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DOE OSTI2021

Universal signatures of Dirac fermions in entanglement and charge fluctuations

We study the entanglement entropy (EE) and charge fluctuations in models where the low-energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, i.e., independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and numbers of Dirac cones, and either for strictly two-dimensional models or for a gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides nonuniversal, geometry-dependent results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Phonon dynamics in the site-disordered Kitaev spin liquid

The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), where spins fractionalize into itinerant Majorana fermions coupled to a static background of ℤ 2 gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like 𝛼−RuCl 3 . Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. As a result, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Expansive open Fermi arcs and connectivity changes induced by infrared phonons in ZrTe 5

Expansive open Fermi arcs covering most of the surface Brillouin zone (SBZ) are desirable for detection and control of many topological phenomena, but they have generally been reported for Kramers-Weyl points, or unconventional chiral fermions, pinned at time-reversal invariant momentum in chiral materials. Here using first-principles band structure calculations, we show that for conventional Weyl points in ZrTe 5 with the chirality of +1/–1 near the BZ center at general momentum induced by one of the infrared phonons—the second lowest $B_{1u}$ mode for breaking inversion symmetry—they can also form expansive open Fermi arcs across the SBZ boundary to occupy most of the SBZ when projected on the (001) surface. In this work, we reveal that such expansive open Fermi arcs are evolved from the topological surface states that connect multiple surface Dirac points on the (001) surface of the topological insulator phases without lattice distortion in ZrTe 5 . Furthermore, we find that the connectivity of the induced open Fermi arcs can be changed by the magnitude of the lattice distortion of this infrared phonon mode. Thus, we propose that using coherent optical phonons to modulate lattice parameters can offer ways to induce unique topological features including expansive open Fermi arcs and to dynamically control Fermi arc connectivity in ZrTe 5 .

36 MATERIALS SCIENCE↗

DOE OSTI2025

Ultrafast dynamics of a fermion chain in a terahertz field-driven optical cavity

In this article, we study the effect of a terahertz field-driven single cavity mode for ultrafast control of a fermion chain with dissipation-induced nonlinearity and quadratic coupling to an infrared-active phonon mode. Unlike the first-order phase transition in the nonequilibrium steady state of the system without a cavity or with a high-quality cavity, we find that a realistic dissipation in a low-quality driven cavity process prevents such a transition. Without realistic photon loss from the cavity, the transition only survives for the lower phonon-polariton branch with strong drive; a weak laser field fails to induce the phase transition and renders the polaritons symmetrical. The ability to control the phase transition is crucial for realizing strongly modulated steady states; we propose experimentally feasible regimes where this occurs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Electronic structure of the quadrupolar ordered heavy-fermion compound YbRu 2 Ge 2 measured by angle-resolved photoemission

We studied the electronic structure of the heavy-fermion compound Yb(Ru 1–x Rh x ) 2 Ge 2 with x = 0 and nominally x = 0.125 using ARPES and LDA calculations. We find a valence band structure of Yb corresponding to a noninteger valence close to 3+. The three observed crystal electric field levels with a splitting of 32 and 75 meV confirm the suggested configuration with a quasiquartet ground state. The experimentally determined band structure of the conduction electrons with predominantly Ru 4d character is well reproduced by our calculations. YbRu 2 Ge 2 undergoes a nonmagnetic phase transition into a ferroquadrupolar ordered state below 10.2 K and then to an antiferromagnetically ordered state below 6.5 K. A small hole Fermi surface shows nesting features in our calculated band structure and its size determined by ARPES is close to the magnetic ordering wave vector found in neutron scattering. The transitions are suppressed when YbRu 2 Ge 2 is doped with 12.5% Rh. In conclusion, the electron doping leads to a shift of the band structure and successive Lifshitz transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Observation of multiple nodal lines in SmSbTe

Having been a ground for various topological fermionic phases, the family of ZrSiS-type 111 materials has been under experimental and theoretical investigations. Within this family of materials, the subfamily LnSbTe (Ln = lanthanide elements) is gaining interest in recent times as the strong correlation effects and magnetism arising from the 4f electrons of the lanthanides can provide an important platform to study the link between topology, magnetism, and correlation. In this Letter, we report the systematic study of the electronic structure of SmSbTe—a member of the Ln SbTe subfamily—by utilizing angle-resolved photoemission spectroscopy in conjunction with first-principles calculations, transport, and magnetic measurements. Our experimental results identify multiple Dirac nodes forming the nodal lines along the Γ–X and Z–R directions in the bulk Brillouin zone (BZ) as predicted by our theoretical calculations. Additionally, a surface Dirac-like state is also observed at the X point of the surface BZ. Our study highlights SmSbTe as a promising candidate to understand the topological electronic structure of LnSbTe materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Kohn-Luttinger superconductivity in monolayer and bilayer semimetals with the Dirac spectrum

The effect of Coulomb interaction in an ensemble of Dirac fermions on the formation of superconducting pairing in monolayer and bilayer doped graphene is studied using the Kohn-Luttinger mechanism disregarding the Van der Waals potential of the substrate and impurities. The electronic structure of graphene is described using the Shubin-Vonsovsky model taking into account the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. The Cooper instability is determined by solving the Bethe-Saltpeter integral equation. The renormalized scattering amplitude is obtained with allowance for the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction. It plays the role of effective interaction in the Bethe-Salpeter integral equation. It is shown that the allowance for the Kohn-Luttinger renormalizations as well as intersite Coulomb interaction noticeably affects the competition between the superconducting phases with the f-wave and d + id-wave symmetries of the order parameter. It is demonstrated that the superconducting transition temperature for an idealized graphene bilayer with significant interlayer Coulomb interaction between electrons is noticeably higher than in the monolayer case.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Interplay of Kondo physics with incommensurate charge density waves in CeTe 3

CeTe 3 is a 2-dimensional (2D) Van der Waals (VdW) material with incommensurate charge density waves (CDW), extremely high transition temperature (T CDW ), and a large momentum-dependent CDW gap that leaves a significant portion of the Fermi surface intact. It is also considered to be a weak Kondo system, a property unexpected for a material with incommensurate CDW, where each atomic site is slightly different. Here, we study the properties of the CDW state in several RTe3 (R is rare earth) materials and examine the hybridization of itinerant states with the localized Ce 4f multiplet in CeTe 3 by using angle resolved photoemission spectroscopy. We find that the renormalization of the itinerant states originating from the hybridization with the deeper localized 4f states at −260 meV is k−dependent and extends to the Fermi level. As these localized states are far from the Fermi level, the observed hybridization affects the effective masses only marginally and does not lead to heavy fermions. However, since the same renormalizing mechanism normally leads to the heavy fermion physics when the localized 4f states are near the Fermi level, our observation of its strong k−dependence suggests that this could be the reason for discrepancy between the heavy masses in specific heat and light ones in Shubnikov de Haas oscillations, often observed in heavy fermions.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Physical properties of the Ce 2 M Al 7 Ge 4 heavy-fermion compounds ( M = Co , Ir , Ni , Pd )

Here, we report the synthesis, crystal structure, and characterization by means of single-crystal x-ray diffraction, neutron powder diffraction, and magnetic, thermal, and transport measurements of the new heavy-fermion compounds Ce 2 MAl 7 Ge 4 (M=Co,Ir,Ni,Pd). These compounds crystallize in a noncentrosymmetric tetragonal space group P$\bar{4}$2 1 m, consisting of layers of square nets of Ce atoms separated by Ge-Al and M-Al-Ge blocks. Ce 2 CoAl 7 Ge 4 ,Ce 2 IrAl 7 Ge 4 , and Ce 2 NiAl 7 Ge 4 order magnetically below TM=1.8, 1.6, and 0.8 K, respectively. There is no evidence of magnetic ordering in Ce 2 PdAl 7 Ge 4 down to 0.4 K. Furthermore, the small amount of entropy released in the magnetic state of Ce 2 MAl 7 Ge 4 (M = Co, Ir, Ni) and the reduced specific heat jump at T M suggest a strong Kondo interaction in these materials. Ce 2 PdAl 7 Ge 4 shows non-Fermi liquid behavior, possibly due to the presence of a nearby quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Electronic structure and relaxation dynamics in a superconducting topological material

Topological superconductors host new states of quantum matter which show a pairing gap in the bulk and gapless surface states providing a platform to realize Majorana fermions. Recently, alkaline-earth metal Sr intercalated Bi2Se3 has been reported to show superconductivity with a Tc~3K and a large shielding fraction. Here we report systematic normal state electronic structure studies of Sr0.06Bi2Se3 (Tc~2.5K) by performing photoemission spectroscopy. Using angle-resolved photoemission spectroscopy (ARPES), we observe a quantum well confined two-dimensional (2D) state coexisting with a topological surface state in Sr0.06Bi2Se3. Furthermore, our time-resolved ARPES reveals the relaxation dynamics showing different decay mechanism between the excited topological surface states and the two-dimensional states. Our experimental observation is understood by considering the intra-band scattering for topological surface states and an additional electron phonon scattering for the 2D states, which is responsible for the superconductivity. Our first-principles calculations agree with the more effective scattering and a shorter lifetime of the 2D states. In conclusion, our results will be helpful in understanding low temperature superconducting states of these topological materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Thermal and Quantum Melting Phase Diagrams for a Magnetic-Field-Induced Wigner Solid

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors ($\textit{ν}$ ≃ 1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings ($\textit{ν}$ ≃ 1/3). Here we report our measurements of the fundamental temperature vs filling phase diagram for the 2D holes’ WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs filling WS-liquid quantum melting phase diagram. In this work, we find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Dependence of the critical temperature in overdoped copper oxides on superfluid density

The physics of underdoped copper-oxide superconductors, including the pseudogap, spin and charge ordering, and their relation to superconductivity 1-3 , is intensely debated. The overdoped side is perceived as simpler, with strongly-correlated fermion physics evolving smoothly into the conventional Bardeen-Cooper-Schrieffer (BCS) behavior. Pioneering studies on a few overdoped samples 4-11 indicated that the superfluid density was much smaller than expected, but this was attributed to pair-breaking, disorder, and phase separation. Here, we test this conjecture by studying how the magnetic penetration depth λ and the phase stiffness ρs depend on temperature and doping, scanning densely the entire overdoped side of the La 2-x Sr x CuO 4 (LSCO) phase diagram. We have measured the absolute values of λ and ρs to the accuracy of ±1% in thousands of cuprate samples; the large statistics reveals clear trends and intrinsic properties. The films are quite homogeneous; variations in the critical temperature (T c ) within a film are very small (< 1 K). At every doping, ρs(T) decreases linearly with temperature. The T c (ρ s0) dependence is linear but with an offset, (T c - T 0 ) ∝ ρs0 where T0 ≈ 7 K, except very close to the origin where Tc ∝ √ρ s0. This scaling law defies the standard BCS description, posing a challenge to theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Location and thermal evolution of the pseudogap due to spin fluctuations

We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the t–t' Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use the eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state the spectral function A k (ω) of a hot fermion at a finite T is exponentially small below the energy scale Δ(T), which scales with SDW order and vanishes at the ordering temperature T N , and has a hump at a larger frequency Δ PG , comparable to the zero-temperature SDW gap Δ(T = 0). We argue that the hump, which we associate with the pseudogap, survives in some T range above T N . We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, Δ PG is weakly temperature dependent, despite the fact that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, Δ PG decreases with increasing T and eventually vanishes. Here, we further argue that a magnetic pseudogap at a finite T emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-T c cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal WTe2

A kind of topological material, the type-II Weyl semimetal, was proposed recently where the Weyl points emerge at the contact points of the electron and hole pockets, resulting in a highly tilted Weyl cone. In type-II Weyl semimetals, the Lorentz invariance is violated and a different type of Weyl fermion is generated that leads to intriguing physical properties. WTe 2 is interesting because it is predicted to be a good candidate for realizing type-II Weyl semimetals. By utilizing laser-based angle-resolved photoemission spectroscopy with high energy and momentum resolutions, we have revealed a full picture of the electronic structure of WTe 2 . A clear surface state has been identified and its connection with the bulk electronic states in the momentum and energy space shows good agreement with band structure calculations. Our results provide electronic signatures that are consistent with type-II Weyl states in WTe 2 . They lay a foundation for further investigations on the topological nature of WTe 2 and the exploration of unique phenomena and physical properties in type-II Weyl semimetals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Evolution of the propagation vector of antiferroquadrupolar phases in Ce 3 Pd 20 Si 6 under magnetic field

Hidden-order phases that occur in a number of correlated $f$-electron systems are among the most elusive states of electronic matter. Their investigations are hindered by the insensitivity of standard physical probes, such as neutron diffraction, to the order parameter that is usually associated with higher-order multipoles of the $f$ orbitals. The heavy-fermion compound Ce 3 Pd 20 Si 6 exhibits magnetically hidden order at subkelvin temperatures, known as phase II. Additionally, for magnetic field applied along the [001] cubic axis, another phase II′ was detected, but the nature of the transition from phase II to phase II′ remained unclear. Here we use inelastic neutron scattering to argue that this transition is most likely associated with a change in the propagation vector of the antiferroquadrupolar order from (111) to (100). Despite the absence of magnetic Bragg scattering in phase II′ , its ordering vector is revealed by the location of an intense magnetic soft mode at the (100) wave vector, that is orthogonal to the applied field. At the II - II′ transition, this mode softens and transforms into quasielastic and nearly Q-independent incoherent scattering, which is likely related to the non-Fermi-liquid behavior recently observed at this transition. Our experiment also reveals sharp collective excitations in the field-polarized paramagnetic phase, after phase II′ is suppressed in fields above 4 T.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets

We present that residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-Z 2 -flux variables in Kitaev models, the freezing of one set of degrees of freedom and the establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of the rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in the triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO 4 by Li et al., we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer-matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. In conclusion, we find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.

2-dimensional systems↗

DOE OSTI2022

Topological kagome magnets and superconductors

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. In conclusion, these developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗