classical, weak-pairing limit that the Majorana vortex states appear as the chemical potential is tuned from either side of the band edge so long as the density of states is sufficient for superconductivity to form. Further, we demonstrate that the previously predicted vortex phase transition survives beyond the semi-classical limit. At chemical potential values smaller than the critical chemical potential, the vortex lattice modes hybridize within the top and bottom surfaces giving rise to a dispersive low-energy mid-gap band. As the chemical potential is increased, the Majorana states become more localized within a single surface but spread into the bulk toward the opposite surface. Eventually, when the chemical potential is sufficiently high in the bulk bands, the Majorana modes can tunnel between surfaces and eventually a critical point is reached at which modes on opposite surfaces can freely tunnel and annihilate leading to the topological phase transition previously studied in the work of Hosur et al.

cond-mat.mes-hall↗

arXiv2012

Anisotropic vortex lattice structures in the FeSe superconductor

In the recent work by Song et al. [Science 332, 1410 (2011)], the scanning tunneling spectroscopy experiment in the stoichiometric FeSe reveals evidence for nodal superconductivity and strong anisotropy. The nodal structure can be explained with the extended s-wave pairing structure with the mixture of the $s_{x^2+y^2}$ and $s_{x^2y^2}$ pairing symmetries. We calculate the anisotropic vortex structure by using the self-consistent Bogoliubov-de Gennes mean-field theory. In considering the absence of magnetic ordering in the FeSe at the ambient pressure, orbital ordering is introduced, which breaks the $C_4$ lattice symmetry down to $C_2$, to explain the anisotropy in the vortex tunneling spectra.

cond-mat.supr-con↗