When the ground state of a localized ion is a non-Kramers doublet, such localized ions may carry multipolar moments. For example, Pr$^{3+}$ ions in a cubic environment would possess quadrupolar and octupolar, but no magnetic dipole, moments. When such multipolar moments are placed in a metallic host, unusual interactions between these local moments and conduction electrons arise, in contrast to the familiar magnetic dipole interactions in the classic Kondo problem. In this work, we consider the interaction between a single quadrupolar-octupolar local moment and conduction electrons with $p$-orbital symmetry as a concrete model for the multipolar Kondo problem. We show that this model can be written most naturally in the spin-orbital entangled basis of conduction electrons. Using this basis, the perturbative renormalization group (RG) fixed points are readily identified. There are two kinds of fixed points, one for the two-channel Kondo and the other for a novel fixed point. We investigate the nature of the novel fixed point non-perturbatively using non-abelian bosonization, current algebra and conformal field theory approaches. It is shown that the novel fixed point leads to a, previously unidentified, non-Fermi liquid state with entangled spin and orbital degrees of freedom, which shows resistivity $ρ\sim T^Δ$ and diverging specific heat coefficient $C/T \sim T^{-1 + 2Δ}$ with $Δ=1/5$. Our results open up the possibility of myriads of non-Fermi liquid states, depending on the choices of multipolar moments and conduction electron orbitals, which would be relevant for many rare-earth metallic systems.
Recently it was shown that the multipolar Kondo problem, wherein a quantum impurity carrying higher-rank multipolar moments interacts with conduction electrons, leads to novel non-Fermi liquid states. Because of the multipolar character of the local moments, the form of the interaction with conduction electrons is strongly dependent on the orbital-symmetry of the conduction electrons via crystalline symmetry constraints. This suggests that there may exist a variety of different non-Fermi liquid states in generic multipolar Kondo problems depending on the character of conduction electrons. In t…
Among heavy fermion materials, there is a set of rare-earth intermetallics with non-Kramers Pr$^{3+}$ $4f^2$ moments which exhibit a rich phase diagram with intertwined quadrupolar orders, superconductivity, and non-Fermi liquid behavior. However, more subtle broken symmetries such as multipolar orders in these Kondo materials remain poorly studied. Here, we argue that multi-spin interactions between local moments beyond the conventional two-spin exchange must play an important role in Kondo materials near the ordered to heavy Fermi liquid transition. We show that this drives a plethora of pha…
Quantum criticality beyond the Landau paradigm represents a fundamental problem in condensed matter and statistical physics. Heavy fermion systems with multipolar degrees of freedom can play an important role in the search for its universal description. We consider a Kondo lattice model with both spin and quadrupole degrees of freedom, which we show to exhibit an antiferroquadrupolar phase. Using a field theoretical representation of the model, we find that Kondo couplings are exactly marginal in the renormalization group sense in this phase. This contrasts with the relevant nature of the Kond…
The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focussed on impurities that have two degenerate internal states. In this work, inspired by recent exp…
Our single crystal study reveals that PrTr2Al20 (Tr = Ti and V) provides the first examples of a cubic Γ3 nonmagnetic ground doublet system that shows the Kondo effect including a -ln T dependent resistivity. The Γ3 quadrupolar moments in PrV2Al20 induce anomalous metallic behavior through hybridization with conduction electrons, such as T^{1/2} dependent resistivity and susceptibility below ~ 20 K down to its ordering temperature T_O = 0.6 K. In PrTi2Al20, however, quadrupoles are well-localized and exhibit an order at T_O = 2.0 K. Stronger Kondo coupling in PrV2Al20 than in PrTi2Al20 suppres…
The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically investigate superconducting instabilities instigated by multipolar Kondo interactions. Employing multipolar fluctuations (mediated by RKKY interaction) coupled to conduction electrons via two-channel Kondo and novel multipolar Kondo interactions, we uncover a variety of superconducting states characterized by higher-angular momentum Cooper pairs, $J=0,1,2,3$. We demo…
Notable non-Fermi liquid and quantum critical behaviors are observed in rare-earth metallic systems with non-Kramers local moments supporting a number of different multipolar moments. A prominent example is $\text{Pr(Ti,V)}_{2}\text{Al}_{20}$, where the non-Kramers doublet of the $\text{Pr}^{3+}$ ion allows quadrupolar and octupolar moments, but lacks a dipolar moment. Previous theoretical studies show that a single impurity Kondo problem with such an unusual local moment leads to novel non-Fermi liquid states. In this work, we investigate possible quantum critical behaviors arising from the c…
A series of Pr(TM)$_2$X$_{20}$ (with TM=Ti,V,Rh,Ir and X=Al,Zn) Kondo materials, containing non-Kramers Pr$^{3+}$ $4f^2$ moments on a diamond lattice, have been shown to exhibit intertwined orders such as quadrupolar order and superconductivity. Motivated by these experiments, we propose and study a Landau theory of multipolar order to capture the phase diagram and its field dependence. In zero magnetic field, we show that different quadrupolar states, or the coexistence of quadrupolar and octupolar orderings, may lead to ground states with multiple broken symmetries. Upon heating, such states…
We review the cubic rare-earth boride series which displays diverse electronic states like localized 4f electron multiplets split by the crystal electric field (CEF), itinerant heavy-fermion quasiparticle bands of the Kondo lattice as well as gapped Kondo insulator or mixed-valent semiconductor states. Fairly exotic states may appear due to the 'hidden' order of multipoles carried by degenerate CEF multiplets, in addition to magnetic order present in many RB6 (R = rare earth) compounds. Most prominent are CeB6 and its La-diluted alloys which exhibit antiferro-quadrupolar and octupolar ordering…
Strongly correlated materials are characterized by the presence of electron-electron interactions in their electronic structure. They often have remarkable properties and transitions between competing phases of very different electronic and magnetic order. This thesis focuses on strongly correlated $f$-electron compounds containing Ce, Sm, and U. These materials exhibit a so-called heavy-fermion or Kondo-lattice behavior. They can become insulating due to hybridization effects (Kondo-insulator) or develop multipolar (hidden) order. Kondo insulators have recently been discussed in the context o…
Discovery of novel spin-orbital entangled quantum ground states paves an important avenue for controllable quantum materials via unique couplings to the lattice and other external perturbations. In this work, motivated by recent experiments on cubic heavy fermion materials with multipolar local moments, we theoretically investigate strongly-interacting spin-orbital entangled quantum ground states in multipolar quantum impurity systems. Here itinerant electrons are interacting with the local moments carrying quadrupolar and octupolar moments, in contrast to the conventional Kondo problem with d…
Heavy fermion metals hosting multipolar local moments set a new stage for exploring exotic spin-orbital entangled quantum phases. In such systems, the quadrupolar Kondo effect serves as the key ingredient in the orbital-driven non-Fermi liquid (NFL) behavior and quantum critical phenomena. The cubic heavy fermion superconductor Pr$Tr_2$Al$_{20}$ ($Tr$: Ti, V) is a prime candidate for realizing the quadrupolar Kondo lattice. Here, we present a systematic study of the NFL phenomena in PrV$_2$Al$_{20}$ based on magnetoresistance (MR), magnetic susceptibility and specific heat measurements. Upon e…
Multipolar orderings in degenerate orbital systems offer unique opportunities for emergent topological phases. The phase diagram of interacting spinless fermions in a $p$-band diamond lattice at unit filling is first studied to elucidate the essential role of orbital multipolar orderings in the evolution of multifold degenerate band nodes. The free band structure around the Brillouin zone center is described by two quadratic band nodes each with a threefold degeneracy, which are spanned by the bonding and anti-bonding $p$-orbital multiplets, respectively. Upon switching on interactions, the tr…
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 nonze…
Polycrystalline CeGe is investigated by means of DC and AC susceptibility, non-linear DC susceptibility, electrical transport and heat capacity measurements in the low temperature regime. This compound shows two peaks at low magnetic field approximately around 10.7 and 7.3 K due to antiferromagnetic ordering and subsequent spin rearrangement respectively. Investigation of non-linear DC susceptibility reveals a presence of higher order magnetization which results in the development of a new order parameter around 10.7 K. This leads to a lowering of symmetry of the magnetic state. The order para…
Cerium hexaboride is a cubic f-electron heavy-fermion compound that displays a rich array of low-temperature magnetic ordering phenomena which have been the subject of investigation for more than 50 years. Its complex behaviour is the result of competing interactions, with both itinerant and local electrons playing important roles. Investigating this material has proven to be a substantial challenge, in particular because of the appearance of a "magnetically hidden order" phase, which remained elusive to neutron-scattering investigations for many years. It was not until the development of mode…
The mechanism of strange metal (SM) with unconventional charge transport near magnetic phase transitions has become an outstanding open problem in correlated electron systems. Recently, an exotic quantum critical SM phase was observed in paramagnetic frustrated heavy-fermion materials near Kondo breakdown. We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel approach to the two-dimensional Kondo-Heisenberg lattice model, where KB transition separates a heavy-Fermi liquid from fermionic spin-liquid state. With Kondo fluctuations being full…
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 qu…
Quantum criticality that goes beyond the Landau framework of order-parameter fluctuations is playing a central role in elucidating the behavior of strange metals. A prominent case appears in Kondo lattice systems, which have been extensively analysed in terms of an effective Bose-Fermi Kondo model. Here, a spin is simultaneously coupled to conduction electron bands and gapless vector bosons that represent magnetic fluctuations. The Bose-Fermi Kondo model features interacting fixed points of Kondo destruction with such properties as dynamical Planckian ($\hbar ω/ k_{\rm B} T$) scaling and loss …
One of the challenges in strongly correlated electron systems, is to understand the anomalous electronic behavior that develops at an antiferromagnetic quantum critical point (QCP), a phenomenon that has been extensively studied in heavy fermion materials. Current theories have focused on the critical spin fluctuations and associated break-down of the Kondo effect. Here we argue that the abrupt change in Fermi surface volume that accompanies heavy fermion criticality leads to critical charge fluctuations. Using a model one dimensional Kondo lattice in which each moment is connected to a separa…
We argue that topological Kondo insulators can also have 'intrinsic' topological order associated with fractionalized excitations on their surfaces. The hydridization between the local moments and conduction electrons can weaken near the surface, and this enables the local moments to form spin liquids. This co-exists with the conduction electron surface states, realizing a surface fractionalized Fermi liquid. We present mean-field solutions of a Kondo-Heisenberg model which display such surfaces.
We report magnetic quantum oscillations measured using torque magnetisation in the Kondo insulator YbB$_{12}$ and discuss the potential origin of the underlying Fermi surface. Observed quantum oscillations as well as complementary quantities such as a finite linear specific heat capacity in YbB$_{12}$ exhibit similarities with the Kondo insulator SmB$_6$, yet also crucial differences. Small heavy Fermi sections are observed in YbB$_{12}$ with similarities to the neighbouring heavy fermion semimetallic Fermi surface, in contrast to large light Fermi surface sections in SmB$_6$ which are more si…
Ground state properties of a Kondo lattice model with random configuration of $f$ electrons are investigated with a variational Monte Carlo method. We show that the crossover from a dilute-Kondo system to a heavy-fermion system occurs when the density of $c$ and $f$ electrons ($n_c$, $n_f$) become comparable, $n_f\lesssim n_c$. In the heavy-fermion region, the correlation between $f$ electrons is strong and the $f$ electrons themselves greatly contribute to the screening of other $f$-electron moments. We propose that the character of Kondo screening changes from "individual" to "collective" ac…
We study the pseudogap Bose-Fermi Anderson model with a continuous-time quantum Monte Carlo (CT-QMC) method. We discuss some delicate aspects of the transformation from this model to the Bose-Fermi Kondo model. We show that the CT-QMC method can be used at sufficiently low temperatures to access the quantum critical properties of these models.
For the last few decades, researchers have been intrigued by multipolar ordering phenomena while looking for the related quantum criticality in the heavy-fermion Kondo system Ce$_{1-x}$La$_{x}$B$_6$. However, critical phenomena induced by substitution level ($x$), temperature ($T$), and magnetic field ($B$) are poorly understood despite a large collection of experimental results is available. In this work, we present $T$-$B$, $x$-$T$, and $x$-$B$ phase diagrams of Ce$_{1-x}$La$_x$B$_6$ ($\mathbf{B}\parallel[110]$). These are completed by analyzing heat capacity, magnetocaloric effect (MCE), an…
Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram co…
I construct non-Fermi liquid (NFL) quantum impurity models that are similar to the overscreened multi-channel Kondo models with the difference that an odd number of electron species screen the impurity. The simplest of them, named sesqui-channel (i.e. one-and-a-half-channel) Kondo (1.5CK) model, has less degrees of freedom and is simpler than the two-channel Kondo model, and yet it exhibits NFL physics. Using representation theory I derive the 1.5CK model for a spin-half impurity surrounded with electrons in cubic crystal field and solve it with the numerical renormalization group.
The breakdown of the lattice Kondo effect in local-moment metals can lead to non-trivial forms of quantum criticality and a variety of non-Fermi-liquid phases. Given indications that Kondo-breakdown transitions involve criticality not only in the spin but also in the charge sector, we investigate the interplay of Kondo breakdown and strong valence fluctuations in generalized Anderson lattice models. We employ a parton mean-field theory to describe the transitions between deconfined fractionalized Fermi liquids and various confined phases. We find that rapid valence changes near Kondo breakdown…
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalizat…
We consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a $\mathbb{Z}_2$ spin liquid and a ferromagnetic phase. The model is amenable to sign free auxiliary field quantum Monte Carlo simulations. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the $\mathbb{Z}_2$ spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per uni…
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-fie…
The conformal field theory (CFT) approach to Kondo problems, originally developed by Affleck and Ludwig (AL), has greatly advanced the fundamental knowledge of Kondo physics. The CFT approach to Kondo impurities is based on a necessary approximation, i.e., the linearization of the low-lying excitations in a narrow energy window about the Fermi surface. This treatment works well in normal metal baths, but encounters fundamental difficulties in systems with Fermi points and high-order dispersion relations. Prominent examples of such systems are the recently-proposed topological semimetals with e…
Fermi Surface Reconstruction without Breakdown of Kondo Screening at Quantum Critical Point
受最近在YbRh $_2$ Si $_2$中的霍尔效应实验的启发，我们用变分蒙特卡罗方法研究了二维正方晶格中Kondo晶格模型的基态性质.我们发现了两种类型的相变：反铁磁相变和拓扑相变（费米面重构）。在很宽的参数范围内，这两个转变同时发生，而没有近藤屏蔽的崩溃，伴随着霍尔系数的不连续变化。这一结果与实验一致，并给出了重费米子系统量子临界点的一个新的理论图象。
Thermodynamic and transport properties of the La-diluted Kondo lattice CeNi2Ge2 were studied in a wide temperature range. The Ce-rich alloys Ce1-xLaxNi2Ge2 were found to exhibit distinct features of the coherent heavy Fermi liquid. At intermediate compositions (0.7 <= x <= 0.9) non-Fermi liquid properties have been observed, followed by the local Fermi liquid behavior in the dilute limit. The 4f-electron contribution to the specific heat was found to follow the predictions of the Kondo impurity model both in the local as well as coherent regimes, with the characteristic Kondo temperature decre…
Strong electron correlations can give rise to extraordinary properties of metals with renormalized quasiparticles which are at the basis of Landau's Fermi liquid theory. Near a quantum critical point, these quasiparticles can be destroyed and non-Fermi liquid behavior ensues. YbRh$_2$Si$_2$ is a prototypical correlated metal as it exhibits quasiparticles formation, formation of Kondo lattice coherence and quasiparticle destruction at a field-induced quantum critical point. Here we show how, upon lowering the temperature, the Kondo lattice coherence develops and finally gives way to non-Fermi l…
We study the two-dimensional Kondo lattice model with an additional Heisenberg exchange between localized spins. In a first step we use mean-field theory with two order parameters. The first order parameter is a complex pairing amplitude between conduction electrons and localized spins which describes condensation of Kondo (or Zhang-Rice) singlets. A nonvanishing value implies that the localized spins contribute to the Fermi surface volume. The second order parameter describes singlet-pairing between the localized spins and competes with the Kondo-pairing order parameter. Reduction of the carr…
