arXiv subjects

Tai Kai Ng

Publications and source records attributed to Tai Kai Ng.

18 recordsLinked to original sources

arXiv2025

Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions

We study the interplay between quantum geometry, interactions, and external fields in complex band systems. When Wannier obstructions preclude a description based solely on atomic-like orbitals, this complicates the prediction of electromagnetic responses particularly in the presence of disorder and interactions. In this work, we introduce a generalized Peierls substitution framework based on Lagrange multipliers to enforce the constraints of the Wannier obstruction in the band of interest. Thus we obtain effective descriptions of interactions and disorder in the presence of non-trivial quantum geometry of that band. We apply our approach to examples including the diamagnetic response in flat-band superconductors and delocalization effects in flat-band metals caused by interactions and disorder.

cond-mat.str-el↗

arXiv2025

A Replica Stoner Theory for Dirty Ferromagnets

This paper investigates the effect of disorder on a ferromagnetic metal with repulsive interactions. We assume that, in the clean limit, the ferromagnetic state can be described by Stoner mean-field theory and study how disorder affects the the system by using a combined replica + Stoner mean-field approach. At zero temperature, we find that a replica-symmetric ferromagnetic mean-field solution exists in the presence of disorder with a modified Stoner criteria where the ferromagnetism is enhanced by disorder. At finite temperature, a Landau theory is employed to construct the phase diagram, revealing that beyond a critical disorder strength, a spin-glass phase may exist between the high-temperature paramagnetic phase and the low-temperature ferromagnetic phase. For weak (repulsive) interaction where the system is non-ferromagnetic in the clean limit, the possibility of a disordered-induced ferromagnetic ground state is observed both at zero temperature and finite temperature. The potential applicability of this framework to realistic materials is briefly discussed.

cond-mat.dis-nn↗

arXiv2025

A Replica-BCS theory for dirty superconductors

In this paper, we revisit the problem of dirty superconductors using a replica-symmetric BCS (RS-BCS) theory. We apply the RS-BCS theory to dirty superconductor grains of size $L^d$, where $L$ is the localization length and $d$ is the dimension of the system, assuming that the macroscopic system is composed of weakly coupled grains. Besides disordered potential, We also consider the case where regions with opposite signs of interaction exist in the grains, with net attractive interaction between electrons. Within the RS-BCS mean field theory, the system phase diagram, single-particle tunneling density of states and the superfluid density are computed within the RS-BCS theory for different strengths of disorder, We show that our result agrees qualitatively with previous numerical studies in the case with pure attractive interaction, and that a Cooper-pair-glass state may exist when regions with opposite sign of interaction exists and the net interaction between electrons is close to zero. The plausible relevance of our result to the anomalous metal state is discussed.

cond-mat.supr-con↗

arXiv2024

Intrinsic Instabilities in Fermi Glasses

We study in this paper the effect of weak, short-ranged interaction on disordered metals. Through analysing the interaction matrix elements between different eigenstates of the non-interacting and corresponding Hartree-Fock single-particle Hamiltonian, we argue that as a result of localized single-particle eigenstates around the Fermi surface, the quasi-particle states on the Fermi surface are unstable towards formation of magnetic moments for arbitrary weak (but finite) repulsive interaction in the thermodynamic limit. This is a mechanism very different from the case of strong interaction $U\sim W_B$ ($W_B=$ bandwidth) or the quantum Griffiths effect where local moments are formed at small localized regions where coupling to the surrounding is weak. Numerical simulations are performed to verify our analysis. We further propose within a Landau Fermi-liquid-type framework that our result is applicable for general electronic systems with weak, short-ranged interaction as long as the quasi-particle states exist and are localized. An analogous result is obtained for attractive interaction, suggesting that Fermi glass state is intrinsically unstable in arbitrary dimension.

cond-mat.dis-nn↗

arXiv2023

Proximity effect and Anomalous metal state in a model of mixed metal-superconductor grains

Motivated by the discovery of the anomalous metal state in thin film systems and suggestions that coexistence of superconducting and metallic components is crucial to the formation of the state, we study in this paper a model of mixed metallic and superconducting grains coupled by electron tunneling - the metallic grains are expected to become superconducting because of proximity effect in a mean-field treatment of the model. When quantum fluctuations in relative phases between different grains are taken into account, we show that the proximity effect can be destroyed and the metallic and superconducting grains become "insulating" with respect to each other when the charging energy between grains are strong enough and tunneling between grains are weak enough, in analogy to superconductor-insulator transition in pure superconducting grains or metal-insulator transition in pure metallic grains. Based on this observation, a physical picture of how the anomalous metal state may form is proposed. An experimental setup to test our proposed physical picture is suggested.

cond-mat.supr-con↗

arXiv2021

Emerging ergodic behavior within many-body localized states

We report in this paper our numerical analysis of energy level spacing statistics for the one-dimensional spin-$1/2$ XXZ model in random on-site longitudinal magnetic fields $B_i$ ($-h\leq B_i\leq h$)). We concentrate on the strong disorder limit $J_{\perp}<<J_z,h)$ where $J_z$ and $J_{\perp}$ are the (nearest neighbor) spin interaction strength in $z$- and planar ($xy$)- directions, respectively. The system is expected to be in a many-body localized (MBL) state in this parameter regime. By analyzing the energy-level spacing statistics as a function of strength of random magnetic field $h$, energy of the many-body state $E$, the number of spin-$\uparrow$ particles in the system $M=\sum_i(s_i^z+{1\over2})$ and the spin interaction strengths $J_z$ and $J_{\perp}$, we show that there exists a small parameter region $J_z\sim h$ where ergodic behaviour emerges at the middle of the many-body energy spectrum when $M\sim{N\over2}$ ($N=$ length of spin chain). The emerging ergodic phase shows qualitatively different behaviour compared with the usual ergodic phase that exists in the weak-disorder limit.

cond-mat.dis-nn↗

arXiv2019

Interaction induced edge states in HgTe/CdTe Quantum Well under magnetic field

In this paper, we study doped HgTe/CdTe quantum well with Hubbard-type interaction under perpendicular magnetic field using a lattice Bernevig-Hughes-Zhang (BHZ) model with a bulk inversion asymmetry (BIA) term. We show that the BIA term is strongly enhanced by interaction around the region when the band inversion of the topological insulator is destroyed by a magnetic field. The enhanced BIA term creates edge-like electronic states which can explain the experimentally discovered edge conductance in doped HgTe/CdTe quantum well at similar magnetic field regime.

cond-mat.str-el↗

arXiv2018

Luttinger theorem and low energy properties of ideal Haldane-Sutherland Liquids

We study in this paper the properties of a many body system of fermions obeying exclusion-statistics (Haldane liquid) where the origin of exclusion statistics is coming from an interaction-induced displacement field $\mathbf{a}_{\mathbf{k}}$ introduced by Sutherland (Haldane-Sutherland liquid). In particular we show how the Luttinger Theorem becomes compatible with exclusion statistics as a result of momentum conservation and adiabaticity. As a result, the low energy properties of Haldane-Sutherland liquids are Fermi/Luttinger liquid-like.

cond-mat.str-el↗

arXiv2017

An exactly solvable BCS-Hubbard Model in arbitrary dimensions

We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard interaction $U$. We show that the model becomes exactly solvable for arbitrary $U$ when the BCS pairing amplitude $Δ$ equals the hopping amplitude $t$. The nature of the solution is described in detail in this paper. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for $S=1/2$ quantum spins and can be viewed as a generalization of Kitaev's construction to $S=1/2$ interacting lattice fermions. The BCS-Hubbard model discussed in this paper is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

cond-mat.str-el↗

arXiv2017

Magnetic properties of 2D topological insulators

The effects of Hubbard-type on-site interactions on the BHZ model is studied in this paper for model parameters appropriate for the HgTe/CdTe quantum well. Within a simple mean field theory we search for plausible magnetic instabilities in the model and find that the ground state becomes {\em ferromagnetic} when the interaction strength between electrons in hole orbital is strong enough. The result can be understood by an approximate mapping of the Hubbard-BHZ model to the one band Hubbard model. The same mapping suggests that the magnetic and/or other ordered phases are more likely to occur in large gap topological insulators whose occupations are close to 1/2 for both electron and hole orbital.

cond-mat.str-el↗

arXiv2016

Superfluid Density of a Spin-orbit Coupled Bose Gas

We discuss the superfluid properties of a Bose-Einstein condensed gas with spin-orbit coupling, recently realized in experiments. We find a finite normal fluid density $ρ_n$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the gapped branch of the elementary excitations and discuss its contributions to various sum rules. Finally, we prove that an independent definition of superfluid density $ρ_s$, using the phase twist method, satisfies the equality $ρ_n+ρ_s=ρ$, the total density, despite the breaking of Galilean invariance.

cond-mat.quant-gas↗

arXiv2016

Anderson Impurity in the Bulk of 3D Topological Insulators: II. The Strong Coupling Regime

Electron scattering off an Anderson impurity immersed in the bulk of a 3D topological insulator is studied in the strong coupling regime, where the temperature $T$ is lower than the Kondo temperature $T_K$. The system displays either a self-screened Kondo effect, or a Kondo effect with SO(3) or SO(4) dynamical symmetries. Low temperature Kondo scattering for systems with SO(3) symmetry displays the behavior of a singular Fermi liquid, an elusive property that so far has been observed only in tunneling experiments. This is demonstrated through the singular behavior as $T \to 0$ of the specific heat, magnetic susceptibility and impurity resistivity, that are calculated using well known (slightly adapted) conformal field theory techniques. Quite generally, the low temperature dependence of some of these observables displays a remarkable distinction between the SO(n=3,4) Kondo effect, compared with the standard SU(2) one.

cond-mat.str-el↗

arXiv2015

Spontaneous modulation of superconducting phase in Kitaev ladder

We study theoretically the two Kitaev chains put in parallel, i.e., Kitaev ladder, coupled by Josephson junction. The $π$-junction between the Majorana bound states at the ends of the chains competes with the usual Josephson coupling along the chain, and this frustration leads to the modulation of the phase difference of the superconducting order parameter between the two chains. We show that this modulation gives the double degeneracy of the ground states, which can be manipulated by external electric and magnetic fields.

cond-mat.supr-con↗

arXiv2014

Renormalization Group Approach to Anderson Impurity in the Bulk of Topological Insulators

It has been recently suggested that when an Anderson impurity is immersed in the bulk of a topological insulator, a Kondo resonant peak will appear simultaneously with an in-gap bound-state when the band-dispersion has an "inverted-Mexican-hat" form. The mid-gap bound-state generates another spin state and the Kondo effect is thereby screened. In this paper we study this problem within a weak-coupling RG scheme where we show that the system exhibits complex crossover behavior between different symmetry configurations and may evolve into a self-screened-Kondo or SO(3) low energy fix point. Experimental consequences of this scenario are pointed out.

cond-mat.str-el↗

arXiv2006

Suppression of superfluid density in the superfluid-supersolid transition

We show that the rather unexpected pressure dependence of superfluid density observed near the superfluid-supersolid transition by Kim {\em et.al.}[M.H.W. Chan, {\em private communication}], can be understood if the transition from superfluid to supersolid state is a second order or weakly first order transition from the superfluid state to a super-CDW state with non-uniform Bose-condensation amplitude. The suppression of superfluid density is a direct consequence of softening of phonon mode at finite wave-vector $|\vec{Q}|\sim Q_0$ around the quantum phase transition.

cond-mat.stat-mech↗

arXiv2000

On the possibility of a metallic phase in granular superconducting films

We investigate the possibility of finding a zero-temperature metallic phase in granular superconducting films. We are able to identify the breakdown of the conventional treatment of these systems as dissipative Bose systems. We do not find a metallic state at zero temperature. At finite temperatures, we find that the system exhibit crossover behaviour which may have implications for the analysis of experimental results. We also investigate the effect of vortex dissipation in these systems.

cond-mat.supr-con↗

arXiv1999

Duality picture between antiferromagnetism and d-wave superconductivity in t-J model at two dimensions

We show in this paper an interesting relation between elementary and topological excitations in the antiferromagnetic and d-wave superconducting phases of the t-J model at two dimenions. The topological spin and charge excitations in one phase have the same dynamics as elementary excitations in the other phase, except the appearance of energy gaps. Moreover, the transition from one phase to another can be described as a quantum disordering transition associated with the topological excitations. Based on the above picture, a plausible phase diagram of t-J model is constructed.

cond-mat.supr-con↗

arXiv1995

Vortices in Schwinger-Boson Mean-Field Theory of Two-Dimensional Quantum Antiferromagnets

In this paper we study the properties of vortices in two dimensional quantum antiferromagnets with spin magnitude S on a square lattice within the framework of Schwinger-boson mean field theory. Based on a continuum description, we show that vortices are stable topological excitations in the disordered state of quantum antiferromagnets. Furthermore, we argue that vortices can be divided into two kinds: the first kind always carries zero angular momentum and are bosons, whereas the second kind carries angular momentum S under favourable conditions and are fermions if S is half-integer. A plausible consequence of our results relating to RVB theories of High-Tc superconductors is pointed out.

cond-mat↗