arXiv subjects

Kevin Ingersent

Publications and source records attributed to Kevin Ingersent.

At least 19 recordsLinked to original sources

arXiv2023

The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum

The Anderson model for a magnetic impurity in a one-dimensional quasicrystal is studied using the numerical renormalization group (NRG). The main focus is elucidating the physics at the critical point of the Aubry-Andre (AA) Hamiltonian, which exhibits a fractal spectrum with multifractal wave functions, leading to an AA Anderson (AAA) impurity model with an energy-dependent hybridization function defined through the multifractal local density of states at the impurity site. We first study a class of Anderson impurity models with uniform fractal hybridization functions that the NRG can solve to arbitrarily low temperatures. Below a Kondo scale $T_K$, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties oscillate with $\log_b T$ about negative average values determined by the fractal dimension of the spectrum. The fractal dimension also enters into a power-law dependence of $T_K$ on the Kondo exchange coupling $J_K$. To treat the AAA model, we combine the NRG with the kernel polynomial method (KPM) to form an efficient approach that can treat hosts without translational symmetry down to a temperature scale set by the KPM expansion order. The aforementioned fractal strong-coupling fixed point is reached by the critical AAA model in a simplified treatment that neglects the wave-function contribution to the hybridization. The temperature-averaged properties are those expected for the numerically determined fractal dimension of $0.5$. At the AA critical point, impurity thermodynamic properties become negative and oscillatory. Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependences on $J_K$ with exponents characteristic of different fractal dimensions. We attribute these signatures to the impurity probing a distribution of fractal strong-coupling fixed points with decreasing temperature.

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arXiv2022

Dynamical Planckian scaling of charge response at a particle-hole-asymmetric quantum critical point with Kondo destruction

Metallic quantum criticality is a central theme in a variety of strongly correlated systems. Recent experiments have raised the fundamental question of how the charge response can be singular in cases where the Landau framework of quantum criticality allows singularity only in the spin channel. Motivated by this emerging issue, we study the particle-hole-asymmetric regime of a Bose-Fermi Anderson model with power-law forms for both the bosonic bath spectrum and the fermionic band density of states. We realize a particle-hole-asymmetric quantum-critical state where quasiparticles are lost due to a critical destruction of Kondo screening, and demonstrate a dynamical Planckian scaling of the charge response. Implications for a new regime of heavy-fermion quantum criticality and for Mott-Hubbard systems are discussed.

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arXiv2021

Unconventional Superconductivity from Fermi Surface Fluctuations in Strongly Correlated Metals

In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivity is both pressing and challenging. Here we do so in the exemplary setting of heavy-fermion metals, where the amplified quantum fluctuations manifest in the form of Kondo destruction and large-to-small Fermi-surface fluctuations. These fluctuations lead to unconventional superconductivity whose transition temperature is exceptionally high relative to the effective Fermi temperature, reaching several percent of the Kondo temperature scale. Our results provide a natural understanding of the enigmatic superconductivity in a host of heavy-fermion metals. Moreover, the qualitative physics underlying our findings and their implications for the formation of unconventional superconductivity apply to a variety of highly correlated metals with strong Fermi surface fluctuations.

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arXiv2020

Critical local moment fluctuations and enhanced pairing correlations in a cluster Anderson model

The appearance of unconventional superconductivity near heavy-fermion quantum critical points (QCPs) motivates investigation of pairing correlations close to a ``beyond Landau'' Kondo-destruction QCP. We focus on a two-Anderson-impurity cluster in which Kondo destruction is induced by a pseudogap in the conduction-electron density of states. Analysis via continuous-time quantum Monte-Carlo and the numerical renormalization group reveals a previously unstudied QCP that both displays the critical-local moment fluctuations characteristic of Kondo destruction and leads to a strongly enhanced singlet-pairing susceptibility. Our results provide new insights into the mechanism for superconductivity in quantum critical metals.

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arXiv2019

Dynamical Kondo effect and Kondo destruction in effective models for quantum-critical heavy fermion metals

Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonzero frequencies. This dynamical effect allows for mass enhancement in the Kondo-destroyed phase. Here, we elucidate the dynamical Kondo effect in Bose-Fermi Kondo/Anderson models, which unambiguously exhibit Kondo-destruction quantum critical points. We show that a simple physical quantity---the expectation value $\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle$ for the dot product of the local ($f$) and conduction-electron ($c$) spins---varies continuously across such quantum critical points. A nonzero $\langle {\bf S}_{f} \cdot {\bf s}_{c} \rangle$ manifests the dynamical Kondo effect that operates in the Kondo-destroyed phase. Implications are discussed for the stability of Kondo-destruction quantum criticality as well as the understanding of experimental results in quantum critical heavy-fermion metals.

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arXiv2019

Sublattice symmetry breaking and Kondo-effect enhancement in strained graphene

Kondo physics in doped monolayer graphene is predicted to exhibit unusual features due to the linear vanishing of the pristine material's density of states at the Dirac point. Despite several attempts, conclusive experimental observation of the phenomenon remains elusive. One likely obstacle to identification is a very small Kondo temperature scale $T_K$ in situations where the chemical potential lies near the Dirac point. We propose tailored mechanical deformations of monolayer graphene as a means of revealing unique fingerprints of the Kondo effect. Inhomogeneous strains are known to produce specific alternating changes in the local density of states (LDOS) away from the Dirac point that signal sublattice symmetry breaking effects. Small LDOS changes can be amplified in an exponential increase or decrease of $T_K$ for magnetic impurities attached at different locations. We illustrate this behavior in two deformation geometries: a circular 'bubble' and a long fold, both described by Gaussian displacement profiles. We calculate the LDOS changes for modest strains and analyze the relevant Anderson impurity model describing a magnetic atom adsorbed in either a 'top-site' or a 'hollow-site' configuration. Numerical renormalization-group solutions of the impurity model suggest that higher expected $T_K$ values, combined with distinctive spatial patterns under variation of the point of graphene attachment, make the top-site configuration the more promising for experimental observation of signatures of the Kondo effect. The strong strain sensitivity of $T_K$ may lift top-site Kondo physics into the range experimentally accessible using local probes such as scanning tunneling microscopy.

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arXiv2018

Long-range entanglement near a Kondo-destruction quantum critical point

The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a pseudogapped density of states $ρ(\varepsilon)\propto|\varepsilon|^r$ ($r>0$) that vanishes at the Fermi energy $\varepsilon=0$. The model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase (reached for impurity-band exchange couplings $J>J_c$) from a local-moment phase ($J<J_c$). The impurity contribution $S_e^{imp}$ to the entanglement entropy between a region of radius $R$ around the magnetic impurity and the rest of the host system reveals a characteristic length scale $R^*$ that distinguishes a regime $R\ll R^*$ of maximal critical entanglement from one $R\gg R^*$ of weaker entanglement. Within each phase, $S_e^{imp}$ is a universal function of $R/R^*$ with a power-law decay for $R/R^*\gg 1$. The entanglement length scale $R^*$ diverges on approach to the QCP with a critical exponent that depends only on $r$.

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arXiv2017

Phase boundaries of the pseudogap Anderson and Kondo models

We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states $ρ(ω)\propto|ω|^r$ that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., $r>0$), we find the phase boundary for (a) $0 1$, where the phases are separated by first-order quantum phase transitions. For the particle-hole-symmetric Kondo model with easy-axis or easy-plane anisotropy of the spin exchange, the phase boundary and scaling trajectories are obtained for both $r>0$ and $r<0$ (the later case describing a density of states that diverges at the Fermi energy). Comparison with nonperturbative results from the numerical renormalization group shows that poor man's scaling correctly describes the shape of phase boundaries expressed as functional relations between model parameters.

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arXiv2016

Quantum criticality and global phase diagram of an Ising-anisotropic Kondo lattice

Recent studies of heavy-fermion systems with tunable quantum fluctuations have focused on a variety of zero-temperature phase transitions that involve not only the onset of magnetic order but also the destruction of Kondo entanglement. Motivated by these developments, we investigate the effect of enhanced quantum fluctuations induced by a transverse magnetic field in an Ising-anisotropic Kondo lattice model, solved within an extended dynamical mean field theory using the numerical renormalization group. A line of locally critical points describes a direct transition from a Kondo-screened paramagnetic heavy-fermion state to a Kondo-destroyed antiferromagnetic phase. Along the line, the extracted critical exponents remain unchanged. By probing the the interplay between quantum fluctuations of the local moments, the Kondo effect, and magnetic order, this study provides significant new insight into the global phase diagram of heavy-fermion systems.

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arXiv2016

Influence of Rashba spin-orbit coupling on the Kondo effect

An Anderson model for a magnetic impurity in a two-dimensional electron gas with bulk Rashba spin-orbit interaction is solved using the numerical renormalization group under two different experimental scenarios. For a fixed Fermi energy, the Kondo temperature T_K varies weakly with Rashba coupling α, as reported previously. If instead the band filling is low and held constant, increasing αcan drive the system into a helical regime with exponential enhancement of T_K. Under either scenario, thermodynamic properties at low temperatures T exhibit the same dependences on T/T_K as are found for α= 0. Unlike the conventional Kondo effect, however, the impurity exhibits static spin correlations with conduction electrons of nonzero orbital angular momentum about the impurity site. We also consider a magnetic field that Zeeman splits the conduction band but not the impurity level, an effective picture that arises under a proposed route to access the helical regime in a driven system. The impurity contribution to the system's ground-state angular momentum is found to be a universal function of the ratio of the Zeeman energy to a temperature scale that is not T_K (as would be the case in a magnetic field that couples directly to the impurity spin), but rather is proportional to T_K divided by the impurity hybridization width. This universal scaling is explained via a perturbative treatment of field-induced changes in the electronic density of states.

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arXiv2015

Pairing Correlations Near a Kondo-Destruction Quantum Critical Point

Motivated by the unconventional superconductivity observed in heavy-fermion metals, we investigate pairing susceptibilities near a continuous quantum phase transition of the Kondo-destruction type. We solve two-impurity Bose-Fermi Anderson models with Ising and Heisenberg forms of the interimpurity exchange interaction using continuous-time quantum Monte-Carlo and numerical renormalization-group methods. Each model exhibits a Kondo-destruction quantum critical point separating Kondo-screened and local-moment phases. For antiferromagnetic interimpurity exchange interactions, singlet pairing is found to be enhanced in the vicinity of the transition. Implications of this result for heavy-fermion superconductivity are discussed.

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arXiv2015

Entanglement Entropy Near Kondo-Destruction Quantum Critical Points

We study the impurity entanglement entropy $S_e$ in quantum impurity models that feature a Kondo-destruction quantum critical point (QCP) arising from a pseudogap in the conduction-band density of states or from coupling to a bosonic bath. On the local-moment (Kondo-destroyed) side of the QCP, the entanglement entropy contains a critical component that can be related to the order parameter characterizing the quantum phase transition. In Kondo models describing a spin-$\Simp$, $S_e$ assumes its maximal value of $\ln(2\Simp+1)$ at the QCP and throughout the Kondo phase, independent of features such as particle-hole symmetry and under- or over-screening. In Anderson models, $S_e$ is nonuniversal at the QCP, and at particle-hole symmetry, rises monotonically on passage from the local-moment phase to the Kondo phase; breaking this symmetry can lead to a cusp peak in $S_e$ due to a divergent charge susceptibility at the QCP. Implications of these results for quantum critical systems and quantum dots are discussed.

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arXiv2015

Critical charge fluctuations in a pseudogap Anderson model

The Anderson impurity model with a density of states $ρ(\varepsilon) \propto |\varepsilon|^r$ containing a power-law pseudogap centered on the Fermi energy ($\varepsilon = 0$) features for $0<r<1$ a Kondo-destruction quantum critical point (QCP) separating Kondo-screened and local-moment phases. The observation of mixed valency in quantum critical $β$-YbAlB$_4$ has prompted study of this model away from particle-hole symmetry. The critical spin response associated with all Kondo destruction QCPs has been shown to be accompanied, for $r=0.6$ and noninteger occupation of the impurity site, by a divergence of the local charge susceptibility on both sides of the QCP. In this work, we use the numerical renormalization-group method to characterize the Kondo-destruction charge response using five critical exponents, which are found to assume nontrivial values only for $0.55\lesssim r < 1$. For $0 < r \lesssim 0.55$, by contrast, the local charge susceptibility shows no divergence at the QCP, but rather exhibits nonanalytic corrections to a regular leading behavior. Both the charge critical exponents and the previously obtained spin critical exponents satisfy a set of scaling relations derived from an ansatz for the free energy near the QCP. These critical exponents can all be expressed in terms of just two underlying exponents: the correlation-length exponent $ν(r)$ and the gap exponent $Δ(r)$. The ansatz predicts a divergent local charge susceptibility for $ν<2$, which coincides closely with the observed range $0.55\lesssim r<1$. Many of these results are argued to generalize to interacting QCPs that have been found in other quantum impurity models.

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arXiv2014

Kondo effect in graphene with Rashba spin-orbit coupling

We study the Kondo screening of a magnetic impurity adsorbed in graphene in the presence of Rashba spin-orbit interaction. The system is described by an effective single-channel Anderson impurity model, which we analyze using the numerical renormalization group. The nontrivial energy dependence of the host density of states gives rise to interesting behaviors under variation of the chemical potential or the spin-orbit coupling. Varying the Rashba coupling produces strong changes in the Kondo temperature characterizing the many-body screening of the impurity spin, and at half filling allows approach to a quantum phase transition separating the strong-coupling Kondo phase from a free-moment phase. Tuning the chemical potential close to sharp features of the hybridization function results in striking features in the temperature dependences of thermodynamic quantities and in the frequency dependence of the impurity spectral function.

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arXiv2013

Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction

We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |ε|^r at the Fermi energy (ε=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |ω|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and ω/T scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum critical point.

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arXiv2013

Quantum phase transitions into Kondo states in bilayer graphene

We study a magnetic impurity intercalated in bilayer graphene. A representative configuration generates a hybridization function with strong dependence on the conduction-electron energy, including a full gap with one hard and one soft edge. Shifts of the chemical potential via gating or doping drive the system between non-Kondo (free-moment) and Kondo-screened phases, with strong variation of the Kondo scale. Quantum phase transitions near the soft edge are of Kosterlitz-Thouless type, while others are first order. Near the hard edge, a bound-state singlet appears inside the gap; although of single-particle character, its signatures in scanning tunneling spectroscopy are very similar to those arising from a many-body Kondo resonance.

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arXiv2013

Quantum critical Kondo destruction in the Bose-Fermi Kondo model with a local transverse field

Recent studies of the global phase diagram of quantum-critical heavy-fermion metals prompt consideration of the interplay between the Kondo interactions and quantum fluctuations of the local moments alone. Toward this goal, we study a Bose-Fermi Kondo model (BFKM) with Ising anisotropy in the presence of a local transverse field that generates quantum fluctuations in the local-moment sector. We apply the numerical renormalization-group method to the case of a sub-Ohmic bosonic bath exponent and a constant conduction-electron density of states. Starting in the Kondo phase at zero transverse-field, there is a smooth crossover with increasing transverse field from a fully screened to a fully polarized impurity spin. By contrast, if the system starts in its localized phase, then increasing the transverse field causes a continuous, Kondo-destruction transition into the partially polarized Kondo phase. The critical exponents at this quantum phase transition exhibit hyperscaling and take essentially the same values as those of the BFKM in zero transverse field. The many-body spectrum at criticality varies continuously with the bare transverse field, indicating a line of critical points. We discuss implications of these results for the global phase diagram of the Kondo lattice model.

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arXiv2013

Spin-polarized conductance in double quantum dots: Interplay of Kondo, Zeeman and interference effects

We study the effect of an external magnetic field in the Kondo regime of a double-quantum-dot system in which a strongly correlated dot (the "hanging dot") is coupled to a second, noninteracting dot that also bridges the gap between two external leads. In zero field, the spectral function of the hanging dot has previously been shown to exhibit a split-peak structure near the Fermi level due to "Kondo resonance filtering" by the bridging dot. We show using the numerical renormalization group that application of a magnetic field leads to a subtle interplay between electronic interference, Kondo physics, and Zeeman splitting with nontrivial consequences for the spectral and transport properties. The value of the hanging-dot spectral function at the Fermi level exhibits a nonuniversal field dependence that can be explained using a generalized Friedel sum rule for a Kondo system with energy-dependent hybridization. The magnetic field also accentuates the exchange-mediated interdot coupling, which dominates the ground state at intermediate fields leading to the formation of antiparallel magnetic moments on the dots. By tuning gate voltages and the magnetic field, one can achieve complete spin polarization of the linear conductance between the leads, raising the prospect of applications of the device as a highly tunable spin filter. The system's low-energy properties are qualitatively unchanged by the presence of weak on-site Coulomb repulsion within the bridging dot.

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