arXiv subjects

Shang-Shun Zhang

Publications and source records attributed to Shang-Shun Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2023

Density of states and spectral function of a superconductor out of a quantum-critical metal

We analyze the validity of a quasiparticle description of a superconducting state at a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-s-wave gap symmetry, and at a first glance, should restore a coherent quasiparticle behavior. We argue that this does not necessarily hold as in some cases the fermionic self-energy remains singular slightly above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to broadening and eventual vanishing of the quasiparticle peak in the spectral function. We analyze the set of quantum-critical models with an effective dynamical 4-fermion interaction, mediated by a gapless boson at a QCP, $V(Ω) \propto 1/Ω^γ$. We show that coherent quasiparticle behavior in a superconducting state holds for $γ<1/2$, but breaks down for larger $γ$. We discuss signatures of quasiparticle breakdown and compare our results with the data.

cond-mat.supr-con↗

arXiv2023

Free energy and specific heat near a quantum critical point of a metal

We analyze free energy and specific heat for fermions interacting with gapless bosons at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes contributions from bosons, fermions, and their interaction, all expressed via fully dressed fermionic and bosonic propagators. The sum of the last two contributions is the free energy $F_γ$ of an effective low-energy model of fermions with boson-mediated dynamical 4-fermion interaction $V (Ω_m) \propto 1/|Ω_m|^γ$ (the $γ-$model). This purely electronic model has been used to analyze the interplay between non-Fermi liquid (non-FL) behavior and pairing near a QCP, which are both independent of the upper energy cutoff $Λ$. However, the specific heat $C_γ(T)$, obtained from $F_γ$, does depend on $Λ$. We argue that this dependence is spurious and cancels out, once we include the contribution from bosons. We compare our $C(T)$ with the one obtained within the $γ-$model using recently proposed regularization of $F_γ$. We argue that for $γ<1$, the full $C(T)$ and the regularized $C_γ(T)$ differ by a $γ-$dependent prefactor, while for $γ>1$, the full $C(T)$ is the sum of $ C_γ(T)$ and the specific heat of free bosons with fully dressed mass. For these $γ$, $C_γ(T)$ is negative. The authors of Ref. [1] argued that a negative $ C_γ(T)$ implies that the normal state becomes unstable at some distance to a QCP. In our calculation, both terms in $C(T)$ come from the same source, and $ C_γ(T)$ is smaller as long as vertex corrections can be safely neglected. We then argue that the normal state remains stable even at a QCP.

cond-mat.str-el↗

arXiv2022

BCS-BEC Crossover of Triplet Exciton Condensation in Bilayer Systems

We study the BCS-BEC crossover phenomenon of triplet exciton condensation using a half-filled bilayer Hubbard model. We calculate the dynamical spin structure factor and the exciton wave function on the phase boundary between the antiferromagnetically ordered and disordered phases. In the BCS regime, the formation and condensation of particle-hole bound states, namely excitons, occur simultaneously at the phase transition point, and the exciton wave function is extended in real space. In the BEC regime, on the other hand, bound states are well defined over the whole Brillouin zone also in the disordered phase, and the size of particle-hole pairs is smaller than a lattice space. Quantum criticality of charge-spin-orbital entangled states can emerge from intermediate coupling materials in the crossover regime.

cond-mat.str-el↗

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

Evidence of Two-Spinon Bound States in the Magnetic Spectrum of Ba$_3$CoSb$_2$O$_9$

Recent inelastic neutron scattering (INS) experiments of the triangular antiferromagnet Ba$_3$CoSb$_2$O$_9$ revealed strong deviations from semiclassical theories. We demonstrate that key features of the INS data are well reproduced by a parton Schwinger boson theory beyond the saddle-point approximation. The measured magnon dispersion is well reproduced by the dispersion of two-spinon bound states (poles of the emergent gauge fields propagator), while the low-energy continuum scattering is reproduced by a quasifree two-spinon continuum, suggesting that a free-spinon gas is a good initial framework to study magnetically ordered states near a quantum melting point.

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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.

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arXiv2022

Schwinger boson theory of ordered magnets

The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the $1/N$ expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in $1/N$, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

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

Variational study of the Kitaev-Heisenberg-Gamma model

We compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.

cond-mat.str-el↗

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↗

arXiv2021

Theory of the Kitaev model in a [111] magnetic field

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev's 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number $C=\pm 1$ transitions into an Abelian liquid with $C=\pm 4$. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

cond-mat.str-el↗

arXiv2021

Exciton condensation in bilayer spin-orbit insulator

We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime. This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength. By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons. These low-energy excitons reemerge on the other side of the QCP as the transverse and longitudinal modes of the AFM state. In particular, the longitudinal mode remains sharp for the model parameters relevant to Sr$_{3}$Ir$_{2}$O$_{7}$ because of the strong easy-axis anisotropy of this material.

cond-mat.str-el↗

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

Observation of 4- and 6-magnon bound-states in the spin-anisotropic frustrated antiferromagnet FeI$_2$

Spin-waves e.g. magnons are the conventional elementary excitations of ordered magnets. However, other possibilities exist. For instance, magnon bound-states can arise due to attractive magnon-magnon interactions and drastically impact the static and dynamic properties of materials. Here, we demonstrate a zoo of distinct multi-magnon quasiparticles in the frustrated spin-1 triangular antiferromagnet FeI$_2$ using time-domain terahertz spectroscopy. The energy-magnetic field excitation spectrum contains signatures of one-, two-, four- and six-magnon bound-states, which we analyze using an exact diagonalization approach for a dilute gas of interacting magnons. The two-magnon single-ion bound states occur due to strong anisotropy and the preponderance of even higher order excitations arises from the tendency of the single-ion bound states to themselves form bound states due to their very flat dispersion. This menagerie of tunable interacting quasiparticles provides a unique platform in a condensed matter setting that is reminiscent of the few-body quantum phenomena central to cold-atom, nuclear, and particle physics experiments.

cond-mat.str-el↗

arXiv2020

Magnetic-field-induced tunability of spin Hamiltonians: Resonances and Efimov states in Yb$_2$Ti$_2$O$_7$

Universality is a powerful concept that arises from the divergence of a characteristic length scale. For condensed matter systems, this length scale is typically the correlation length, which diverges at critical points separating two different phases. Few-particle systems exhibit a simpler form of universality when the $s$-wave scattering length diverges. A prominent example of universal phenomena is the emergence of an infinite tower of three-body bound states obeying discrete scale invariance, known as the Efimov effect, which has been subject to extensive research in chemical, atomic, nuclear and particle physics. In principle, these universal phenomena can also emerge in the excitation spectrum of condensed matter systems, such as quantum magnets~[Y. Nishida, Y. Kato, and C. Batista, Nat. Phys. 9, 93 (2013)]. However, the limited tunability of the effective inter-particle interaction relative to the kinetic energy has precluded so far their observation. Here we demonstrate that a high degree of magnetic-field-induced tunability can also be achieved in quantum magnets with strong spin-orbit coupling: a two-magnon resonance condition can be achieved in Yb$_2$Ti$_2$O$_7$ with a field of $\sim$ 13~T along the [110] direction, which leads to the formation of Efimov states in the three-magnon spectrum of this material. Raman scattering experiments can reveal the field-induced two-magnon resonance, as well as the Efimov three-magnon bound states that emerge near the resonance condition.

cond-mat.str-el↗

arXiv2020

Hybridized quadrupolar excitations in the spin-anisotropic frustrated magnet FeI2

Magnetic order is usually associated with well-defined magnon excitations. Exotic magnetic fluctuations with fractional, topological or multipolar character, have been proposed for radically different forms of magnetic matter such as spin-liquids. As a result, considerable efforts have searched for, and uncovered, low-spin materials with suppressed dipolar order at low temperatures. Here, we report neutron-scattering experiments and quantitative theoretical modeling of an exceptional spin-1 system -- the uniaxial triangular magnet FeI2 -- where a bright and dispersive band of mixed dipolar-quadrupolar fluctuations emerges just above a dipolar ordered ground-state. This excitation arises from anisotropic exchange interactions that hybridize overlapping modes carrying fundamentally different quantum numbers. Remarkably, a generalization of spin-wave theory to local SU(3) degrees of freedom accounts for all details of the low-energy dynamical response of FeI2 without going beyond quadratic order. Our work highlights that quantum excitations without classical counterparts can be realized even in presence of fully developed magnetic order.

cond-mat.str-el↗

arXiv2019

Toward Kitaev's sixteenfold way in a honeycomb lattice model

Kitaev's sixteenfold way is a classification of exotic topological orders in which $\mathbb{Z}_2$ gauge theory is coupled to Majorana fermions of Chern number $C$. The $16$ distinct topological orders within this class, depending on $C \, \mathrm{mod} \, 16$, possess a rich variety of Abelian and non-Abelian anyons. We realize more than half of Kitaev's sixteenfold way, corresponding to Chern numbers $0$, $\pm 1$, $\pm 2$, $\pm 3$, $\pm 4$, and $\pm 8$, in an exactly solvable generalization of the Kitaev honeycomb model. For each topological order, we explicitly identify the anyonic excitations and confirm their topological properties. In doing so, we observe that the interplay between lattice symmetry and anyon permutation symmetry may lead to a "weak supersymmetry" in the anyon spectrum. The topological orders in our honeycomb lattice model could be directly relevant for honeycomb Kitaev materials, such as $α$-RuCl$_3$, and would be distinguishable by their specific quantized values of the thermal Hall conductivity.

cond-mat.str-el↗

arXiv2019

Real space Berry curvature of itinerant electron systems with spin-orbit interaction

By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $γ$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, $γ=Ω/2$, where $Ω$ is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of $γ$ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or $π$, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials.

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