arXiv subjects

Han-Yong Choi

Publications and source records attributed to Han-Yong Choi.

At least 19 recordsLinked to original sources

arXiv2024

Collective mode across the BCS-BEC crossover in Holstein model

We investigate the emergence of the collective mode in the phonon spectra of the superconducting state within the Holstein model by varying the electron-phonon coupling. Using dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG) technique, we calculate the phonon spectra. In the superconducting state with a pairing gap ($Δ_P$), the peak position of the collective mode ($ω_{col}$) evolves from the Bardeen-Cooper-Schrieffer (BCS) regime, manifesting near $2Δ_P$ and increasing with coupling, to the Bose-Einstein condensation (BEC) regime, where $ω_{col}$ decreases with increasing coupling. The decrease of $ω_{col}$ matches well with the reduction of superfluid stiffness, which originates from the increasing phase fluctuations of local pairs with coupling strength. In the crossover regime with intermediate coupling, $ω_{col}$ aligns with the soft phonon mode ($ω_s$) of the normal state and decreases with increasing coupling when $ω_s < 2Δ_P$. Additionally, comparing the collective mode weight to $Δ_P$ suggests that the collective mode predominantly stems from U(1) gauge symmetry breaking across all coupling strengths.

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arXiv2024

Non-Fermi liquid over extended range at zero temperature without quantum criticality

A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.

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arXiv2023

ARPES Detection of Superconducting Gap Sign in Unconventional Superconductors

Superconductivity is realized by opening a gap in the superconducting state. The gap symmetry is crucial in understanding the underlying superconductivity mechanism. The magnitude and the phase are essential in fully characterizing the superconducting gap. Angle-resolved photoemission spectroscopy (ARPES) has played a key role in determining the gap symmetry in unconventional superconductors. However, it has been considered so far that ARPES can only measure the magnitude of the superconducting gap but not its phase; the phase has to be detected by other phase-sensitive techniques. Here we propose a new method to directly detect the superconducting gap sign by using ARPES. This method is successfully validated in a cuprate superconductor with a well-known $d$-wave gap symmetry. When two bands are nearby in momentum space and have a strong interband interaction, the resulted electronic structures in the superconducting state are sensitive to the relative gap sign between the two bands which can be captured by ARPES measurements. Our present work provides a new way to detect the gap sign and can be applied to various superconductors, particularly those with multiple orbitals like the iron-based superconductors. It also makes ARPES more powerful to determine both the gap magnitude and the phase that are significant in understanding the superconductivity mechanism of unconventional superconductors.

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arXiv2022

Ubiquitous Coexisting Electron-Mode Couplings in High Temperature Cuprate Superconductors

In conventional superconductors, the electron-phonon coupling plays a dominant role in pairing the electrons and generating superconductivity. In high temperature cuprate superconductors, the existence of the electron coupling with phonons and other boson modes and its role in producing high temperature superconductivity remain unclear. The evidence of the electron-boson coupling mainly comes from the angle-resolved photoemission (ARPES) observations of the ~70meV nodal dispersion kink and the ~40meV antinodal kink. However, the reported results are sporadic and the nature of the involved bosons are still under debate. Here we report new findings of ubiquitous two coexisting electron-mode couplings in cuprate superconductors. By taking ultra-high resolution laser-based ARPES measurements, combined with the improved second derivative analysis method, we discovered that the electrons are coupled simultaneously with two sharp phonon modes with energies of ~70meV and ~40meV in different superconductors with different doping levels, over the entire momentum space and at different temperatures above and below the superconducting transition temperature. The observed electron-phonon couplings are unusual because the associated energy scales do not exhibit an obvious change across the superconducting transition. We further find that the well-known "peak-dip-hump" structure, which has long been considered as a hallmark of superconductivity, is also omnipresent and consists of finer structures that originates from electron coupling with two sharp phonon modes. These comprehensive results provide a unified picture to reconcile all the reported observations and pinpoint the origin of the electron-mode couplings in cuprate superconductors. They provide key information to understand the role of the electron-phonon coupling in generating high temperature superconductivity.

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arXiv2021

The maximal superconductivity in proximity to charge density wave quantum critical point in Cu$_x$TiSe$_2$

Superconductivity emerges in $1T$-TiSe$_2$ when its charge density wave (CDW) order is suppressed by Cu intercalation or pressure. Since the CDW state is thought to be an excitonic insulator, an interesting question is whether the superconductivity is also mediated by the excitonic fluctuations. We investigated this question as to the nature of doping induced superconductivity in Cu$_x$TiSe$_2$ by asking if it is consistent with the phonon-mediated pairing. We employed the {\it ab initio} density functional theory and density functional perturbation theory to compute the electron-phonon coupling Eliashberg function from which to calculate the superconducting (SC) critical temperature $T_c$. The calculated $T_c $ as a function of the doping concentration $x$ exhibits a dome shape with the maximum $T_c$ of $2-6$ K at $x \approx 0.05$ for the Coulomb pseudopotential $0 \leq μ^* \leq 0.1$. The maximal $T_c$ was found to be pinned to the quantum critical point at which the CDW is completely suppressed and the corresponding phonon mode becomes soft. Underlying physics is that the reduced phonon frequency enhances the electron-phonon coupling constant $λ$ which overcompensates the frequency decrease to produce a net increase of $T_c$. The doping induced superconductivity in Cu$_x$TiSe$_2$ seems to be consistent with the phonon-mediated pairing. Comparative discussion was made with the pressure induced superconductivity in TiSe$_2$.

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arXiv2021

Excitonic insulator emerging from semiconducting normal state in $1T$-TiSe$_{2}$

A new state of matter, an excitonic insulator (EI) state, was predicted to emerge from Bose-Einstein condensation of electron-hole pairs. Some candidate materials were suggested but it has been elusive to confirm its existence. Recent works gave renewed support for the EI picture of the charge density wave (CDW) state below the critical temperature $T_c \approx 200 $ K of $1T$-TiSe$_{2}$. Yet, an important link to its establishment is to show that a majority fraction of the measured $T_c$ indeed follows from the Coulomb interaction alone, while a quantitative match of the $T_c$ may require assistance from the electron-lattice coupling. This will establish that the CDW is formed predominantly by the Coulomb interaction and help confirm the EI view for TiSe$_2$. Here, we provide such calculations by solving the exciton gap equation with material specific electronic structures. We obtain, with no fitting parameters, $T_c \approx 135 \pm 27$ K for the normal state gap of $E_g \approx 74 \pm 15$ meV. It seems that the calculated $T_c$ from Coulomb interaction gives a majority fraction of experimental $T_c$ for recently determined values of $E_g$. The measured doping dependence of $T_c$ was satisfactorily reproduced as well. Also in agreement with experiments are the same set of calculations of the photoemission spectroscopy and density of states. The semiconducting state above and EI below $T_c$ together should give a coherent picture of $1T$-TiSe$_2$.

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arXiv2018

Dynamical effects on superconductivity in BCS-BEC crossover

We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half-filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique. The dynamical effects induce distinct features such as absenceof the dispersion back-bending of Bogoliubov quasi-particles, non-monotonous coupling dependence of the pairing gap, and the soft phonon spectrum due to the Goldstone mode of local pair phase fluctuations. Also interesting is the maximum critical temperature being at the normal state phase boundary. Some of these features have intriguing similarities with the recent observations in the FeSe$_{1-x}$S$_x$ and Fe$_{1+y}$Se$_x$Te$_{1-x}$ iron-chalcogenides in the BCS-BEC crossover.

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arXiv2017

How to pin down the pairing interaction for high Tc superconductivity in cuprates

The normal and pairing self-energies are the microscopic quantities which reflect and characterize the underlying interaction in superconductors. The momentum and frequency dependence of the self-energies, therefore, provides the experimental criteria which can single out the long sought-after pairing interaction among many proposed ideas. This line of research to pin down the pairing interaction for the cuprate superconductors has been carried out with some success by analyzing the momentum distribution curves of laser angle-resolved photo-emission spectroscopy (ARPES) data. Some progress and results are presented and compared with theoretical calculations based on leading proposals. Comments are made on the proposed scenarios from the comparisons.

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arXiv2016

Quantitative Determination of the Pairing Interactions for High Temperature Superconductivity in Cuprates

A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated strange metal state. Here we report the quantitative determination of the normal and pairing self-energies, made possible by laser-based angle-resolved photoemission measurements with unprecedented accuracy and stability. Through a precise inversion procedure, both the effective interactions in the attractive d-wave symmetry and the repulsive part in the full symmetry are determined. The latter are nearly angle independent. Near Tc both interactions are nearly independent of frequency, and have almost the same magnitude, over the complete energy range of up to about 0.4 eV except for a low energy feature around 50 meV present only in the repulsive part which has less than 10% of the total spectral weight. Well below Tc, they both change similarly by superconductivity induced features at low energies. Besides finding the pairing self-energy and the attractive interactions for the first time, these results expose a central paradox of the high Tc problem: how the same frequency independent fluctuations can dominantly scatter at angles +-pi/2 in the attractive channel as well as lead to angle-independent repulsive scattering. The experimental results are compared with the available theoretical calculations based on antiferromagnetic fluctuations, Hubbard model and the quantum-critical fluctuations of loop-current order.

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arXiv2014

Sharp low energy feature in single-particle spectra due to forward scattering in $d$-wave cuprate superconductors

There is an enormous interest in renormalization of quasi-particle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature $T_c$ because it enables determination of the fluctuation spectrum to which the qps are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to $T_c$ and its intensity increasing sharply below $T_c$. This unexpected feature needs to be reconciled with $d$-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below $T_c$ and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.

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arXiv2013

Angle and frequency dependence of self-energy from spin fluctuations mediated d-wave pairing for high temperature superconductors

We investigated the characteristics of the spin fluctuations mediated superconductivity employing the Eliashberg formalism. The effective interaction between electrons was modeled in terms of the spin susceptibility measured by the inelastic neutron scattering experiments on single crystal La2-xSrxCuO4 superconductors. The diagonal self-energy and off-diagonal self-energy were calculated by solving the coupled Eliashberg equation self-consistently for chosen spin susceptibility and tight-binding dispersion of electrons. The full momentum and frequency dependence of the self-energy is presented for the optimal, overdoped, and underdoped LSCO cuprates in superconductive state. These results may be compared with the experimentally deduced self-energy from ARPES experiments.

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arXiv2012

Comments on the d-wave pairing mechanism for cuprate high $T_c$ superconductors: Higher is different?

The question of pairing glue for the cuprate superconductors (SC)is revisited and its determination through the angle resolved photo-emission spectroscopy (ARPES) is discussed in detail. There are two schools of thoughts about the pairing glue question: One argues that superconductivity in the cuprates emerges out of doping the spin singlet resonating valence bond (RVB) state. Since singlet pairs are already formed in the RVB state there is no need for additional boson glue to pair the electrons. The other instead suggests that the d-wave pairs are mediated by the collective bosons like the conventional low $T_c$ SC with the alteration that the phonons are replaced by another kind of bosons ranging from the antiferromagnetic (AF) to loop current fluctuations. An approach to resolve this dispute is to determine the frequency and momentum dependences of the diagonal and off-diagonal self-energies directly from experiments like the McMillan-Rowell procedure for the conventional SC. In that a simple d-wave BCS theory describes superconducting properties of the cuprates well, the Eliashberg analysis of well designed high resolution experimental data will yield the crucial frequency and momentum dependences of the self-energies. This line of approach using ARPES are discussed in more detail in this review, and some remaining problems are commented.

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arXiv2011

Superconductivity in the Cuprates: Deduction of Mechanism for D-Wave Pairing Through Analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions $(α^2 F)_n(ω, θ)$ and $(α^2 F)_{p,d}(ω)$ determine, respectively, the "normal" and the "pairing" self-energies. We present a quantitative analysis of the high-resolution laser based ARPES data on the compound Bi-2212 to deduce the function$(α^2 F)_n(ω, θ)$. Besides its detailed $ω$ dependence, we find the remarkable result that this function is nearly independent of $θ$ between the ($π,π$)-direction and 25 degrees from it. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function $(α^2 F)_{p,d}(ω)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(α^2 F)_n(θ, ω)$. We show that the deduced $(α^2 F)_n(θ, ω)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(α^2 F)_{p,d}(ω)$ consistent with such a correlation length and the symmetry of matrix-elements scattering fermions off AFM fluctuations, we calculate $T_c$ an show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantum-critical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the $θ$ and $ω$ dependence of the deduced $(α^2 F)_n(ω, θ)$. The pairing kernel $(α^2 F)_{p,d}(ω)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.

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arXiv2011

Analysis of Laser ARPES from Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in superconductive state: angle resolved self-energy and fluctuation spectrum

We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy $\w$ employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $θ$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $ω$ is directly obtained from the fitting. The obtained angle resolved self-energy is then used to deduce the Eliashberg function $α^2 F^{(+)}(þ,\w)$ in the diagonal channel by inverting the d-wave Eliashberg equation using the maximum entropy method. Besides a broad featureless spectrum up to the cutoff energy $ω_c$, the deduced $α^2 F$ exhibits two peaks around 0.05 eV and 0.015 eV. The former and the broad feature are already present in the normal state, while the latter emerges only below $T_c$. Both peaks become enhanced as $T$ is lowered or the angle $þ$ moves away from the nodal direction. The implication of these findings are discussed.

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arXiv2010

Interplay between spin density wave and $π$ phase shifted superconductivity in the Fe pnictide superconductors

We explore if the phase separation or coexistence of the spin density wave (SDW) and superconductivity (SC) states has any relation to the incommensurability of the SDW in the Fe pnictide superconductors. A systematic method of determining the phase separation or coexistence was employed by computing the anisotropy coefficient $β$ from the the 4th order terms of the Ginzburg--Landau (GL) expansion of the free energy close to the tricritical/tetracritical point. It was complemented by the self-consistent numerical iterations of the gap equations to map out the boundaries between the phase separation and coexistence of the SDW and SC phases, and between commensurate (C) and incommensurate (IC) SDW in the temperature--doping plane. Our principal results for the sign reversed $s$-wave pairing SC, in terms of the multicritical temperature, $T_c$, the phase separation/coexistence boundary between the SDW and SC, $T^*$, and the boundary between C/IC SDW, $T_M^*$, are: (a) IC-SDW and SC coexist for $T_c < T^*$ and phase separate otherwise, (b) SDW takes the C form for $T_c>T_M^*$ and IC form for $T_c<T_M^*$, and (c) the thermodynamic first order phase transition intervenes in between the C-SDW and IC-SDW boundary for large $T_M^0$, where $T_M^0$ is the SDW transition temperature at zero doping, $T^*=0.35 ~T_M^0$ and $T_M^*=0.56\ T_M^0$. The intervention makes the phase diagram more complicated than previously reported. By contrast no coexistence was found for the equal sign pairing SC. These results will be compared with the experimental reports in the Fe pnictide superconductors.

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arXiv2010

The dynamically induced Fermi arcs and Fermi pockets in two dimensions: a model for underdoped cuprates

We investigate the effects of the dynamic bosonic fluctuations on the Fermi surface reconstruction in two dimensions as a model for the underdoped cuprates. At energies larger than the boson energy $ω_b$, the dynamic nature of the fluctuations is not important and the quasi-particle dispersion exhibits the shadow feature like that induced by a static long range order. At lower energies, however, the shadow feature is pushed away by the finite $ω_b$. The detailed low energy features are determined by the bare dispersion and the coupling of quasi-particles to the dynamic fluctuations. We present how these factors reconstruct the Fermi surface to produce the Fermi arcs or the Fermi pockets, or their coexistence. Our principal result is that the dynamic nature of the fluctuations, without invoking a yet-to-be-established translational symmetry breaking hidden order, can produce the Fermi pocket centered away from the $(π/2,π/2)$ towards the zone center which may coexist with the Fermi arcs. This is discussed in comparison with the experimental observations.

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arXiv2010

Momentum Dependence of the Single-Particle Self-Energy and Fluctuation Spectrum of Slightly Underdoped Bi_2 Sr_2 CaCu_2 O_{8+δ} from High Resolution Laser ARPES

We deduce the normal state angle-resolved single-particle self-energy $Σ(θ, ω)$ and the Eliashberg function (i.e., the product of the fluctuation spectrum and its coupling to fermions) $α^2 F(θ,ω)$ for the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ from the ultra high resolution laser angle-resolved photoemission spectroscopy (ARPES). The self-energy $Σ(θ, ω)$ at energy $ω$ along several cuts normal to the Fermi surface at the tilt angles $θ$ with respect to the nodal direction in a slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ were extracted by fitting the ARPES momentum distribution curves. Then, using the extracted self-energy as the experimental input, the $α^2 F(θ,ω)$ is deduced by inverting the Eliashberg equation employing the adaptive maximum entropy method. Our principal new result is that the Eliashberg function $α^2F(θ,ω)$ collapse for all $θ$ onto a single function of $ω$ up to the upper cut-off energy despite the $θ$ dependence of the self-energy. The in-plane momentum anisotropy is therefore predominantly due to the anisotropic band dispersion effects. The obtained Eliashberg function has a small peak at $ω\approx0.05$ eV and flattens out above 0.1 eV up to the angle-dependent cut-off. It takes the intrinsic cut-off of about 0.4 eV or the energy of the bottom of the band with respect to the Fermi energy in the direction $θ$, whichever is lower. The angle independence of the $α^2 F(θ,ω)$ is consistent only with the fluctuation spectra which have the short correlation length on the scale the lattice constant. This implies among others that the antiferromagnetic fluctuations may not be underlying physics of the deduced fluctuation spectrum.

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arXiv2009

Model for the inverse isotope effect of FeAs-based superconductors in the $π$-phase-shifted pairing state

The isotope effects for Fe based superconductors are considered by including the phonon and magnetic fluctuations within the two band Eliashberg theory. We show that the recently observed inverse isotope effects of Fe, $α_{Fe} \approx -0.18 \pm 0.03 $,\cite{Shirage0903.3515} as well as the large positive isotope exponent ($α\approx 0.35$) can naturally arise for the magnetically induced sign revered s-wave pairing state within reasonable parameter range. Either experimental report can not be discarded from the present analysis based on the parameter values they require. The inverse and positive isotope effects mean, respectively, the interband and intraband dominant eletron-phonon interaction. We first make our points based on the analytic result from the square well potential model and present explicit numerical calculations of the two band Eliashberg theory.

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