arXiv subjects

Yi-Ming Wu

Publications and source records attributed to Yi-Ming Wu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moiré twisted bilayers with time-reversal symmetry and spin $s_z$ conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles, the emergent moiré flatbands can be topologically nontrivial due to inversion symmetry breaking. Each of these flatbands for each spin projection admits a lowest-Landau-level description in the chiral limit and at magic twist angle. This allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

cond-mat.mes-hall↗

arXiv2023

Sublattice Interference promotes Pair Density Wave order in Kagome Metals

Motivated by the observation of a pair density wave (PDW) in the kagome metal CsV${}_3$Sb${}_5$, we consider the fate of electrons near a p-type van Hove singularity (vHS) in the presence of local repulsive interactions. We study the effect of such interactions on Fermi surface "patches" at the vHS. We show how a feature unique to the Kagome lattice known as sublattice interference crucially affects the form of the interactions among the patches. The renormalization group (RG) flow of such interactions results in a regime where the nearest neighbor interaction $V$ exceed the onsite repulsion $U$. We identify this condition as being favorable for the formation of charge-density-wave (CDW) and PDW orders. In the weak coupling limit, we find a complex CDW order as the leading instability, which breaks time reversal symmetry. Beyond RG, we perform a Hartree-Fock study to a $V$-only model and find the pair-density-wave order indeed sets in at some intermediate coupling.

cond-mat.str-el↗

arXiv2023

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density-waves and superconductivity. Importantly, we show that repulsive interactions can stabilize long-sought pair-density wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. This framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

cond-mat.str-el↗

arXiv2022

Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate

Recent ARPES experiments on doped 1D cuprates revealed the importance of effective near-neighbor (NN) attractions in explaining certain features in spectral functions. Here we investigate spectral properties of the extended Hubbard model with the on-site repulsion $U$ and NN interaction $V$, by employing bosonization analysis and the high-precision time-dependent variational principle (TDVP) calculations of the model on 1D chain with up to 300 sites. From state-of-the-art TDVP calculations, we find that the spectral weights of the holon-folding and $3k_F$ branches evolve oppositely as a function of $V$. This peculiar dichotomy may be explained in bosonization analysis from the opposite dependence of exponent that determines the spectral weights on Luttinger parameter $K_ρ$. Moreover, our TDVP calculations of models with fixed $U=8t$ and different $V$ show that $V\approx -1.7t$ may fit the experimental results best, indicating a moderate effective NN attraction in 1D cuprates that might provide some hints towards understanding superconductivity in 2D cuprates.

cond-mat.str-el↗

arXiv2022

Refined quantum gates for $Λ$-type atom-photon hybrid systems

High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level $Λ$-typle atom-cavity system, we present some refined protocols for realizing controlled-not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of our gates is encoded on a flying photon, and the rest qubits are encoded on the atoms in optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi-qubit CNOT, Fredkin and Toffoli gates with O(n) optical elements without auxiliary photons or atoms. Further, the simplest single-qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.

quant-ph↗

arXiv2022

Pair-density-wave and chiral superconductivity in twisted bilayer transition-metal-dichalcogenides

We theoretically explore possible unconventional superconductivity induced by weak repulsive interactions in twisted bilayer TMD (e.g. WSe$_2$) in the presence of an out-of-plane electric field. Using renormalization group (RG) analysis, we show that topological chiral superconducting states with Chern number $\mathcal{N}=1,2,4$ (namely $p+ip$, $d+id$, $g+ig$) appear over a large parameter region with moire filling factor around $n=1$. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair density wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasi-particle interference. Moreover, the spin-polarized PDW could lead to spin-polarized superconducting diode effect.

cond-mat.supr-con↗

arXiv2022

Pair density wave order from electron repulsion

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially-uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. We describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large $N$ limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long range PDW order are that the repulsive BCS couplings must be non-monotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order, and a $T=0$ quantum critical point, where non-Fermi liquid behavior occurs.

cond-mat.supr-con↗

arXiv2022

Superconductivity out of a non-Fermi liquid. Free energy analysis

In this paper, we present in-depth analysis of the condensation energy $E_c$ for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in a metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective $0+1$ dimensional model with the effective dynamical interaction $V(Ω_m) = {\bar g}^γ/|Ω_m|^γ$, where $γ$ is model-specific (the $γ$-model). In previous papers, we argued that the pairing in the $γ$ model is qualitatively different from that in a Fermi liquid, and the gap equation at $T=0$ has an infinite number of topologically distinct solutions, $Δ_n (ω_m)$, where an integer $n$, running between $0$ and infinity, is the number of zeros of $Δ_n (ω_m)$ on the positive Matsubara axis. This gives rise to the set of extrema of $E_c$ at $E_{c,n}$, of which $E_{c,0}$ is the global minimum. The spectrum $E_{c,n}$ is discrete for a generic $γ<2$, but becomes continuous at $γ= 2-0$. Here, we discuss in more detail the profile of the condensation energy near each $E_{c,n}$ and the transformation from a discrete to a continuous spectrum at $γ\to 2$. We also discuss the free energy and the specific heat of the $γ$-model in the normal state.

cond-mat.supr-con↗

arXiv2022

Odd frequency pairing in a quantum critical metal

We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(Ω_n)\sim 1/|Ω_n|^γ$ (the $γ$-model). This interaction gives rise to a non-Fermi liquid in the normal state and is attractive for pairing. The two trends compete with each other. We search for odd-frequency solutions for the pairing gap $Δ(ω_m)= -Δ(ω_m)$. We show that for $γ<1$, odd-frequency superconductivity looses the competition with a non-Fermi liquid and does not develop. We show that the pairing does develop in the extended model in which interaction in the pairing channel is larger than the one in the particle-hole channel. For $γ>1$, we argue that the original model is at the boundary towards odd-frequency pairing and analyze in detail how superconductivity is triggered by a small external perturbation. In addition, we show that for $γ>2$, the system gets frozen at the critical point towards pairing in a finite range in the parameter space. This give rise to highly unconventional phase diagrams with flat regions.

cond-mat.str-el↗

arXiv2021

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. VI. The $γ$ model and its phase diagram at $2 < γ<3$

In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V(Ω_m) = {\bar g}^γ/|Ω_m|^γ$ (the $γ$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous Papers I-V we analyzed the $γ$ model for $γ\leq 2$ and argued that the ground state is an ordinary superconductor for $γ<1$, a peculiar one for $1<γ<2$, when the phase of the gap function winds up along real frequency axis due to emerging dynamical vortices in the upper half-plane of frequency, and that there is a quantum phase transition at $γ=2$, when the number of dynamical vortices becomes infinite. In this paper we consider larger $2< γ<3$ and address the issue what happens on the other side of this quantum transition. We argue that the system moves away from criticality in that the number of dynamical vortices becomes finite and decreases with increasing $γ$. The ground state is again a superconductor, however a highly unconventional one with a non-integrable singularity in the density of states at the lower edge of the continuum. This implies that the spectrum of excited states now contains a level with a macroscopic degeneracy, proportional to the total number of states in the system. We argue that the phase diagram in variables $(T,γ)$ contains two distinct superconducting phases for $γ<2$ and $γ>2$, and an intermediate pseudogap state of preformed pairs.

cond-mat.supr-con↗

arXiv2021

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal: V. The $γ$ model and its phase diagram. The case $γ=2$

This paper is a continuation and a partial summary of our analysis of the pairing at a quantum-critical point (QCP) in a metal for a set of quantum-critical systems, whose low-energy physics is described by an effective model with dynamical electron-electron interaction $V(Ω_m) = ({\bar g}/|Ω_m|)^γ$ (the $γ$-model). Examples include pairing at the onset of various spin and charge density-wave and nematic orders and pairing in SYK-type models. In previous papers, we analyzed the physics for $γ<2$. We have shown that the onset temperature for the pairing $T_p$ is finite, of order ${\bar g}$, yet the gap equation at $T=0$ has an infinite set of solutions within the same spatial symmetry. As the consequence, the condensation energy $E_c$ has an infinite number of minima. The spectrum of $E_c$ is discrete, but becomes more dense as $γ$ increases. Here we consider the case $γ=2$. The $γ=2$ model attracted special interest in the past as it describes the pairing by an Einstein phonon in the limit when the dressed phonon mass $ω_D$ vanishes. We show that for $γ=2$, the spectrum of $E_c$ becomes continuous. We argue that the associated gapless "longitudinal" fluctuations destroy superconducting phase coherence at a finite $T$, such that at $0<T< T_p$ the system displays pseudogap behavior. We show that for each gap function from the continuum spectrum, there is an infinite array of dynamical vortices in the upper half-plane of frequency. For the electron-phonon case, our results show that $T_p =0.1827 {\bar g}$, obtained in earlier studies, marks the onset of the pseudogap behavior of preformed pairs, while the actual superconducting $T_c$vanishes at $ω_D \to 0$.

cond-mat.supr-con↗

arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The $γ$ model and its phase diagram at $1<γ<2$

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical (QC) systems with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model). In previous papers we studied the cases $0<γ<1$ and $γ\approx 1$. We argued that the pairing by a gapless boson is fundamentally different from BCS/Eliashberg pairing by a massive boson as for the former there exists an infinite number of topologically distinct solutions for the gap function $Δ_n (ω_m)$ at $T=0$ ($n=0,1,2...$), each with its own condensation energy $E_{c,n}$. Here we extend the analysis to larger $1< γ<2$. We argue that the discrete set of solutions survives, and the spectrum of $E_{c,n}$ gets progressively denser as $γ$ approaches $2$ and eventually becomes continuous at $γ\to 2$. This increases the strength of "longitudinal" gap fluctuations, which tend to reduce the actual superconducting $T_c$ and give rise to a pseudogap region of preformed pairs. We also detect two features on the real axis for $γ>1$ which become critical at $γ\to 2$. First, the density of states evolves towards a set of discrete $δ-$functions. Second, an array of dynamical vortices emerges in the upper frequency half-plane. These two features come about because on a real axis, the real part of the interaction, $V' (Ω) \propto \cos(πγ/2)/|Ω|^γ$, becomes repulsive for $γ>1$, and the imaginary $V^{''} (Ω) \propto \sin(πγ/2)/|Ω|^γ$, gets progressively smaller at $γ\to 2$. The features on the real axis are consistent with the development of a continuum spectrum of $E_{c,n}$ obtained using $Δ_n (ω_m)$ on the Matsubara axis. We consider the case $γ=2$ separately in the next paper.

cond-mat.supr-con↗

arXiv2020

Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. III: The $γ$ model and its phase diagram across $γ= 1$

In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model). We analyze both the original model and its extension, in which we introduce an extra parameter $N$ to account for non-equal interactions in the particle-hole and particle-particle channel. In two previous papers(arXiv:2004.13220 and arXiv:2006.02968), we considered the case $0 < γ<1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions, $Δ_n (ω_m)$, all with the same spatial symmetry, and (ii) each $Δ_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper, we analyze how the system behavior changes between $γ<1$ and $γ>1$, both at $T=0$ and a finite $T$. The limit $γ\to 1$ is singular due to infra-red divergence of $\int d ω_m V(Ω_m)$, and the system behavior is highly sensitive to how this limit is taken. We show that for $N =1$, the divergencies in the gap equation cancel out, and $Δ_n (ω_m)$ gradually evolve through $γ=1$ both at $T=0$ and a finite $T$. For $N \neq 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $γ>1$. Namely, the form of $Δ_n (ω_m)$ changes qualitatively, and the spectrum of condensation energies, $E_{c,n}$ becomes continuous at $T=0$. We introduce different extension of the model, which is free from singularities for $γ>1$.

cond-mat.supr-con↗

arXiv2019

The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal

Near a quantum-critical point, a metal reveals two competing tendencies: destruction of fermionic coherence and attraction in one or more pairing channels. We analyze the competition within Eliashberg theory for a class of quantum-critical models with an effective dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$ (the $γ$-model) for $0 < γ<1$. We argue that the two tendencies are comparable in strength, yet the one towards pairing is stronger, and the ground state is a superconductor. We show, however, that there exist two distinct regimes of system behavior below the onset temperature of the pairing $T_p$. In the range $T_{cr} < T < T_p$ fermions remain incoherent and the density of states $N(ω)$ displays "gap filling" behavior in which the position of the maximum in $N(ω)$ is set by temperature rather than the pairing gap. At lower $T < T_{cr}$, fermions acquire coherence, and $N(ω)$ displays a conventional "gap closing" behavior. We argue that the existence of the two regimes comes about because of special behavior of fermions with frequencies $ω= \pm πT$ along the Matsubara axis. Specifically, for these fermions, the component of the self-energy, which competes with the pairing, vanishes in the normal state. We further argue that the crossover at $T \sim T_{cr}$ comes about because Eliashberg equations allow an infinite number of topologically distinct solutions for the onset temperature of the pairing within the same gap symmetry. Only one solution, with the highest $T_p$, actually emerges, but other solutions are generated and modify the form of the gap function at $T \leq T_{cr}$. Finally, we argue that the actual $T_c$ is comparable to $T_{cr}$, while at $T_{cr} < T < T_{p}$ phase fluctuations destroy superconducting long-range order, and the system displays pseudogap behavior.

cond-mat.supr-con↗

arXiv2018

The special role of the first Matsubara frequency for superconductivity near a quantum-critical point -- the non-linear gap equation below $T_c$ and spectral properties in real frequencies

Near a quantum-critical point in a metal a strong fermion-fermion interaction, mediated by a soft boson, destroys fermionic coherence and also gives rise to superconductivity. In a class of large $N$ models, one would naively expect an incoherent (non-Fermi liquid) normal state behavior to persist down to $T=0$. However, this is not the case for quantum-critical systems described by Eliashberg theory, where non-Fermi liquid part of the self-energy $Σ(ω_m)$ is large for a generic Matsubara frequency $ω_m = πT(2m+1)$, but vanishes at $ω_m = \pm πT$, while the pairing interaction between fermions with these two frequencies remains strong. This peculiarity gives rise to a non-zero $T_c$ even at large $N$[Y. Wang et al PRL 117, 157001 (2016)]. We consider the system behavior below $T_c$ and contrast the two cases when $ω_m = \pm πT$ are either special or not. We obtain the solution of the non-linear gap equations in real frequency axis and obtain the spectral function $A(ω)$ and the density of states $N(ω)$. In a conventional BCS-type superconductor $A(ω)$ and $N(ω)$ are peaked at the gap value $Δ(T)$, and the peak position shifts to a smaller $ω$ as temperature increases, i.e. the gap "closes in". However when superconductivity is induced by fermions with $ω_m = \pm πT$, the peak in $N(ω)$ remains at a finite frequency even at $T =T_c-0$, the gap just "fills in". The spectral function $A(ω)$ either shows almost the same "gap filling" behavior, or its peak position shifts to zero frequency already at a finite $Δ$ ("emergent Fermi arc" behavior), depending on the strength of the thermal contribution. We compare our results with the data for the cuprates and argue that "gap filling" behavior holds in the antinodal region, while the "emergent Fermi arc" behavior holds in the nodal region.

cond-mat.supr-con↗

arXiv2018

Superconductivity above a quantum critical point in a metal -- gap closing vs gap filling, Fermi arcs, and pseudogap behavior

We consider a quantum-critical metal with interaction mediated by fluctuations of a critical order parameter. This interaction gives rise to two competing tendencies -- pairing and non-Fermi liquid behavior. Due to competition, the pairing develops below a finite $T_p $, however its prominent feedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At $T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor -- the density of states (DOS) and the spectral function (SF) have sharp gaps which close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip, which {\it fills in} with increasing $T$. The SF in this region shows either the same behavior as the DOS, or has a peak at $ω=0$ (the Fermi arc), depending on the position on the Fermi surface. We argue that phase fluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$, while $T_p$ marks the onset of pseugogap behavior. We compare our theory with the behavior of optimally doped cuprates.

cond-mat.supr-con↗

arXiv2018

Multiple pairing states and temperature-dependent gap anisotropy for superconductivity near a nematic quantum-critical point

Superconductivity in many strongly correlated materials appears in proximity to a density-wave or nematic order and is believed to be mediated by quantum-critical (QC) fluctuations of the corresponding order parameter. We argue that fingerprints of QC pairing can be extracted from the angular dependence of the gap $Δ(θ)$. We consider pairing by QC nematic fluctuations and show that there exist multiple pairing instabilities within the same symmetry ($s-$wave in our case), with closely spaced transition temperatures $T_{c,n}$. The corresponding $Δ_n (θ)$ change sign $8n$ times along the FS. Only the solution with the highest $T_{c,0} =T_c$ develops, but other gap components are induced below $T_c$ and get resonantly enhanced below $T_{c,n}$. This gives rise to strong variation of the angular dependence of the gap below $T_c$. The effect gets much weaker away from a quantum-critical point.

cond-mat.supr-con↗

arXiv2018

Pairing in quantum-critical systems: $T_c$, $Δ$, and their ratio

We compute the ratio of the pairing gap $Δ$ at $T=0$ and $T_c$ for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility $χ(Ω) \propto 1/|Ω|^γ$ (the $γ$ model). The limit $γ= 0+$ ($χ(Ω) =\log {|Ω|}$) describes color superconductivity, and models with $γ>0$ describe superconductivity in a metal at the onset of charge or spin order. The ratio $2Δ/T_c$ has been recently computed numerically for $0<γ<2$ within Eliashberg theory and was found to increase with increasing $γ$ [T-H Lee et al, arXiv:1805.10280]. We argue that the origin of the increase is the divergence of $2Δ/T_c$ at $γ=3$. We obtain an approximate analytical formula for $2Δ/T_c$ for $γ\leq 3$ and show that it agrees well with the numerics. We also consider in detail the opposite limit of small $γ$. Here we obtain the explicit expressions for $T_c$ and $Δ$, including numerical prefactors. We show that these prefactors depend on fermionic self-energy in a rather non-trivial way. The ratio $2Δ/T_c$ approaches the BCS value $3.53$ at $γ\to 0$.

cond-mat.supr-con↗