arXiv subjects

Daniel J. Schultz

Publications and source records attributed to Daniel J. Schultz.

12 recordsLinked to original sources

arXiv2026

Direct Evidence of Unconventional Superconductivity in Doped Kagome system RV$_3$Sb$_5$

The superconducting pairing symmetry of kagome metals remains a central unresolved question largely because phase-sensitive experiments capable of distinguishing between different possible order parameters have been difficult to implement. The spatial and energetic characteristics of impurity bound states measured by spectroscopic-imaging scanning tunneling microscopy encode information on the superconducting order parameter. Here, we use impurity-bound state spectroscopy to investigate optimally doped RbV$_3$Sb$_{5}$ where the charge-density wave instability is fully suppressed. We find that the superconducting state is fully gapped and exhibits two distinct energy scales, consistent with a multiband order parameter. Atomic-scale spectroscopy around nonmagnetic defects reveals pronounced particle-hole asymmetric bound states. Comparison with theoretical calculations demonstrates that these bound states are incompatible with conventional $s$-wave and sign-changing $s^{\pm}$ pairing. Our calculations also show that the data are fully consistent with a chiral order parameter. Our results establish impurity-bound-state spectroscopy as a powerful phase-sensitive probe of superconductivity in kagome materials and provide strong evidence that optimally doped RbV$_3$Sb$_{5}$ realizes a fully gapped chiral superconducting state.

cond-mat.supr-con↗

arXiv2026

Discovery of an odd-parity f-wave charge order in a kagome metal

The spontaneous breaking of symmetries is a cornerstone of physics, defining the phases of matter from the cosmological scale to the quantum realm. In condensed matter, electronic orders are classified by their behavior under fundamental symmetries like spatial inversion (parity). While even-parity orders, such as conventional superconductivity and charge density waves, are ubiquitous, their odd-parity counterparts--predicted to host exotic phenomena such as gapless quasiparticle excitations and novel collective modes--are comparatively elusive states of quantum matter. Here, using high-resolution scanning tunneling microscopy and angle-resolved photoemission spectroscopy on the kagome metal CsV$_3$Sb$_5$, we report the discovery of an inversion symmetry-breaking $f$-wave charge bond order. We show that this phase, which preserves translation symmetry, is stabilized by the spontaneous opening of a spectral gap at a previously overlooked Dirac point, providing a textbook condensed-matter realization of the Gross-Neveu model for dynamical mass generation and parity breaking. Intriguingly, this $f$-wave order is itself a intervening phase, vanishing abruptly below a temperature of 10\,K and pointing to a subsequent transition into a `hidden' electronic state that is invisible to local STM probes. Our findings establish odd-parity charge order as a novel phase of matter, here, embedded within the intricate hierarchy of correlated electronic orders on the kagome lattice.

cond-mat.str-el↗

arXiv2025

Interplay of competing bond-order and loop-current fluctuations as a possible mechanism for superconductivity in kagome metals

The pairing symmetry and underlying mechanism for superconducting state of AV${}_3$Sb${}_5$ (A=K, Rb, Cs) kagome metal has been a topic of intense investigation. In this work, we consider an 8-band minimal model, which includes V, and the two types of Sb, both within and above/below the kagome plane. This model captures the Fermi surface pocket with significant in-plane Sb contribution near the zone center, and also has the two types of van Hove singularities (VHS), one of which has a strong out of plane Sb weight. By including V-V and V-planar Sb nearest-neighbor Coulomb interactions, we obtain the susceptibilities for fluctuating bond-order and loop-current in both charge and spin channels, and examine the resulting superconducting instabilities. In particular, we find that the time-reversal odd (even) charge-loop-current (charge bond-order) fluctuations favor unconventional (conventional) pairing symmetry such as $s_{+-}$ and $d+id$ ($s_{++}$). Recent experimental works have highlighted the presence of $s$-wave pairing with two distinct gaps, one isotropic and one anisotropic. We discuss how this scenario may be compatible with either $s_{++}$ or $s_{+-}$ pairing, with an isotropic gap on the pocket dominated by in-plane Sb, but a highly anisotropic gap on V-dominated bands.

cond-mat.supr-con↗

arXiv2025

Superconductivity in kagome metals due to soft loop-current fluctuations

We demonstrate that soft fluctuations of translation symmetry-breaking loop currents provide a mechanism for unconventional superconductivity in kagome metals that naturally addresses the multiple superconducting phases observed under pressure. Focusing on the rich multi-orbital character of these systems, we show that loop currents involving both vanadium and antimony orbitals generate low-energy collective modes that couple efficiently to electrons near the Fermi surface and mediate attractive interactions in two distinct unconventional pairing channels. While loop-current fluctuations confined to vanadium orbitals favor chiral $d+id$ superconductivity, which spontaneously breaks time-reversal symmetry, the inclusion of antimony orbitals stabilizes an $s^{\pm}$ state that is robust against disorder. We argue that these two states are realized experimentally as pressure increases and the antimony-dominated Fermi surface sheet undergoes a Lifshitz transition.

cond-mat.supr-con↗

arXiv2025

Local spectroscopy of loop current order with individual magnetic atoms

Hidden ordered states--characterized by order parameters that elude conventional probes--pose a fundamental challenge for their identification in quantum materials. Recent experiments report evidence for time-reversal symmetry breaking orbital magnetic order and anomalous transport signatures in the $2a\times2a$ charge density wave state of the kagome metal CsV$_3$Sb$_5$ at a temperature $T<30\,$K. Theoretical analyses propose that a time-reversal symmetry breaking loop-current order could exist as the ground state of this charge density wave. However, this microscopic interpretation remains debated and experimentally unverified. In this work, we employ individual magnetic atoms as local quantum sensors to examine the quasiparticle excitations of the charge density wave in CsV$_3$Sb$_5$ with the scanning tunneling microscope. Our spectroscopic measurements show that the magnetic moment of Co induces a spatially localized $dI/dV$ peak inside the spectral gap of the charge density wave near the Fermi energy. Conducting temperature-dependent spectroscopy, we find that this spectral feature emerges at $T<30\,$K. By comparing our experimental observations with results of quantum many-body simulations and realistic tight-binding model calculations, we show that this spectroscopic signature can be naturally interpreted as a local flux defect in a loop current ordered state, arising from the Kondo coupling of the magnetic moment of Co with the loop current electrons. The excellent agreement between our experimental and theoretical results suggests the presence of loop-current order in the $2a\times2a$ charge density wave of CsV$_3$Sb$_5$ at $T<30\,$K. Our results provide a microscopic picture to the observation of time-reversal symmetry breaking orbital magnetism and anomalous transport signatures detected in measurements of the macroscopic material properties.

cond-mat.str-el↗

arXiv2024

Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling

The weak Mott insulating regime of the triangular lattice Hubbard model exhibits a rich magnetic phase diagram as a result of the ring exchange interaction in the spin Hamiltonian. These phases include the Kalmeyer-Laughlin type chiral spin liquid (CSL) and a valence bond solid (VBS). A natural question arises regarding the robustness of these phases in the presence of a weak spin-orbit coupling (SOC). In this study, we derive the effective spin model for the spin-orbit coupled triangular lattice Hubbard model in the weak Mott insulting regime, including all SOC-mediated spin-bilinears and ring-exchange interactions. We then construct a simplified spin model keeping only the most relevant SOC-mediated spin interactions. Using infinite density matrix renormalization group (iDMRG) we show that the CSL and VBS phases of the triangular lattice Hubbard model can be stabilized in the presence of a weak SOC. The stabilization results from a compensation between the Dzyaloshinskii-Moriya interaction and a SOC-mediated ring exchange interaction. We also provide additional qualitative arguments to intuitively understand the compensation mechanism in the iDMRG quantum phase diagrams. This mechanism for stabilization can potentially be useful for the experimental realization of quantum spin liquids.

cond-mat.str-el↗

arXiv2023

Electric field control of a quantum spin liquid in weak Mott insulators

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to onsite Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$ that can difficultly be tuned with external stimuli. One approach to address this problem is applying a DC electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$. Through density matrix renormalization group calculations, we compute the ground state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.

cond-mat.str-el↗

arXiv2023

Quantum impurity model for two-stage multipolar ordering and Fermi surface reconstruction

Classification and understanding of quantum phase transitions and critical phenomena in itinerant electron systems are outstanding questions in quantum materials research. Recent experiments on heavy fermion systems with higher-rank multipolar local moments provide a new platform to study such questions. In particular, experiments on $\text{Ce}_{3}\text{Pd}_{20}\text{(Si,Ge)}_{6}$ show novel quantum critical behaviors via two consecutive magnetic field-driven quantum phase transitions. At each transition, the derivative of the Hall resistivity jumps discontinuously, which was attributed to sequential Fermi surface reconstructions. Motivated by this discovery, we consider an effective quantum impurity model of itinerant electrons coupled to local dipolar, quadrupolar, and octupolar moments arising from $\text{Ce}^{3+}$ ions. Using renormalization group analyses, we demonstrate that two-stage multipolar ordering and Fermi surface reconstruction arise depending on which multipolar moments participate in the Fermi surface and which other moments are decoupled via Kondo destruction.

cond-mat.str-el↗

arXiv2023

Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid

Non-Hermitian physics in open quantum many-body systems provides novel opportunities for the discovery of exotic quantum phenomena unexpected in Hermitian systems. A previous study of the non-Hermitian Kondo problem in ultracold atoms reports reversion of renormalization group flows which violates the $g$ theorem and produces an unusual quantum phase transition. In this work, we study the effect of electron-electron interactions by considering the non-Hermitian Kondo problem in a Luttinger liquid. By performing a perturbative renormalization group analysis to two-loop order, we find that the interplay between non-Hermitian Kondo couplings and electron-electron interactions can produce a pair of complex fixed points. Complex fixed points have often been discussed in an attempt to understand the extremely long correlation length of Hermitian systems with weakly first-order transitions. Here, we show that complex fixed points arise naturally and can be physically realized in open quantum systems. We discuss consequences of the complex fixed points and future directions.

cond-mat.str-el↗

arXiv2022

Non-Fermi liquid behavior and quantum criticality in cubic heavy fermion systems with non-Kramers multipolar local moments

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 competition between non-Fermi liquid states and multipolar-ordered phases induced by the RKKY interaction. We consider a local version of the corresponding Kondo lattice model, namely the Bose-Fermi Kondo model. Here, the multipolar local moments are coupled to fermionic and bosonic bath degrees of freedom representing the multipolar Kondo effect and RKKY interactions. Using a perturbative renormalization group (RG) study up to two loop order, we find critical points between non-Fermi liquid Kondo fixed points and a quadrupolar ordered fixed point. The critical points describe quantum critical behaviors at the corresponding phase transitions and can be distinguished by higher order corrections in the octupolar susceptibility that can be measured by ultrasound experiments. Our results imply the existence of a rich expansion of the phases and quantum critical behaviors in multipolar heavy fermion systems.

cond-mat.str-el↗

arXiv2021

Non-Trivial Fixed Points and Truncated SU(4) Kondo Models in a Quasi-Quartet Multipolar Quantum Impurity Problem

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 experiments on the tetragonal material YbRu$_{2}$Ge$_{2}$, which has been shown to exhibit a local moment with a quasi-fourfold degenerate ground state, we consider the Kondo effect for such a quasi-quartet multipolar impurity. In the tetragonal crystal field environment, the local moment supports dipolar, quadrupolar, and octupolar moments, which interact with conduction electrons in entangled spin and orbital states. Using renormalization group analysis, we uncover a number of emergent quantum ground states characterized by non-trivial fixed points. It is shown that these previously unidentified fixed points are described by truncated SU(4) Kondo models, where only some of the SU(4) generators (representing the impurity degrees of freedom) are coupled to conduction electrons. Such novel non-trivial fixed points are unique to the quasi-quartet multipolar impurity, reinforcing the idea that an unexplored rich diversity of phenomena may be produced by multipolar quantum impurity systems.

cond-mat.str-el↗

arXiv2021

Rise and Fall of Non-Fermi Liquid Fixed Points in Multipolar Kondo Problems

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, namely $p$-wave and $f$-wave symmetries. 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.

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