arXiv subjects

Yu-Li Lee

Publications and source records attributed to Yu-Li Lee.

At least 19 recordsLinked to original sources

arXiv2023

Magnetic impurities in an altermagnetic metal

We study the physics of dilute magnetic impurities in a two-dimensional altermagnetic metal. For the single impurity case, although the spin degeneracy is broken in an altermagnetic metal, we show that the antiferromagnetic Kondo coupling still flows to the strong coupling regime at low energies in terms of the one-loop renormalization-group equation. Moreover, the Kondo temperature may be enhanced or reduced, depending on the band structure and the electron density. To study the ground-state properties, we employ the variational wavefunction approach. We find that the impurity spin is completely screened at long distances, in contrast to the usual antiferromagnet. The $d$-wave nature of the spin-split Fermi surfaces in an altermagnetic metal is reflected in the correlation between the impurity and conduction electron spins, which exhibits the $C_{4z}$ symmetry of the altermagnet at long distances. The spin correlation decays as $1/r^3$ at long distances, and its amplitude oscillates with four different periods due to the interference between the spin splitting Fermi surfaces. Moreover, the values of these periods depend on the direction of observation. Similar phenomena also occur in the RKKY interaction in an AM metal.

cond-mat.str-el↗

arXiv2021

Correlated second-order Dirac semimetals with Coulomb interactions

We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation symmetry is broken even in the continuum limit, and thus the low-energy physics is controlled by two dimensionless parameters: the dimensionless coupling constant and the ratio of the anisotropy parameters. We show that the former flows to zero and the latter flows to a fixed value at low energies. Thus, one may calculate physical quantities in terms of the renormalized perturbation theory. As an application, we determine the temperature dependence of the specific heat by solving the renormalization-group equations. Following from the breaking of the full rotation symmetry, there exists a crossover temperature scale $T_c$ (and a length scale $L_c$). Physical quantities approach the values for the first-order Dirac semimetal only when the temperature is much smaller than $T_c$. Similarly, the screened Coulomb potential will become anisotropic when the distance is smaller than $L_c$, while the unscreened form is recovered at its tail.

cond-mat.mes-hall↗

arXiv2020

Magnetic impurity in a triple-component semimetal

We investigate the effects of a magnetic impurity in a multiband touching fermion system, specifically, a triple-component semimetal with a flat band, which can be realized in a family of transition metal silicides (CoSi family). When the chemical potential coincides with the flat band, it is expected that the impurity response of this system will be very different from that of an ordinary Dirac or Weyl semimetal of which the density of states at the Fermi level vanishes. We first determine the phase diagram within the mean-field approximation. Then, we study the local moment regime by employing two different methods. In the low temperature regime, the Kondo screening is analyzed by the variational wavefunction approach and the impurity contributions to the magnetic susceptibility and heat capacity are obtained, while at higher temperature, we use the equation of motion approach to calculate the occupation number of the impurity site and the impurity magnetic susceptibility. The results are compared and contrasted with those in the usual Fermi liquid and the Dirac/Weyl semimetals.

cond-mat.str-el↗

arXiv2019

The phase diagram of a two-dimensional dirty tilted Dirac semimetal

We investigate the effects of quenched disorder on a non-interacting tilted Dirac semimetal in two dimensions. Depending on the magnitude of the tilting parameter, the system can have either Fermi points (type-I) or Fermi lines (type-II). In general, there are three different types of disorders for Dirac fermions in two dimensions, namely, the random scalar potential, the random vector potentials along and perpendicular to the tilting direction, and the random mass. We study the effects of weak disorder in terms of the renormalization group, which is performed by integrating out the modes with large energies, instead of large momenta. Since the parametrization of the low-energy degrees of freedom depends on the structure of the Fermi surface, the resulting one-loop renormalization-group equations depend on the type of tilted Dirac fermions. Whenever the disorder is a marginal perturbation, we examine its role on low-energy physics by a mean-field approximation of the replica field theory or the first-order Born approximation. Based on our analysis, we suggest the phase diagrams of a two-dimensional tilted Dirac fermion in the presence of different types of disorder.

cond-mat.dis-nn↗

arXiv2017

On the renormalization of Coulomb interactions in two-dimensional tilted Dirac fermions

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar\cite{Shankar}, by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

cond-mat.str-el↗

arXiv2017

On the nature of the magnetic phase transition in a Weyl semimetal

We investigate the nature of the magnetic phase transition induced by the short-ranged electron-electron interactions in a Weyl semimetal by using the perturbative renormalization-group method. We find that the critical point associated with the quantum phase transition is characterized by a Gaussian fixed point perturbed by a dangerously irrelevant operator. Although the low-energy and long-distance physics is governed by a free theory, the velocities of the fermionic quasiparticles and the magnetic excitations suffer from nontrivial renormalization effects. In particular, their ratio approaches one, which indicates an emergent Lorentz symmetry at low energies. We further investigate the stability of the fixed point in the presence of weak disorder. We show that while the fixed point is generally stable against weak disorder, among those disorders that are consistent with the emergent chiral symmetry of the clean system, a moderately strong random chemical potential and/or random vector potential may induce a quantum phase transition towards a disorder-dominated phase. We propose a global phase diagram of the Weyl semimetal in the presence of both electron-electron interactions and disorder based on our results.

cond-mat.str-el↗

arXiv2016

Interplay between Coulomb blockade and Josephson effect in a topological superconductor-quantum dot device

We study the behavior of a topological Josephson junction in which two topological superconductors are coupled through a quantum dot. We focus on the case with the bulk superconducting gap being the largest energy scale. Two parameter regimes are investigated: a weak tunneling between the dot and the superconductors, with the dot near its charge degeneracy point, and a strong tunneling regime in which the transmission between the dot and the superconductors is nearly perfect. We show that in the former situation, the Andreev spectrum for each sector with fixed fermion parity consists of only two levels, which gives rise to the nontrivial current-phase relation. Moreover, we study the Rabi oscillation between the two levels and indicates that the corresponding frequency is a $4π$-periodic function of the phase difference between the two superconductors, which is immune to the quasiparticle poisoning. In the latter case, we find that the Coulomb charging energy enhances the effect of backscattering at the interfaces between the dot and the superconductors. Both the temperature and the gate-voltage dependence of the critical Josephson current are examined.

cond-mat.supr-con↗

arXiv2015

Electrical control and interaction effects of the RKKY interaction in helical liquids

We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms but also the nematic-type term that is not present originally, with the range functions depending on the strength of the Rashba coupling. We also show that the electron-electron interaction changes the strength of the RKKY interaction by modifying the power of the $1/|x|$ dependence of the range functions. In particular, by varying the strength of the interaction or the Rashba coupling, there is an (impurity) quantum phase transition involving the sign change of the RKKY interaction at the value of the Luttinger liquid parameter $K=1/2$. Since both the strength of the Rashba coupling and the chemical potential of the helical edge states are electrically controllable by external gate voltages, our results not only shed light on the nature of magnetic impurity correlations in the edge of a two-dimensional topological insulator, but also pave a way to manipulate the qubits in quantum computing.

cond-mat.mes-hall↗

arXiv2014

Electrical transport through a quantum dot side-coupled to a topological superconductor

We propose to measure the differential conductance $G$ as a function of the bias $V$ for a quantum dot side-coupled to a topological superconductor to detect the existence of the chiral Majorana edge states. It turns out that $G$ for the spinless dot is an oscillatory (but not periodic) function of $eV$ due to the coupling to the chiral Majorana edge states, where $-e$ is the charge carried by the electron. The behavior of $G$ versus $eV$ is distinguished from the one for a multi-level dot in three respects. First of all, due to the coupling to the topological superconductor, the value of $G$ will shift upon adding or removing a vortex in the topological superconductor. Next, for an off-resonance dot, the conductance peak in the present case takes a universal value $e^2/(2h)$ when the two leads are symmetrically coupled to the dot. Finally, for a symmetric setup and an on-resonance dot, the conductance peak will approach the same universal value $e^2/(2h)$ at large bias.

cond-mat.mes-hall↗

arXiv2014

Tunneling between a topological superconductor and a Luttinger liquid

We study the quantum point contact between the topological superconductor and the helical Luttinger liquid. The effects of the electron-electron interactions in the helical Luttinger liquid on the low-energy physics of this system are analyzed by the renormalization group. Among the various couplings at the point contact which arise from the tunneling via the Majorana edge channel, the induced backscattering in the helical Luttinger liquid is the most relevant for repulsive interactions. Hence, at low temperatures, the helical Luttinger liquid is effectively cut into two separated half wires. As a result, the low-temperature physics is described by a fixed point consisting of two leads coupled to the topological superconductor, and the electrical transport properties through the point contact at low temperature and low bias are dominated by the tunneling via the Majorana edge channel. We compute the temperature dependence of the zero-bias tunneling conductance and study the full counting statistics for the tunneling current at zero temperature.

cond-mat.str-el↗

arXiv2013

Nonequilibrium noise correlations in a point contact of helical edge states

We investigate theoretically the nonequilibrium finite-frequency current noise in a four-terminal quantum point contact of interacting helical edge states at a finite bias voltage. Special focus is put on the effects of the single-particle and two-particle scattering between the two helical edge states on the fractional charge quasiparticle excitations shown in the nonequilibrium current noise spectra. Via the Keldysh perturbative approach, we find that the effects of the single-particle and the two-particle scattering processes on the current noise depend sensitively on the Luttinger liquid parameter. Moreover, the Fano factors for the auto- and cross correlations of the currents in the terminals are distinct from the ones for tunneling between the chiral edge states in the quantum Hall liquid. The current noise spectra in the single-particle-scattering-dominated and the two-particle-scattering-dominated regime are shown. Experimental implications of our results on the transport through the helical edges in two-dimensional topological insulators are discussed.

cond-mat.str-el↗

arXiv2013

Electrically tunable two-channel Kondo fixed points in helical liquids

We study a quantum dot coupled to two edge states of a quantum spin Hall insulator through electron tunnelings in the presence of a Rashba spin-orbital interaction induced by an external electric field. We show that if the electron interactions on the edge states are repulsive, there are two possible phases, depending on the Luttinger liquid parameter $K$. For $1/2<K<1$, the low-temperature physics is controlled by a previously identified two-channel Kondo fixed point. For the edge states with even stronger repulsive interactions, i.e. $1/4<K<1/2$, the system reaches another phase at low temperatures, described by a new two-channel Kondo fixed point. This phase is separated from the original one by a continuous phase transition upon varying the value of $K$ through the external electric field. The corresponding critical point is described by a free Dirac fermion backscattered by a local potential. We investigate the low-temperature properties associated with this new fixed point and also discuss the scaling behaviors of the system at the critical point.

cond-mat.str-el↗

arXiv2011

The stability of the low-dimensional mixtures of dilute quantum gases

We study the stability of the dilute Bose-Fermi and Bose-Bose mixtures with repulsive interactions in one and two dimensions in terms of the renormalization group. For the Bose-Fermi mixture, we show that the uniform mixture is stable against de-mixing in the dilute limit. For the Bose-Bose mixture, we give the stability conditions in the dilute limit. As a byproduct, we also calculate the critical temperature for the superfluid phase of the two-dimensional Bose-Fermi mixture in the extremely dilute limit.

cond-mat.quant-gas↗

arXiv2010

The Universality and stability for a dilute Bose gas with a Feshbach resonance

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero density fixed point. Moreover, we find that the T=0 thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.

cond-mat.quant-gas↗

arXiv2007

Low-energy Effective Theory for One-dimensional Lattice Bosons near Integer Filling

A low-energy effective theory for interacting bosons on a one-dimensional lattice at and near integer fillings is proposed. It is found that two sets of bosonic phase fields are necessary in order to explain the complete phase diagram. Using the present effective theory, the nature of the quantum phase transitions among various phases can be identified. Moreover, the general condition for the appearance of the recently proposed Pfaffian-like state can be realized from our effective action.

cond-mat.supr-con↗

arXiv2007

Low-energy properties of the ferromagnetic metallic phase in manganites: Slave fermion approach to the quantum double exchange model

We study the low energy properties of the one-orbital quantum double-exchange model by using the slave fermion formulation. We construct a mean-field theory which gives a simple explanation for the magnetic and thermodynamic properties of the ferromagnetic metallic phase in manganites at low energy. The resulting electron spectral function and tunneling density of states show an incoherent asymmetric peak with weak temperature dependence, in addition to a quasiparticle peak. We also show that the gauge fluctuations in the ferromagnetic metallic phase are completely screened due to the Anderson-Higgs mechanism. Therefore, the mean-field state is robust against gauge fluctuations and exhibits spin-charge separation at low energy.

cond-mat.str-el↗

arXiv2005

Quantum phases of a Feshbach-resonant atomic Bose gas in one dimension

We study an atomic Bose gas with an s-wave Feshbach resonance in a one-dimensional optical lattice, with the densities of atoms and molecules incommensurate with the lattice. At zero temperature, most of the parameter region is occupied by a phase in which the superfluid fluctuations of atoms and molecules are the predominant ones, due to the phase fluctuations of atoms and molecules being locked by a Josephson coupling between them. When the density difference between atoms and molecules is commensurate with the lattice, two additional phases may exist: the two component Luttinger liquid where both the atomic and molecular sectors are gapless, and the inter-channel charge density wave where the relative density fluctuations between atoms and molecules are frozen at low energy.

cond-mat.supr-con↗

arXiv2004

Quantum phase transition in an atomic Bose gas near a Feshbach resonance

We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.

cond-mat.stat-mech↗