Session Y43: Multi-Polar, Multi-Channel, and Semimetal Kondo systems

Live

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 this work, using renormalization group analysis, we investigate a model where the multipolar local moment is coupled to conduction electrons with two different orbital-symmetry components. When each orbital-symmetry component is present alone, non-Fermi liquid states with exactly the same thermodynamic singularities appear. When both orbital-symmetry components are allowed, however, a completely different non-Fermi liquid state arises via the quantum fluctuations in the mixed scattering channels. This remarkable result suggests that the multipolar Kondo problem presents novel opportunities for the discovery of unexpected non-Fermi liquid states.   

Live

The embedding of multipolar local moments in a metallic host offers a route to uncover novel spin-orbital entangled quantum ground states. In this talk, we theoretically investigate the multipolar Kondo problem, where conduction electrons interact with localized higher-rank multipolar moments (such as quadrupolar or octupolar moments). Using non-abelian bosonization, current algebra, and conformal field theory approaches, we demonstrate the appearance of a novel non-Fermi liquid state, which is characterized by highly singular power-law behaviours in its physical properties. This work provides the foundation for the discovery of a variety of non-Fermi liquid ground states in quantum materials through the introduction of multipolar moments in itinerant electron systems.   

Live

One of the central mysteries of strongly correlated electronic systems is the origin of the non-Fermi liquid (NFL) phase — a highly entangled quantum state that holds abiding fascination owing to its prime connections with unconventional superconductivity and quantum critically [1]. Metallic systems with strong hybridization between multipolar local moments and conduction electrons offer a fascinating stage for exploring the purely orbital-driven NFL and quantum criticality. The heavy-fermion superconductor PrV₂Al₂₀ is a model system of this kind, which features a nonmagnetic ground-state doublet, hosting both electric quadrupoles and magnetic octupoles [2,3]. Here, we present a comprehensive study of the NFL behavior in PrV₂Al₂₀ single crystals using transport and thermodynamic measurements [3]. Our findings reveal that the multipolar Kondo effect plays a crucial role in shaping the NFL behavior in PrV₂Al₂₀ and leads to field-induced quantum critical phenomena radically different from that observed in magnetic heavy fermion systems.

[1] P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008)
[2] A. Sakai and S. Nakatsuji, J. Phys. Soc. Jpn. 80, 063701 (2011)
[3] M. Tsujimoto, et al., Phys. Rev. Lett. 113, 267001 (2014)
[3] M. Fu et al., J. Phys. Soc. Jpn. 89, 013704 (2020)   

Live

Motivated by a recent experiment [Z. Iftikhar et al, Nature 526, 233 (2015)], we report a time-dependent Density-Matrix Renormalization-Group computation of the low-temperature non-equilibrium current across a microscopic metallic island coupled to two independent leads. At low T, the nearly complete freezing of the island degrees of freedom leaves only two degenerate states, whose charges differ by one electron. The dynamics of charge conduction through the island is modeled by an anisotropic two-channel Kondo Hamiltonian, in which the two impurity-spin components represent the island states, a spin flip emulating the transfer of one electron to or from the leads. We have computed the current, following the application of a sudden bias eV, over time intervals substantially longer than the characteristic time \hbar/(eV), albeit short on the Kondo time scale. For symmetric couplings, plotted as a function of eV, the differential conductances show universal behavior. For asymmetric couplings, the differential conductances display the expected crossover from Fermi-liquid to non-Fermi-liquid behavior as eV grows.   

Live

Floquet engineering consists of coupling a system to a periodic potential, typically light, leading to transient phases rare or even impossible to find in equilibrium. We show that the Kondo lattice can be Floquet-tuned to generate multichannel Kondo physics even when the equilibrium case has a single channel. By changing the driving protocol, we can tune to two and three-channel multicritical points. These emergent channels are differentiated by symmetry, and their strength can be controlled by light polarization, frequency, and amplitude. We first demonstrate our findings in a toy model on the square lattice. Then, we explore a realistic model for J = 5/2 Ce ions in a tetragonal environment, which presents unique features arising from spin-orbit coupling. Unpolarized light, constructed by polarization averaging [V. L. Quito and R. Flint, arXiv:2003.04272], can be particularly useful for designing multichannel Kondo lattices that present Floquet-induced Kondo models not found in equilibrium. The multichannel Kondo lattice can give rise to composite pair superconductivity, and we discuss how the nature of the superconductivity can be tuned, with application to the 115 materials.   

Live

Non-abelian anyons are highly desired for topological quantum computation purposes, with Majorana fermions a promising possibility, particularly localized zero modes with non-trivial mutual statistics. Yet realizing Majorana zero modes in matter is a challenge, with proposals in fractional quantum hall states, chiral superconductors and spin liquids, but no clear successes. Heavy fermion materials have long been known to host Majoranas at two-channel Kondo impurities, however, these impurities are difficult to manipulate, and moreover occur in metals, where Majoranas at different impurities can communicate and lose their topological nature. Here, we show that topological defects in a lattice of these two-channel Kondo impurities can also host Majoranas, but can be engineered to avoid the above difficulties, providing the novel possibility of non-trivial, stable and manipulable Majorana zero modes in a two-channel Kondo insulator. We examine this effect in a simple square octagon model at quarter filling with an antiferrohastatic order that opens up a hybridization gap at the quadratic band touching point and show that skyrmionic defects in this state host Majorana zero modes.   

Live

When high-intensity light interacts with solid state materials, nonlinear processes generate higher-order harmonics of the incident light. In the presence of strong correlations, high harmonic generation (HHG) characterizes many-body properties such as coherent excitations & charge dynamics, whereas in topological matter, nontrivial Berry curvature contributes to second harmonic generation (SHG) through interband transitions. In light of the discovery of strong-correlation-driven topology in both experimental^1-3 & theoretical^4-6 studies of a Weyl-Kondo semimetal (WKSM), we study the HHG of the WKSM. Using a Peierls-substituted noncentrosymmetric periodic Anderson model including spin orbit coupling, we elucidate the effect of strong correlations on the SHG order and its intensity.
¹S. Dzsaber et al PRL 118 246601 2017
²S. Dzsaber et al arXiv:1811.02819 2018
³S. Dzsaber et al arXiv:1906.01182 2019
⁴H.-H. Lai, S. E. Grefe, S. Paschen & Q. Si, PNAS 115 93 2018
⁵S. E. Grefe, H.-H. Lai, S. Paschen & Q. Si, PRB 101, 075138 2020
⁶S. E. Grefe, H.-H. Lai, S. Paschen & Q. Si, unpub. 2020; JPS Conf. Proc. 30, 011013 2020   

Live

Quantum critical points (QCPs) and the beyond-Landau physics of Kondo destruction [1,2] are being studied in systems with multipolar degrees of freedom. The compound Ce₃Pd₂₀Si₆ shows evidence for two consecutive Fermi surface collapsing QCPs as it is tuned from a paramagnetic to an antiferroquadrupolar and then to an antiferromagnetic state [3]. A theory was advanced [3] for a sequential destruction of spin-orbital-coupled Kondo effect in an SU(4) Bose-Fermi Kondo model, an effective model for a multipolar Kondo lattice. Here we report an analytical renormalization group calculation of the model with Ising anisotropy. We show that a generic trajectory in the parameter space contains two QCPs associated with the destruction of the orbital and spin Kondo effects, respectively. Our work establishes a firm theoretical ground for the notion of sequential Kondo destruction. Implications for metallic quantum criticality in general are discussed.

[1] Q. Si et al, Nature 413, 804 (2001)
[2] S. Paschen et al, Nature 432, 881 (2004)
[3] V. Martelli, A. Cai, E. Nica, M. Taupin, A. Prokofiev, C.-C. Liu, H. Lai, R. Yu, K. Ingersent, R. Küchler, A. M. Strydom, D. Geiger, J. Haenel, J. Larrea, Q. Si, S. Paschen, PNAS 116, 17701 (2019)   

Live

Quantum criticality has been an active research topic in condensed matter physics, with major efforts being devoted to the heavy fermion metals [1]. From a theoretical perspective, the interplay between different kinds of degrees of freedom makes it challenging to develop a unified framework to study the quantum criticality. Here we approach the problem from the magnetically ordered side, and represent the Kondo lattice model using a quantum non-linear sigma model with an additional coupling to itinerant fermions. By treating the renormalization of the bosonic and fermionic degrees of freedom on an equal footing, we analyze the effect of the Kondo coupling on the quantum criticality. Our results shed new light on the global phase diagram of the heavy fermion systems [2] and, especially, the behavior of frustrated Kondo lattice [3,4].

[1] S. Paschen & Q. Si, Nat. Rev. Phys. (arXiv:2009.03602); S. Kirchner et al, Rev. Mod. Phys. 92, 011002 (2020); Q. Si et al., Nature 413, 804 (2001).
[2] Q. Si, Physica B378, 23 (2006); Phys. Status Solidi B 247, 476 (2010).
[3] H. Zhao et al, Nat. Phys. 15, 1261 (2019).
[4] M. Kavai et al, arXiv:2006.07424.   

Live

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 (KB). We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel ap- proach 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 fully considered, we find a distinct SM behavior with quasi-linear-in-temperature scattering rate associated with KB. When particle-hole symmetry is present, signatures of a critical spin-liquid SM phase as T → 0 are revealed with ω/T scaling extended to a wide range. We attribute these features to the interplay of critical bosonic charge (Kondo) fluctuations and gapless fermionic spinons. The implications of our results for the experiments are discussed. Please refer to arXiv :2005.03427.   

Live

Quantum impurity models - systems of a few strongly interacting degrees of freedom coupled to a large bath of noninteracting fermions - constitute an important class of problems in condensed matter physics. Despite the small number of interacting modes involved, this class of problems can exhibit rich many-body physics phenomena. Motivated by recent formal results, showing that a coherent superposition of non-orthogonal fermionic Gaussian states is an efficient approximation to the ground states to quantum impurities [Bravyi and Gosset, Comm. Math. Phys., 356 451 (2017)], we present a new practical approach for performing variational calculations for quantum impurity problems. The method uses an approximate projection of imaginary-time equations of motion that decouples the dynamics of each Gaussian state forming the ansatz. As a first application of the method, we calculate properties of the screening cloud of an Anderson impurity and the impurity contribution to the entanglement entropy. We also benchmark our approach using density matrix renormalization group (DMRG) calculations. Finally, we present ongoing work on the study of the ground state of the overscreened multichannel Kondo model, a problem difficult to tackle using conventional numerical tools.   

Live

In strongly correlated settings, how space group symmetry influences electronic
topology is a general question that has been little explored. Motivated by recent
developments on Weyl-Kondo semimetals, and guided by space-group symmetry
constraints, we study the Kondo lattice Hamiltonian on several lattices in two and three
dimensions. We find that the Kondo effect in these lattices drives Weyl or Dirac nodes
and pins them to the vicinity of the Fermi energy. This robust feature captures the
interplay between strong correlations on the one hand and constraints of space-group
symmetry and electron filling on the other. The overall implications of our results for strongly
correlated topology are discussed.   

Live

Recently a Weyl-Kondo semimetal (WKSM) has been concurrently discovered in theoretical^1,2 and experimental^3,4 studies. In the solutions to the Anderson lattice model with a nonsymmorphic, noncentrosymmetric crystalline lattice, in the presence of spin-orbit coupling, the Kondo effect cooperates with the space-group symmetry to drive the Weyl nodes and pin them at the Fermi energy. Intriguingly, recent experiments have uncovered how the magnetic field quenches the WKSM.⁵ Here, we studied the Anderson lattice model with a broken time reversal symmetry, via a Zeeman coupling.⁶ Tuning the Zeeman coupling controls the position and number of Weyl nodes and leads to the eventual annihilation of the nodes before the Kondo energy scale vanishes. Our results provide a microscopic understanding of the high-field experiments on the WKSM.

¹H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, PNAS 115, 93 2018
²S. E. Grefe, H.-H. Lai, S. Paschen, and Q. Si, PRB 101, 075138 2020
³S. Dzsaber et al., PRL 118, 246601 2017
⁴S. Dzsaber et al., arXiv:1811.02819 2018
⁵S. Dzsaber et al., arXiv:1906.01182 2019
⁶S. E. Grefe, H.-H. Lai, S. Paschen, and Q. Si, Weyl-Kondo semimetal: towards control of Weyl nodes, 2020   

Live

Multichannel Kondo Hamiltonians are of interest in a wide variety of problems and have been studied using a range of techniques. Here we are interested in employing bosonization methods for these Hamiltonians. Building on the recently developed consistent framework [1,2], and using old and new guidelines for bosonization-debosonization procedure for theories with boundary degrees of freedom, we gain new insights about the refermionization of these Hamiltonians. We analyze and evaluate these using Green-function based calculations, both in and out of equilibrium.

[1] N. Shah and C.J. Bolech, Phys. Rev. B 93, 085440 (2016)
[2] C.J. Bolech and N. Shah, Phys. Rev. B 93, 085441 (2016)   

Live

Recently it has become clear that a nonlinear Hall effect(NLH) can emerge even in a time-reversal symmetric system, which is closely connected with the topological nature of the material, namely the “Berry curvature dipole”[1]. This characteristic makes the NLH an alternative to studying the topology of the material, even when it is difficult to determine the band structure directly, e.g., in strongly correlated topological materials.
Recently, in Ce3Bi4Pd3, a promising candidate for a Weyl-Kondo semimetal(WKSM), a giant spontaneous Hall effect has been experimentally observed[2]. This experiment implies that strong correlations can enhance NLH. However, the relation between strong correlations and NLH is still poorly understood.
In this work, we focus on NLH in WKSM. Specifically, we analyze a periodic Anderson model corresponding to a WKSM using dynamical mean-field theory combined with the numerical renormalization group. We use an extension of the Kubo formula for nonlinear responses to calculate the NLH. We find that the temperature dependence of NLH in our calculation is consistent with the experiment. We also show that strong correlation effects can enhance NLH.

[1] Inti Sodemann and Liang Fu, Phys, Rev, Lett. 115, 216806 (2015).
[2] Dzsaber et al., arXiv:1811.02819 (2018).