Abstract
It is becoming increasingly clear that breakthrough in quantum applications necessitates materials innovation. In high demand are conductors with robust topological states that can be manipulated at will. This is what we demonstrate in the present work. We discover that the pronounced topological response of a strongly correlated “WeylKondo” semimetal can be genuinely manipulated—and ultimately fully suppressed—by magnetic fields. We understand this behavior as a Zeemandriven motion of Weyl nodes in momentum space, up to the point where the nodes meet and annihilate in a topological quantum phase transition. The topologically trivial but correlated background remains unaffected across this transition, as is shown by our investigations up to much larger fields. Our work lays the ground for systematic explorations of electronic topology, and boosts the prospect for topological quantum devices.
Similar content being viewed by others
Introduction
Key to uncovering the richness of phenomena displayed by strongly correlated electron systems and to understanding the underlying mechanisms has been the great tunability of these systems, which enabled a systematic exploration of the landscape of their lowtemperature phases^{1,2,3,4}. As an example, such studies led to the discovery that hightemperature superconductivity is in many, if not all cases an emergent phase stabilized by quantum critical fluctuations^{5,6}, and that critical electron delocalization transitions^{7,8} may play an important role therein^{9}. Such deep insight is indispensable to tailoring properties at will, and ultimately exploiting them for applications.
Electrons are strongly correlated if their mutual Coulomb repulsion reaches or exceeds the same order as their kinetic energy. In bulk materials, this regime is typically realized by means of f and/or d orbitals with a suitable strength of orbital overlap. Flat bands, renormalized by orders of magnitude compared to simple metals and pinned to the Fermi energy, can be achieved via the Kondo effect, driven by a spin exchange interaction between localized (typically 4f) and itinerant (s, p, d) electrons^{10}. Recently, it has been demonstrated that such very strongly correlated conductors may also exhibit extreme signatures of nontrivial topology^{11}. This raises the question as to whether the excellent tunability in terms of correlation physics can also be exploited to control topology per se.
Our work shows that this can indeed be achieved. Upon tuning Ce_{3}Bi_{4}Pd_{3}^{12}, a WeylKondo semimetal^{11,12,13}, by magnetic field we observe a continuous suppression of the giant topological response associated with the material’s Kondodriven Weyl nodes, and the annihilation of the nodes. This transition is characterized by the suppression of singularities in the Berry curvature instead of a Landau order parameter; as such, it is a topological quantum phase transition. An important and surprising aspect is that this transition happens in an only smoothly varying correlated background; one could instead have expected topological states to be essentially inert to tuning parameter changes. This discovery opens up a new regime in the correlation–topology interplay, and will facilitate a systematic search for new correlationdriven topological phases.
Results and discussion
Before presenting our results and explaining them in detail, we summarize the key signatures of the WeylKondo semimetal Ce_{3}Bi_{4}Pd_{3} in zero magnetic field^{11,12} (see Supplementary Note 1 for details). They are (i) an electronic specific heat coefficient ΔC/T that is linear in T^{2}, with a giant slope, evidencing ultraslow quasiparticles with linear electronic dispersion^{12}; and (ii) a giant spontaneous Hall effect as a result of Weyl nodes—sources and sinks of Berry curvature—pinned to the immediate vicinity of the Fermi level^{11}. We note that the semimetallic ground state of Ce_{3}Bi_{4}Pd_{3} is well documented (Supplementary Note 2). As will be shown in what follows, the momentumspace separation of the Weyl nodes, which are positioned in a Kondo insulating background, is successively reduced with increasing magnetic field, until the Weyl nodes meet in momentum space and annihilate. Only at considerably larger magnetic fields, the Kondo insulator gap is quenched and the system becomes a heavy fermion metal (see Supplementary Note 3 and Supplementary Fig. 2 for a cartoon of the correlated electronic bandstructure). The latter transition has also been observed in^{14}.
Figure 1 gives an overview of our electrical transport and specific heat data. Salient transport features in zero magnetic field are an electrical resistivity that increases moderately with decreasing temperature (Fig. 1a) and a linearresponse Hall coefficient with two ranges of thermally activated behavior and a saturation to a constant value at the lowest temperatures (Fig. 1b). A plausible interpretation, which will receive further support from the fielddependent data presented below, is that this behavior results from a (pseudo)gapped background density of states, within which a narrow (Kondo insulator) gap forms at lower temperatures, against which a small residual density of states associated with the Fermilevelbound Weyl nodes becomes apparent at the lowest temperatures (see cartoon in Supplementary Fig. 2). The presence of a (pseudo)gap in the noninteracting density of states is in agreement with density functional theory (DFT) calculations, although the theoretical gap size is considerably larger^{15}.
The application of magnetic fields gradually suppresses the lowtemperature resistivity upturn. This is the case until, ultimately, metallic behavior is seen, albeit with higher resistivity and a different temperature dependence than in the nonmagnetic reference compound La_{3}Bi_{4}Pd_{3} (Fig. 1a). This indicates that Kondo physics is at play even at our largest field of 37 T. Isothermal magneticfielddependent measurements of the electrical resistivity ρ_{xx}(B) (Fig. 1c) and Hall resistivity ρ_{xy}(B) (Fig. 1d) reveal that this fieldinduced transformation occurs in two stages. The signatures thereof are most pronounced in the lowesttemperature data. Here, the electrical resistivity displays a shoulder at about 9 T and a crossover to almost fieldindependent behavior at about 14 T (see arrows labeled B_{c1} and B_{c2}, respectively, and Supplementary Note 4 for further analyses). The corresponding signatures in the Hall resistivity are kinks at the same two fields. A quantitative analysis, presented further below (Fig. 2), reveals that this behavior reflects a twostage Fermi surface reconstruction at two quantum phase transitions.
We first examine the effect the magnetic field has on the material’s topological characteristics. The most direct signature is a giant spontaneous as well as eveninfield nonlinear topological Hall effect, which evidences Berry curvature singularities from Weyl nodes in close vicinity to the Fermi energy^{11}. Somewhat more indirect evidence is a temperaturedependent electronic specific heat that varies linearly in T^{3}, with a slope that even surpasses the (Debyelike) phonon contribution, and evidences linearlydispersing electronic bands with ultralow velocity^{12,13}. Together they have established the inversion symmetry (IS)broken (noncentrosymmetric and nonsymmorphic) but time reversal symmetry (TRS)preserving heavy fermion compound Ce_{3}Bi_{4}Pd_{3} as a model case of a strongly correlated topological semimetal^{11,12} (see Supplementary Note 1 for further details).
In Fig. 1e we show how isothermal eveninfield (symmetrized and corrected for contact misalignment, see Supplementary Note 6 with Supplementary Fig. 5, and Ref. 11) topological Hall resistivities \({\rho }_{{{{{{{{\rm{x}}}}}}}}y}^{{{{{{{{\rm{even}}}}}}}}}\) are successively suppressed by magnetic field. The apparent fine structure in this suppression, seen in the isotherms below 2 K, may reflect various regimes of Weyl node configurations in momentum space. Indeed, a rich sequence of Weyl node motion and annihilation under magnetic field tuning was found in Kondo model calculations on a diamond lattice^{16,17}, which is an interesting topic for further investigations. Here, we focus on the ultimate total suppression of the effect, which occurs at \({B}_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{even}}}}}}}}}\) (see arrow in Fig. 1e for the lowest temperature isotherm). Also the linearinT^{3} electronic specific heat (corresponding to an electronic specific heat coefficient ΔC/T = ΓT^{2}, see Supplementary Note 5 for details) is successively suppressed by magnetic fields, which we quantify by the parameter T_{C/T} (see arrow in Fig. 1f on the zerofield curve). Interestingly, this suppression happens at constant Γ, indicating that the shape (slope and energy) of the Weyl dispersion remains unchanged as the Weyl nodes move in momentum space. Finally, we point to another feature that accompanies these two key signatures. It appears as an anomaly in the (normal, antisymmetrized and thus oddinfield) Hall resistivity isotherms (see arrow denoting \({B}_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{odd}}}}}}}}}\) as upper end of the grey shading, marked on the lowesttemperature isotherm in Fig. 1d) and is known as the anomalous topological Hall effect in TRSbroken Weyl semimetals^{18}. It is associated with a magnetic fieldinduced eveninmomentum Berry curvature, which is in addition to the intrinsic (zerofield) oddinmomentum Berry curvature of Ce_{3}Bi_{4}Pd_{3} (see also Ref. 11).
All these results together establish that magnetic field quenches the topological response, apparently via a process that moves the Weyl nodes at equal energy in momentum space. This raises the following questions: Which mechanism underlies this effect? Does magnetic field suppress the Kondo effect just as increasing the temperature above the Kondo coherence scale does^{11}, thereby removing the correlated electrons and thus the basis for the WeylKondo semimetal formation? Or did we succeed to annihilate the Weyl nodes in an intact Kondo coherent system? The Kondolike electrical resistivity in 37 T suggests that some form of Kondo correlations persist. To show that the magnetic field indeed controls Kondodriven Weyl nodal excitations, however, what needs to be established is that the Kondo effect as realized in zero magnetic field operates over the entire field range with topological response. We now turn to the search for such evidence.
We start with a quantitative analysis of the (normal, antisymmetrized) Hall resistivity isotherms ρ_{xy}(B) of Fig. 1d. As established previously^{7}, when magnetic field drives transitions between ground states with different Fermi volumes, the resulting (finite temperature) crossovers manifest as (broadened) kinks in ρ_{xy}(B), and (broadened) steps in the differential Hall coefficient \({\tilde{R}}_{{{{{{{{\rm{H}}}}}}}}}(B)=\partial {\rho }_{xy}(B)/\partial B\). Such behavior has been observed in a number of heavy fermion metals^{7,19,20,21} driven by magnetic field across quantum critical points. From fits with a phenomenological crossover function^{7} (see Supplementary Note 7 for details) one can extract not only the \({\tilde{R}}_{{{{{{{{\rm{H}}}}}}}}}\) values associated with the different phases, but also the crossover fields B^{*} and sharpnesses, quantified by the full width at half maximum (FWHM). In Fig. 2a, b we show two representative fits, for data at 0.5 K (for which we have subtracted the abovediscussed anomalous topological Hall effect contribution) and 1.9 K, respectively. Fits of similar quality are obtained at all temperatures up to 10 K (Supplementary Fig. 6). At higher temperatures, we lose track of the twostage nature and thus this model does no longer give meaningful results. Note that anomalous (nontopological) Hall contributions and multiband effects do not play significant roles here (see Supplementary Notes 8 and 9). The temperaturedependent fit parameters are shown in Fig. 2c–f. The two crossover fields \({B}_{1}^{*}\) and \({B}_{2}^{*}\) (Fig. 2b), determined for all available isotherms, are plotted as characteristic temperatures \({T}_{1}^{*}(B)\) and \({T}_{2}^{*}(B)\) in Fig. 2c. The extrapolations to T = 0 of these curves identify B_{c1} and B_{c2} (see arrows in Fig. 2c). Both crossovers sharpen considerably with decreasing temperature (Fig. 2e, f), indicating that the phase diagram of magnetic fieldtuned Ce_{3}Bi_{4}Pd_{3} comprises three phases with distinct Fermi volumes: a phase below B_{c1} with a small holelike Fermi volume, an intermediatefield phase between B_{c1} and B_{c2} with an even smaller electronlike Fermi volume, and a highfield phase beyond B_{c2} with a much larger Fermi volume.
To understand this behavior and elucidate the character of these phases we have carried out torque magnetometry measurements. At low magnetic fields, and in particular across \({B}_{1}^{*}(T)\), no sizable torque signal is detected (Fig. 3a), thus ruling out that a magnetic phase transition occurs at this field (see Supplementary Note 10 and Supplementary Fig. 10). A pronounced torque signal appears only above about 14 T; it corresponds to the onset of nonlinearity in the magnetization^{14}. Similar behavior, albeit with a much larger magnetic field scale, is also seen in the canonical Kondo insulator Ce_{3}Bi_{4}Pt_{3}, which we have studied for comparison (Fig. 3b). The corresponding characteristics in the first and second derivative with respect to the magnetic field are a steplike increase and a maximum, respectively. For Ce_{3}Bi_{4}Pt_{3}, the step in the lowest temperature isotherm occurs at 38.9 T (blue arrow in Fig. 3c), which is close to the field where a Kondo insulator to metal transition has previously been evidenced by a jump of the Sommerfeld coefficient^{22}. The very similar feature seen for Ce_{3}Bi_{4}Pd_{3} (red urve in Fig. 3c) then suggests that also in this system a Kondo insulator to metal transition takes place, albeit at much lower fields. As characteristic field B_{τ} of this transition, which is welldefined for all isotherms, we use the middle field at half height of the second derivative curves (Fig. 3d).
We also performed temperaturedependent electrical resistivity measurements at fields around this Kondo insulator to metal transition. On the highfield side of the transition, we observe Fermi liquid behavior, ρ = ρ_{0} + AT^{2} (see Fig. 3e, bottom and left axes, for data at 15 T). This confirms that Ce_{3}Bi_{4}Pd_{3} has indeed metallized. The A coefficient measures the strength of electronic correlations. Values in the range of several μΩcm/K^{2}, as observed here, are typical of heavy fermion metals^{23} (see Supplementary Note 11 for details). Thus, the quenching of the Kondo insulator gap by the magnetic field has indeed (as already indicated by the highfield resistivity curves in Fig. 1a) still not suppressed the Kondo interaction. Thus, what happens at B_{c2} is a fieldinduced Kondo insulator to heavy fermion metal transition, which was also studied in Ref. 14. In Fig. 3f we plot the A coefficient determined also for other fields (see Supplementary Fig. 11) as function of the magnetic field. Upon approaching the transition from the highfield side, the A coefficient increases, and is well described by a divergence, A ∝ 1/(B − B_{c2}), with the critical field B_{c2} = 13.8 T from the Hall resistivity analysis (see caption of Fig. 3 for details). Such behavior is known from heavy fermion metals tuned by a magnetic field to a quantum critical point (QCP)^{21,24}. In this case, also nonFermi liquid (NFL) behavior should develop^{25,26}, which we indeed observe in the form of a linearintemperature resistivity at 15 T, at temperatures above the Fermi liquid behavior seen at the lowest temperatures (Fig. 3e, top and right axes). This confirms that, at 15 T, Ce_{3}Bi_{4}Pd_{3} is slightly away from a QCP. Closer to the expected quantum critical field B_{c2}, the resistivity appears to be influenced by the nearby Kondo insulator phase, as seen by a rapid suppression of the A coefficient and a crossover to T^{2} behavior with a negative slope (Supplementary Fig. 11h), as well as an increase of the residual resistivity ρ_{0} not only towards but even across B_{c2} (Supplementary Fig. 11i). Whether these (nonmetallic) characteristics are generic to fieldinduced Kondo insulator to heavy fermion metal transitions is an interesting topic for future studies (we note that in a related pressureinduced transition in SmB_{6} no such effects were seen^{27,28}, but this may reflect the need of extending those measurements down to the temperature range of dilution refrigerators). Clearly, they do not represent normal (metallic) behavior and thus we define the upper boundary of Fermi liquid behavior T_{FL} (see arrows in Fig. 3e and Supplementary Fig. 11) only in the field range where these effects have minor influence. We conclude that a heavy Fermi liquid phase exists at fields above B_{c2}. In turn, this implies that the Kondo effect as operating at B = 0 remains intact across B_{c1}.
We are now in the position to construct a temperaturemagnetic field phase diagram that assembles the abovediscussed characteristics (Fig. 4a). At low fields, these are T_{C/T}(B), \({T}_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{even}}}}}}}}}(B)\), and \({T}_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{odd}}}}}}}}}(B)\), all denoting temperatures up to which, at a given field, a certain signature of WeylKondo semimetal behavior is detected. These scales all collapse at a critical field B_{c1} of 9 T. Importantly, the correlated background remains essentially unchanged across this field and no magnetic phase transition takes place. At high fields, we plot the scales T_{τ}(B) and T_{FL}(B) associated with the torque anomaly and Fermi liquid behavior, respectively, and also include the inverse of the Fermi liquid resistivity coefficient, 1/A, which hits zero at the effective mass divergence. In addition, we show the \({T}_{1}^{*}(B)\) and \({T}_{2}^{*}(B)\) scales extracted from our quantitative Hall resistivity analysis. Note that all these temperature scales are crossovers; they do not represent phase boundaries in the thermodynamic sense as none of the phases is associated with an order parameter.
In Fig. 4b we plot the charge carrier concentration n (in units of carriers per Ce atom) of the three phases, extracted in a singleband model from the lowesttemperature values of the differential Hall coefficients (Fig. 2d). It changes from about 0.01 holes below B_{c1}, via 0.007 electrons between B_{c1} and B_{c2}, to 0.18 electrons beyond B_{c2}. The 25fold increase across B_{c2} is independent evidence for the abovediscussed Kondo insulator to heavy fermion metal transition. The more modest reduction of the absolute value of the carrier concentration across B_{c1} indicates a Fermi surface reconstruction that involves only a fraction of momentum space. The annihilation and associated gappingout of Weyl nodes is exactly such a phenomenon. Also the sign change of n across B_{c1} can be understood in this scenario (see Supplementary Note 12 and Supplementary Fig. 12). That n is field independent below B_{c1} (as seen from the linearinfield behavior of the Hall resistivity in this regime, Fig. 2b) confirms that magnetic field moves the Weyl nodes at constant energy. The only process that can then remove them is their mutual annihilation, which we thus propose to happen at B_{c1}. Importantly, this takes place in a background of unchanged symmetry and with the Kondo effect continuing to operate. In other words, we have realized a controlled suppression of the Kondodriven topological semimetal. A corollary is that we have isolated the tuning of topology from the tuning of correlation physics as such.
In Fig. 4c we summarize these findings in a schematic zerotemperature phase diagram. The lowfield phase is a WeylKondo semimetal (WKSM)^{11,12,13} that, as evidenced here, consists of Weyl nodes situated within the narrow energy gap of a Kondo insulator. As function of magnetic field a sequence of two Fermi volumechanging quantum phase transitions is observed. At B_{c1}, all signatures of the WeylKondo semimetal disappear as the Weyl nodes annihilate in a topological quantum phase transition. At B_{c2}, the Kondo insulator with gappedout Weyl nodes (denoted by the symbol Δ) transforms into a heavy fermion (HF) metal, in a transition that displays signatures of quantum criticality and must thus be at least nearly continuous.
This raises the question of why the phenomena of genuine topology tuning and Weyl node annihilation have remained elusive in the much more extensively studied noninteracting regime^{29}? A magnetic field can either act on the spin (via the Zeeman effect) or the charge of an electron (via the orbital effect). In Kondo systems the former dominates, in highmobility semimetals the latter. The momentum space motion of Weyl nodes requires sizable Zeeman coupling^{16,17}. In its absence^{30}, fielddriven changes of topological signatures^{31,32} can arise from orbital effects such as the tunneling between zeroth Landau level states of adjacent Weyl nodes^{31}, at finite Weyl node separation. Of course, also changes in a material’s broken symmetry state can be accompanied by changes of topology^{33}, but this is not the topic of interest to us here (see Supplementary Notes 13 and 14 for further details).
In summary, we have demonstrated the genuine control of Weyl nodes, with clarity and ease. The clarity is attributed to the fact that in Ce_{3}Bi_{4}Pd_{3} the Weyl nodes form within a (strongly correlated, Kondo insulating) gapped state and are positioned in close vicinity of the Fermi energy. Because topologically trivial states are gapped out, there is no need to disentangle Weyl fermions from topologically trivial carriers, which hampers the field of weakly interacting Weyl semimetals. The ease of control—namely that a rather modest field of 9 T was not only enough to manipulate the positions of the Weyl nodes in momentum space, but even drive their annihilation—shows that the wellknown excellent tunability of (topologically trivial) strongly correlated electron systems^{1,2,3,4} holds also for topological features in such systems. As such, our study lays the ground for establishing a global phase diagram for strongly correlated topological materials. Key open questions to address include whether the phases and transitions discovered here exist also in other materials and are thus universal, and whether quantum criticality plays an important role in stabilizing them. The latter is hinted at by recent inelastic neutron scattering experiments^{34}.
Our findings may also guide investigations in related materials classes. Much effort is currently devoted to artificial materials such as twisted bilayer systems where correlations can be enhanced via a moiré potential^{35,36,37,38}. Additional tuning knobs in such heterostructures are the dielectric displacement and electrostatic doping, which may become powerful if further advances towards highly reproducible structures can be accomplished. Finally, we point to the potential of strongly correlated bulk materials such as Ce_{3}Bi_{4}Pd_{3} for quantum devices^{4,39,40,41}, where the robust and giant topological response—together with the high level of topology control demonstrated here—opens new opportunities. As an example we name microwave nonreciprocity at zero magnetic field, a key functionality needed in circuit quantum electrodynamics systems^{42}, that could be realized via the spontaneous Hall response of Ce_{3}Bi_{4}Pd_{3}.
Methods
Synthesis
Single crystals of Ce_{3}Bi_{4}Pd_{3}, Ce_{3}Bi_{4}Pt_{3}, and of the nonmagnetic reference compound La_{3}Bi_{4}Pd_{3} were grown using the flux method. For Ce_{3}Bi_{4}Pt_{3}, elementary Ce, Pt, and Bi in an atomic ratio of 1:1:7 were placed in an alumina crucible, and heated to 1100^{∘}C in a vacuumsealed quartz tube, using a box furnace. The melt was then slowly cooled to 600^{∘}C after a dwell time of 12 h at 1100^{∘}C, with a cooling rate of 1^{∘}C/h, and then left annealing for 12 h. Crystals of typically 1 mm in diameter were then extracted from the melt using a centrifuge. For Ce_{3}Bi_{4}Pd_{3} and La_{3}Bi_{4}Pd_{3}, as the primary stable phases at Bi excess are CeBi_{2}Pd and LaBi_{2}Pd, the Bi content was strongly reduced to about 1:1:1.5 (see also Ref. 12). The chemical composition and crystal structure of the samples were determined by energy dispersive xray spectroscopy and powder xray diffraction. Laue diffraction was utilized to determine the crystallographic orientation of selected samples.
Measurement setups
Highfield experiments
Magnetoresistance, Hall effect, and torque magnetization measurements in DC fields up to 37 T were performed at the HFMLEMFL facility at Nijmegen. Magnetotransport data were measured using Stanford Research SR830 lockin amplifiers, with the measured voltage signal preamplified 100 times using Princeton Applied Research lownoise transformers. Electrical contacts where made by either spot welding or gluing with silver paint 12 μm diameter gold wires to the samples in a 5wire configuration. All displayed Hall resistivity curves were obtained by the standard antisymmetrizing procedure of the resistivity \({\rho }_{xy}^{{{{{{{{\rm{meas}}}}}}}}}\) measured across the Hall contacts, i.e., \({\rho }_{xy}(B)=[{\rho }_{xy}^{{{{{{{{\rm{meas}}}}}}}}}(+B){\rho }_{xy}^{{{{{{{{\rm{meas}}}}}}}}}(B)]/2\). This cancels out both the spontaneous Hall effect (zerofield signal) and any eveninfield component. Torque and magnetization measurements in pulsed fields up to 65 T were performed at the NHMFLLANL facility at Los Alamos. Magnetization data were obtained only for Ce_{3}Bi_{4}Pt_{3}, using an extraction magnetometer and the "samplein/sampleout” technique to separate the sample signal from the background. In this case, the magnetic field was not aligned to any particular crystallographic axis. In all torque experiments, piezocantilevers were used for enhanced sensitivity. Samples were attached to the levers with Dow Corning high vacuum grease. The measured torque signal was obtained after balancing a Wheatstone bridge containing the resistance of the sample’s cantilever and a "dummy” (empty lever) resistor. Due to the small samples required for this technique, the magnetic field was initially not aligned to any particular crystallographic axis. A sample rotator was used to scan the torque signal across different orientations. In all cases, temperatures down to 0.35 K were obtained using a ^{3}He cryostat.
Lowtemperature experiments
Additional magnetoresistance, Hall effect, and specific heat measurements were obtained in Vienna using a Quantum Design Physical Property Measurement System, equipped with ^{3}He options. Lowtemperature electrical resistivity measurements down to 70 mK and in magnetic fields up to 15 T were performed in an Oxford dilution refrigerator.
Data availability
All data that are necessary to interpret, verify, and extend the presented research are contained in the main part of this article. They are provided through deposition in the repository Zenodo (https://doi.org/10.5281/zenodo.7043820).
Change history
31 October 2022
A Correction to this paper has been published: https://doi.org/10.1038/s41467022343145
References
Tokura, Y. & Nagaosa, N. Orbital physics in transitionmetal oxides. Science 288, 462 (2000).
v. Löhneysen, H., Rosch, A., Vojta, M. & Wölfle, P. Fermiliquid instabilities at magnetic quantum critical points. Rev. Mod. Phys. 79, 1015 (2007).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to hightemperature superconductivity in copper oxides. Nature 518, 179 (2015).
Paschen, S. & Si, Q. Quantum phases driven by strong correlations. Nat. Rev. Phys. 3, 9–26 (2021).
Mathur, N. et al. Magnetically mediated superconductivity in heavy fermion compounds. Nature 394, 39–43 (1998).
Michon, B. et al. Thermodynamic signatures of quantum criticality in cuprate superconductors. Nature 567, 218 (2019).
Paschen, S. et al. Halleffect evolution across a heavyfermion quantum critical point. Nature 432, 881 (2004).
Prochaska, L. et al. Singular charge fluctuations at a magnetic quantum critical point. Science 367, 285 (2020).
Badoux, S. et al. Change of carrier density at the pseudogap critical point of a cuprate superconductor. Nature 531, 210–214 (2016).
Hewson, A. C.The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1997).
Dzsaber, S. et al. Giant spontaneous Hall effect in a nonmagnetic WeylKondo semimetal. Proc. Natl. Acad. Sci. U.S.A. 118, e2013386118 (2021).
Dzsaber, S. et al. Kondo insulator to semimetal transformation tuned by spinorbit coupling. Phys. Rev. Lett. 118, 246601 (2017).
Lai, H.H., Grefe, S. E., Paschen, S. & Si, Q. WeylKondo semimetal in heavyfermion systems. Proc. Natl. Acad. Sci. USA. 115, 93 (2018).
Kushwaha, S. K. et al. Magnetic fieldtuned Fermi liquid in a Kondo insulator. Nat. Commun. 10, 5487 (2019).
Tomczak, J. M. Thermoelectricity in correlated narrowgap semiconductors. J. Phys.: Condens. Matter 30, 183001 (2018).
Grefe, S. E., Lai, H.H., Paschen, S. & Si, Q. WeylKondo semimetal: towards control of Weyl nodes. JPS Conf. Proc. 30, 011013 (2020).
Grefe, S. E., Lai, H.H., Paschen, S. & Si, Q. Extreme response of WeylKondo semimetal to Zeeman coupling. arXiv:2012.15841 (2020).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539 (2010).
Friedemann, S. et al. Fermisurface collapse and dynamical scaling near a quantumcritical point. Proc. Natl. Acad. Sci. USA. 107, 14547 (2010).
Custers, J. et al. Destruction of the Kondo effect in the cubic heavyfermion compound Ce_{3}Pd_{20}Si_{6}. Nat. Mater. 11, 189 (2012).
Martelli, V. et al. Sequential localization of a complex electron fluid. Proc. Natl. Acad. Sci. U.S.A. 116, 17701 (2019).
Jaime, M. et al. Closing the spin gap in the Kondo insulator Ce_{3}Bi_{4}Pt_{3} at high magnetic fields. Nature 405, 160 (2000).
Kadowaki, K. & Woods, S. B. Universal relationship of the resistivity and specific heat in heavyfermion compounds. Solid State Commun. 58, 507–509 (1986).
Gegenwart, P. et al. Magneticfield induced quantum critical point in YbRh_{2}Si_{2}. Phys. Rev. Lett. 89, 056402 (2002).
Si, Q., Rabello, S., Ingersent, K. & Smith, J. Locally critical quantum phase transitions in strongly correlated metals. Nature 413, 804 (2001).
Custers, J. et al. The breakup of heavy electrons at a quantum critical point. Nature 424, 524 (2003).
Gabáni, S. et al. Pressureinduced Fermiliquid behavior in the Kondo insulator SmB_{6}: Possible transition through a quantum critical point. Phys. Rev. B 67, 172406 (2003).
Zhou, Y. et al. Quantum phase transition and destruction of Kondo effect in pressurized SmB_{6}. Sci. Bull. 62, 1439 (2017).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in threedimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Baidya, S. & Vanderbilt, D. Firstprinciples theory of the Dirac semimetal Cd_{3}As_{2} under Zeeman magnetic field. Phys. Rev. B 102, 165115 (2020).
Ramshaw, B. J. et al. Quantum limit transport and destruction of the Weyl nodes in TaAs. Nat. Commun. 9, 2217 (2018).
Liang, T. et al. A pressureinduced topological phase with large Berry curvature in Pb_{1−x}Sn_{x}Te. Sci. Adv. 3 (2017).
Schoop, L. M. et al. Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe. Sci. Adv. 4, eaar2317 (2018).
Fuhrman, W. T. et al. Pristine quantum criticality in a Kondo semimetal. Sci. Adv. 7 (2021).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted doublelayer graphene. Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011).
Cao, Y. et al. Unconventional superconductivity in magicangle graphene superlattices. Nature 556, 43–50 (2018).
Choi, Y. et al. Correlationdriven topological phases in magicangle twisted bilayer graphene. Nature 589, 536–541 (2021).
Kennes, D. M. et al. Moiré heterostructures as a condensedmatter quantum simulator. Nat. Phys. 17, 155–163 (2021).
de Leon, N. P. et al. Materials challenges and opportunities for quantum computing hardware. Science 372, eabb2823 (2021).
Ball, P. Quantum materials: where many paths meet. MRS Bulletin 42, 698 (2017).
Keimer, B. & Moore, J. E. The physics of quantum materials. Nat. Phys. 13, 1045 (2017).
Viola, G. & DiVincenzo, D. P. Hall effect gyrators and circulators. Phys. Rev. X 4, 021019 (2014).
Acknowledgements
The authors wish to thank H.H. Lai, S. E. Grefe, and A. P. Higginbotham for fruitful discussions. We acknowledge support of the HFMLRU/NWOI, member of the European Magnetic Field Laboratory (EMFL). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR1157490 and DMR1644779, the State of Florida and the United States Department of Energy. M.J. acknowledges support from the US DOE Basic Energy Science project “Science at 100T”. The work in Vienna was supported by the Austrian Science Fund (I2535, S.P.; I4047, D.Z.; 29279, S.P.; I5868–FOR5249, S.P.), the European Union’s Horizon 2020 Research and Innovation Programme (824109EMP, S.P.), and the European Research Council (ERC Advanced Grant 101055088CorMeTop, S.P.). The work at Rice was in part supported by the NSF (DMR2220603, Q.S.), the AFOSR (FA95502110356, Q.S.), and the Robert A. Welch Foundation (C1411, Q.S.).
Author information
Authors and Affiliations
Contributions
S.P. designed and guided the research. X.Y. and A.P. synthesized and characterized the material. S.D., D.Z., A.M., F.W., R.M., L.T., B.V., L.E.W., and M.J. performed the highfield experiments, M.T., S.D., G.E., and D.Z. the lowtemperature experiments. S.D. analyzed the data, with contributions from D.Z., M.T., G.E., and S.P. The manuscript was written by S.P., with contributions from S.D., D.Z., and Q.S. All authors contributed to the discussion.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks Shuang Jia and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dzsaber, S., Zocco, D.A., McCollam, A. et al. Control of electronic topology in a strongly correlated electron system. Nat Commun 13, 5729 (2022). https://doi.org/10.1038/s41467022333698
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467022333698
This article is cited by

Flat bands, strange metals and the Kondo effect
Nature Reviews Materials (2024)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.