Quantum Critical Fluctuations Research Articles

Nuclear magnetic resonance studies in a model transverse field Ising system

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases.

Quantum critical fluctuations in a transverse-field Ising magnet

CoNb2O6 is a model system for a spin-1/2 one-dimensional (1D) transverse-field Ising magnet (TFIM) with a rather low three-dimensional (3D) Néel ordering temperature at TN=2.95 K. We studied CoNb2O6 using ultrasound measurements down to 0.3 K in transverse magnetic fields applied along the b direction. Upon entering the 3D ordered state, we observe pronounced anomalies in the transverse acoustic mode c 66. In particular, from 1.3 to 1.5 K and around 4.7 T, this mode reveals an almost diverging softening, which is considerably reduced at lower and higher magnetic fields. We interpret this as an influence of quantum critical fluctuations emerging from the quantum critical point (QCP) of the 1D Ising spin chains at about 4.75 T, which lies below the QCP of the 3D ordering at about 5.4 T. This is clear experimental evidence of the predicted generic phase diagram for a TFIM with superimposed 3D ordering.

Proximate deconfined quantum critical point in SrCu2(BO3)2.

The deconfined quantum critical point (DQCP) represents a paradigm shift in quantum matter studies, presenting a "beyond Landau" scenario for order-order transitions. Its experimental realization, however, has remained elusive. Using high-pressure 11B nuclear magnetic resonance measurements on the quantum magnet SrCu2(BO3)2, we here demonstrate a magnetic field-induced plaquette singlet to antiferromagnetic transition above 1.8 gigapascals at a notably low temperature, Tc ≃ 0.07 kelvin. First-order signatures of the transition weaken with increasing pressure, and we observe quantum critical scaling at the highest pressure, 2.4 gigapascals. Supported by model calculations, we suggest that these observations can be explained by a proximate DQCP inducing critical quantum fluctuations and emergent O(3) symmetry of the order parameters. Our findings offer a concrete experimental platform for investigation of the DQCP.

Transformer spin-triplet superconductivity at the onset of isospin order in bilayer graphene

The quest for unconventional superconductivity governed by Coulomb repulsion between electrons rather than phonon attraction received new momentum with the advent of moir\'e graphene. Initially, delineating the phonon and Coulomb-repulsion-based pairing mechanisms has proven to be a challenging task, however the situation has changed after recent discovery of superconductivity in non-twisted graphene bilayers and trilayers. Superconductivity occurring at the phase boundaries of spin and valley polarized orders calls for non-phonon scenarios, yet the specific pairing mechanisms remain to be understood. Here we analyze a striking example -- superconductivity in graphene bilayers occurring at the onset of valley-polarized order induced by a magnetic field. We describe an attraction-from-repulsion mechanism for pairing mediated by a quantum-critical mode, which fully explains the observed phenomenology. While it is usually notoriously difficult to infer the pairing mechanism from the observed superconducting phases, this case presents a rare exception, allowing for a fairly unambiguous identification of the origin of the pairing glue. A combination of factors such as the location of superconducting phase at the onset of isospin-polarized phase, a threshold in a magnetic field, above which superconductivity occurs, and its resilience at high magnetic fields paints a clear picture of a triplet superconductivity driven by quantum-critical fluctuations.

Non-Fermi liquid behavior at flat hot spots from quantum critical fluctuations at the onset of charge- or spin-density wave order

We analyze quantum fluctuation effects at the onset of charge- or spin-density wave order with a $2{k}_{F}$ wave vector $\mathbf{Q}$ in two-dimensional metals, for the special case where $\mathbf{Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergencies with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.

Propagating charge carrier plasmons in Sr2RuO4

We report on studies of charge carrier plasmon excitations in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ by transmission electron energy-loss spectroscopy. In particular, we present results on the plasmon dispersion and its width as a function of momentum transfer. The dispersion can be qualitatively explained in the framework of random phase approximation calculations, using an unrenormalized tight-binding band structure. The constant long-wavelength width of the plasmon indicates that it is caused by a decay into interband transitions and not by quantum critical fluctuations. The results from these studies on a prototypical correlated metal system show that the long-wavelength plasmon excitations near 1 eV are caused by resilient quasiparticles and are not influenced by correlation effects.

Direct measurement of the evolution of magnetism and superconductivity toward the quantum critical point

Nontrivial quantum states can be realized in the vicinity of the quantum critical point (QCP) in many strongly correlated electron systems. In particular, an emergence of unconventional superconductivity around the QCP strongly suggests that the quantum critical fluctuations play a central role in the superconducting pairing mechanism. However, a clear signature of the direct coupling between the superconducting pairing states and the quantum criticality has not yet been elucidated by the microscopic probes. Herein, we present muon spin rotation/relaxation and neutron diffraction measurements in the superconducting dome of CeCo(In1 - xZnx)5. It was found that a magnetically ordered state develops at x≥ 0.03, coexisting with the superconductivity. The magnitude of the ordered magnetic moment is continuously reduced with decreasing x, and it disappears below x∼ 0.03, indicating a second-order phase transition and the presence of the QCP at this critical Zn concentration. Furthermore, the magnetic penetration depth diverges toward the QCP. These facts provide evidence for the intimate coupling between quantum criticality and Cooper pairing.

Mott domain walls: A (strongly) non-Fermi liquid state of matter

Most Mott systems display a low-temperature phase coexistence region around the metal-insulator transition. The domain walls separating the respective phases have very recently been observed both in simulations and in experiments, displaying unusual properties. First, they often cover a significant volume fraction, thus cannot be neglected. Second, they neither resemble a typical metal nor a standard insulator, displaying unfamiliar temperature dependence of (local) transport properties. Here we take a closer look at such domain wall matter by examining an appropriate unstable solution of the Hubbard model. We show that transport in this regime is dominated by the emergence of "resilient quasiparticles" displaying strong non-Fermi liquid features, reflecting the quantum-critical fluctuations in the vicinity of the Mott point.

Tunable quantum criticalities in an isospin extended Hubbard model simulator

Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau’s framework1. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics2–22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin–valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.

Quantum critical fluctuations in an Fe-based superconductor

Quantum critical fluctuations may prove to play an instrumental role in the formation of unconventional superconductivity. Here, we show that the characteristic scaling of a marginal Fermi liquid is present in inelastic light scattering data of an Fe-based superconductor tuned through a quantum critical point (QCP) by chemical substitution or doping. From the doping dependence of the imaginary time dynamics we are able to distinguish regions dominated by quantum critical behavior from those having classical critical responses. This dichotomy reveals a connection between the marginal Fermi liquid behavior and quantum criticality. In particular, the overlap between regions of high superconducting transition temperatures and quantum critical scaling suggests a contribution from quantum fluctuations to the formation of superconductivity.

Nuclear-Order-Induced Quantum Criticality and Heavy-Fermion Superconductivity at Ultra-low Temperatures in YbRh2Si2

The tetragonal heavy-fermion metal YbRh2Si2 orders antiferromagnetically at TN = 70 mK and exhibits an unconventional quantum critical point (QCP) of Kondo-destroying type at BN = 60 mT, for the magnetic field applied within the basal (a, b) plane. Ultra-low-temperature magnetization and heat-capacity measurements at very low fields indicate that the 4f-electronic antiferromagnetic (AF) order is strongly suppressed by a nuclear-dominated hybrid order (“A-phase”) at TA ≤ 2.3 mK, such that quantum critical fluctuations develop at B ≈ 0 (Schuberth et al., Science, 2016, 351, 485–488). This enables the onset of heavy-fermion superconductivity (Tc = 2 mK) which appears to be suppressed by the primary antiferromagnetic order at elevated temperatures. Measurements of the Meissner effect reveal bulk superconductivity, with Tc decreasing under applied field to Tc < 1 mK at B > 20 mT. The observation of a weak but distinct superconducting shielding signal at a temperature as high as 10 mK suggests the formation of insulated random islands with emergent A-phase order and superconductivity. Upon cooling, the shielding signal increases almost linearly in temperature, indicating a growth of the islands which eventually percolate at T ≈ 6.5 mK. Recent electrical-resistivity results by Nguyen et al. (Nat. Commun., 2021, 12, 4341) confirm the existence of superconductivity in YbRh2Si2 at ultra-low temperatures. The combination of the results of Schuberth et al. (2016) and Nguyen et al. (2021) at ultra-low temperatures below BN, along with those previously established at higher temperatures in the paramagnetic state, provide compelling evidence that the Kondo-destruction quantum criticality robustly drives unconventional superconductivity.

Quantum-Critical Resistivity of Strange Metals in a Magnetic Field.

Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy fermions, Fe chalogenides and pnictides, Moiré bilayer graphene, and WSe_{2} is linear in temperature T as well as in the magnetic field H_{z} perpendicular to the planes. Scattering of fermions by the fluctuations of a time-reversal odd polar vector field Ω has been shown to give a linear in T resistivity and other marginal Fermi-liquid properties. An extension of this theory to an applied magnetic field is presented. A magnetic field is shown to generate a density of vortices in the field Ω proportional to H_{z}. The elastic scattering of fermions from the vortices gives a resistivity linear in H_{z} with the coefficient varying as the marginal Fermi-liquid susceptibility ln(ω_{c}/T). Quantitative comparison with experiments is presented for cuprates and Moiré bilayer graphene.

Nature of field-induced antiferromagnetic order in Zn-doped CeCoIn5 and its connection to quantum criticality in the pure compound

Quantum criticality plays an important role in the unconventional nature of superconductivity in strongly correlated electron systems. However, the intrinsic antiferromagnetic (AFM) order parameter responsible for quantum criticality has been unidentified in the prototypical unconventional superconductor ${\mathrm{CeCoIn}}_{5}$. In this work, magnetization and specific-heat measurements for $\mathrm{CeCo}{({\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x})}_{5}$ with $x\ensuremath{\le}0.07$ demonstrate that the field-induced AFM order develops with Zn doping, along with a continuous increase in its critical field up to 10 T at $x=0.07$. The weak signals associated with the AFM phase transition strongly suggest spatially inhomogeneous evolution of the AFM phase, whose feature becomes pronounced with decreasing the Zn concentration. The temperature, magnetic field, and Zn concentration phase diagram is constructed from those experimental results. It is found that, in this diagram, extrapolating the $x$ dependence of the AFM critical field yields the value of $\ensuremath{\approx}5\phantom{\rule{4pt}{0ex}}\mathrm{T}$ for $x\ensuremath{\rightarrow}0$, which coincides with the location of the quantum critical point in ${\mathrm{CeCoIn}}_{5}$. The specific heat shows $\ensuremath{-}lnT$ diverging behavior characteristic of the non-Fermi-liquid state at the AFM critical fields for all of the $x$ range. The scaling analysis for the specific-heat data above critical fields leads to continuous variations of the scaling parameters as a function of $x$. These findings provide strong evidence that the quantum critical fluctuations in ${\mathrm{CeCoIn}}_{5}$ originate from the order parameter corresponding to the field-induced AFM state observed in Zn-doped systems.

Enhanced superconductivity and ferroelectric quantum criticality in plastically deformed strontium titanate.

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach using irreversible, plastic deformation of single crystals. We show that compressive plastic deformation induces low-dimensional superconductivity well above the superconducting transition temperature (Tc) of undeformed SrTiO3, with evidence of possible superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The enhanced superconductivity is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe deformation-induced signatures of quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order using Raman scattering. Our results suggest that strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence Tc, consistent with a theory of superconductivity enhanced by soft polar fluctuations. Our results demonstrate the potential of plastic deformation and dislocation engineering for the manipulation of electronic properties of quantum materials.

Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning.

Quantum criticality may be essential to understanding a wide range of exotic electronic behavior; however, conclusive evidence of quantum critical fluctuations has been elusive in many materials of current interest. An expected characteristic feature of quantum criticality is power-law behavior of thermodynamic quantities as a function of a nonthermal tuning parameter close to the quantum critical point (QCP). Here, we observed power-law behavior of the critical temperature of the coupled nematic/structural phase transition as a function of uniaxial stress in a representative family of iron-based superconductors, providing direct evidence of quantum critical nematic fluctuations in this material. These quantum critical fluctuations are not confined within a narrow regime around the QCP but rather extend over a wide range of temperatures and compositions.

Quantum criticality in a layered iridate

Iridates provide a fertile ground to investigate correlated electrons in the presence of strong spin-orbit coupling. Bringing these systems to the proximity of a metal-insulator quantum phase transition is a challenge that must be met to access quantum critical fluctuations with charge and spin-orbital degrees of freedom. Here, electrical transport and Raman scattering measurements provide evidence that a metal-insulator quantum critical point is effectively reached in 5% Co-doped Sr2IrO4 with high structural quality. The dc-electrical conductivity shows a linear temperature dependence that is successfully captured by a model involving a Co acceptor level at the Fermi energy that becomes gradually populated at finite temperatures, creating thermally-activated holes in the Jeff = 1/2 lower Hubbard band. The so-formed quantum critical fluctuations are exceptionally heavy and the resulting electronic continuum couples with an optical phonon at all temperatures. The magnetic order and pseudospin-phonon coupling are preserved under the Co doping. This work brings quantum phase transitions, iridates and heavy-fermion physics to the same arena.

Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal

We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.

Sizable Suppression of Thermal Hall Effect upon Isotopic Substitution in SrTiO_{3}.

We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a 2 orders of magnitude difference in the thermal Hall conductivity between SrTi^{16}O_{3} and ^{18}O-enriched SrTi^{18}O_{3} samples. In most temperature ranges, the magnitude of thermal Hall conductivity (κ_{xy}) in SrTi^{18}O_{3} is proportional to the magnitude of the longitudinal thermal conductivity (κ_{xx}), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the thermal Hall angle ratio (|κ_{xy}/κ_{xx}|) shows anomalously decreasing behavior below the ferroelectric Curie temperature T_{c}∼25 K. This observation suggests a new underlying mechanism, as the conventional scenario cannot explain such differences within the slight change in phonon spectrum. Notably, the difference in magnitude of thermal Hall conductivity and rapidly decreasing thermal Hall angle ratio in SrTi^{18}O_{3} is correlated with the strength of quantum critical fluctuations in this displacive ferroelectric. This relation points to a link between the quantum critical physics of strontium titanate and its thermal Hall effect, a possible clue to explain this example of an exotic phenomenon in nonmagnetic insulating systems.

Quantum criticality in NdFe2Ga8 under magnetic field

We studied the magnetism in ${\mathrm{NdFe}}_{2}{\mathrm{Ga}}_{8}$ by magnetic susceptibility, specific heat, and resistivity measurements, which show ${\mathrm{Nd}}^{3+}$ ions forming one-dimensional chains along the $c$ axis. At zero field, two magnetic transitions are found at about 15 and 11 K. For field vertical to the $c$ axis, no significant effects on the magnetic orders are found. On the other hand, the two transitions are merged together at about 4 T for field parallel to the $c$ axis and completely suppressed at about 7 T. The suppression of the magnetic order results in quantum critical behaviors of the conventional three-dimensional spin-density-wave type, such as $\ensuremath{\rho}\ensuremath{\sim}{T}^{1.5}$ and $C/T\ensuremath{\sim}{T}^{\ensuremath{-}0.5}$. However, the temperature dependence of the resistivity is replaced by a ${T}^{0.5}$ behavior at very low temperatures for field larger than 3 T, which is attributed to the field-induced ferromagnetic moment. Our results suggest that there may be couplings between the antiferromagnetic quantum critical fluctuations and the field-induced ferromagnetic fluctuations.

Theoretical progress and material studies of heavy fermion superconductors

Heavy fermion superconductors belong to a special class of strongly correlated systems and unconventional superconductors. The emergence of superconductivity in these materials is closely associated with the presence of quantum critical fluctuations. Heavy fermion superconductors of different structures often exhibit distinct competing orders and superconducting phase diagrams, implying sensitive dependence of their electronic structures and pairing mechanism on the crystal symmetry. Here we give a brief introduction on recent theoretical and experimental progress in several different material families. We develop a new phenomenological framework of superconductivity combining the Eliashberg theory, a phenomenological form of quantum critical fluctuations, and strongly correlated band structure calculations for real materials. Our theory provides a unified way for systematic understanding of various heavy fermion superconductors.