arXiv subjects

Tai-Kai Ng

Publications and source records attributed to Tai-Kai Ng.

At least 19 recordsLinked to original sources

arXiv2021

Creating Localized Majorana Zero Modes in Quantum Anomalous Hall Insulator/Superconductor Heterostructures with a Scissor

In this work, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing superconductivity on the helical channel through proximity effect will create Majorana zero energy modes (MZMs) at the ends of the cut. In this geometry, there is no need for the proximity gap to overcome the bulk insulating gap of the QAHI to create MZMs as in the two-dimensional QAHI/superconductor (QAHI/SC) heterostructures. Therefore, the topological regime with MZMs is greatly enlarged. Furthermore, due to the presence of a single helical channel, the generation of low energy in-gap bound states caused by multiple conducting channels is avoided such that the MZMs can be well separated from other in-gap excitations in energy. This simple but practical approach allows the creation of a large number of MZMs in devices with complicated geometry such as hexons for measurement-based topological quantum computation. We further demonstrate how braiding of MZMs can be performed by controlling the coupling strength between the counter-propagating electron modes.

cond-mat.mes-hall↗

arXiv2020

Beyond Fermi-Liquid Theory: the $k$-Fermi liquids

We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable $k$-Fermi liquid models with spin-charge separation are discussed as examples.

cond-mat.str-el↗

arXiv2019

Generalized Falicov-Kimball Models

In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles.

cond-mat.str-el↗

arXiv2018

Non-Abelian Chiral Spin Liquid on the Kagome Lattice

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.

cond-mat.str-el↗

arXiv2017

Quantum Spin Liquid States

This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($κ$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories.

cond-mat.str-el↗

arXiv2016

$U(1)$ Fermi liquid theory - A Fermi liquid state that supports exclusion statistics

We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy $ξ_{\mathbf{k}}$, the kinetic momentum $\mathbf{k}$ of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum ($k$)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call $U(1)$-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.

cond-mat.str-el↗

arXiv2015

Equilibrium angular momentum and edge current in Bose-condensed cold atom systems with k-space Berry curvature

In this paper we study the properties of cold bosons in a two-dimensional optical lattice system where Bose-condensation occurs at a momentum point k with non-zero k-space Berry curvature. By combining results from both analytic and numerical approaches, we show that the boson system carries non-universal, temperature dependent equilibrium angular momentum and edge current at low temperatures.

cond-mat.mes-hall↗

arXiv2015

Nonlinear optical conductivity of $U(1)$ spin liquids with large spinon Fermi surfaces

In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law ($\simω^η$) response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3ω$ inside the spin liquids.

cond-mat.str-el↗

arXiv2014

Optical conductivity and surface plasmon modes of U(1) spin liquid states with large spinon Fermi surfaces

In this paper we study the optical properties of $U(1)$ spin liquids with large spinon Fermi surfaces based on a simple formula for the bulk optical conductivity obtained through the Ioffe-Larkin composition rule. We show that the optical conductivity of $U(1)$ spin liquids at energies above the charge gap has a unique feature that distinguishes them from ordinary insulators. In particular we show the existence of a long-life surface plasmon mode propagating along the interface between a linear medium and the spin liquid at frequencies above the charge gap, which can be detected by the widely used Kretschmann-Raether three-layer configuration.

cond-mat.str-el↗

arXiv2014

Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains

In a previous paper [Phys. Rev. B 85,195144 (2012)], variational Monte Carlo method (based on Gutzwiller projected states) was generalized to $S=1$ systems. This method provided very good trial ground states for the gapped phases of $S=1$ bilinear-biquadratic (BLBQ) Heisenberg chain. In the present paper, we extend the approach to study the low-lying elementary excitations in $S=1$ chains. We calculate the one-magnon and two-magnon excitation spectra of the BLBQ Heisenberg chain and the results agree very well with recent data in literature. In our approach, the difference of the excitation spectrum between the Haldane phase and the dimer phase (such as the even/odd size effect) can be understood from their different topology of corresponding mean field theory. We especially study the Takhtajan-Babujian critical point. Despite the fact that the `elementary excitations' are spin-1 magnons which are different from the spin-1/2 spinons in Bethe solution, we show that the excitation spectrum, critical exponent ($η=0.74$) and central charge ($c=1.45$) calculated from our theory agree well with Bethe ansatz solution and conformal field theory predictions.

cond-mat.str-el↗

arXiv2013

Non-Fermi liquid behavior in Bose-Fermi mixtures at two dimensions

In this paper we study the low temperature behaviors of a system of Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram approximation, we show that at nonzero temperatures $T\rightarrow0$ the fermions exhibit non-fermi liquid behavior. We propose that this is a general feature of Bose-Fermi mixtures at two dimensions. An experimental signature of this new state is proposed.

cond-mat.str-el↗

arXiv2013

Spin Liquid States at the vicinity of metal-insulator transition

We study in this paper quantum spin liquid states (QSLs) at the vicinity of metal-insulator transition. Assuming that the low energy excitations in the QSLs are labeled by "spinon" occupation numbers with the same Fermi surface structure as in the corresponding metal (Fermi-liquid) side, we propose a phenomenological Landau-like low energy theory for the QSLs and show that the usual U(1) QSLs is a representative member of this class of spin liquids. Based on our effective low energy theory, an alternative picture to the Brinkman-Rice picture of Mott metal-insulator transition is proposed. The charge, spin and thermal responses of QSLs are discussed under such a phenomenology.

cond-mat.str-el↗

arXiv2013

Quantum impurity in the bulk of topological insulator

We investigate physical properties of an Anderson impurity embedded in the bulk of a topological insulator. The slave-boson mean-field approximation is used to account for the strong electron correlation at the impurity. Different from the results of a quantum impurity on the surface of a topological insulator, we find for the band-inverted case, a Kondo resonant peak and in-gap bound states can be produced simultaneously. However, only one type of them appears for the normal case. It is shown that the mixed-valence regime is much broader in the band-inverted case, while it shrinks to a very narrow regime in the normal case. Furthermore, a self-screening of the Kondo effect may appear when the interaction between the bound-state spin and impurity spin is taken into account.

cond-mat.str-el↗

arXiv2013

Magnetic impurities on the surface of topological superconductor

We consider the effects of magnetic impurities on the surface of superconducting Cu doped $Bi_{2}Se_{3}$ in the odd parity pairing phase which support topologically protected Majorana fermions surface states with linear spectrum. We show that a single magnetic impurity on the surface may induce a pair of in-gap localized bound states. The energy of the in-gap state is extremely sensitive to the orientation of the magnetic impurity due to the so-called Ising properties of Majorana fermions. The magnetic impurity induced spin-texture, which can be measured using spin sensitive STM, is calculated. We also show that the RKKY interactions between magnetic impurities mediated via the Majorana fermions are always ferromagnetic and dense enough magnetic impurities will develop long-range magnetic order and break the time-reversal symmetry on the material surface eventually.

cond-mat.supr-con↗

arXiv2012

Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains

We study in this paper a series of Gutzwiller Projected wavefunctions for S=1 spin chains obtained from a fermionic mean-field theory for general S>1/2 spin systems [Phys. Rev. B 81, 224417] applied to the bilinear-biquadratic (J-K) model. The free-fermion mean field states before the projection are 1D paring states. By comparing the energies and correlation functions of the projected pairing states with those obtained from known results, we show that the optimized Gutzwiller projected wavefunctions are very good trial ground state wavefunctions for the antiferromagnetic bilinear-biquadratic model in the regime K 0). We find that different topological phases of the free-fermion paring states correspond to different spin phases: the weak pairing (topologically non-trivial) state gives rise to the Haldane phase, whereas the strong pairing (topologically trivial) state gives rise to the dimer phase. In particular the mapping between the Haldane phase and Gutwziller wavefunction is exact at the AKLT point K=1/3. The transition point between the two phases determined by the optimized Gutzwiller Projected wavefunction is in good agreement with the known result. The effect of Z2 gauge fluctuations above the mean field theory is analyzed.

cond-mat.str-el↗

arXiv2011

Possibility of a zero-temperature metallic phase in granular two-band superconducting films

A variational approach is used to study the superconductor-insulator transition in two-band granular superconducting films using a resistance-shunted Josephson junction array model in this letter. We show that a zero-temperature metallic phase may exist between the superconducting and insulator phases which is absent in normal single band granular superconducting films. The metallic phase may be observable in some dirty pnictide superconductor films.

cond-mat.supr-con↗

arXiv2011

Impurity scattering in the bulk of topological insulators

We study in this paper time-reversal $δ$-impurity scattering effects in the bulk of topological insulators (TI) in two and three dimensions. Specifically we consider how impurity scattering strength is affected by the bulk band structure of topological insulators. An interesting band inversion effect associated with the change of the system from ordinary to topological insulator is pointed out. Experimental consequences of our findings are discussed.

cond-mat.mtrl-sci↗

arXiv2011

Tunneling between edge states of a 2D topological insulator and a Fermi liquid lead through a quantum dot

In this paper we study a non-equilibrium resonant tunnelling problem where a non-interacting quantum dot is connected to two leads, one being the edge of an interacting 2-D topological insulator (Luttinger liquid) and the other being a usual Fermi liquid. We show that the current passing through the system can be expressed in terms of a non-equilibrium local single-particle Green's function of the Luttinger liquid lead which can be analysed using standard bosonization- Renormalization Group (RG) technique. In particular, some exact results can be extracted in the small bias limit with repulsive electron-electron interaction. A simple formula which captures the qualitative feature of the I-V relation over whole temperature and voltage bias range is being proposed and studied.

cond-mat.mes-hall↗