Tunable positions of Weyl nodes via magnetism and pressure in the ferromagnetic Weyl semimetal CeAlSi

The noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi with simultaneous space-inversion and time-reversal symmetry breaking provides a unique platform for exploring novel topological states. Here, by employing multiple experimental techniques, we demonstrate that ferromagnetism and pressure can serve as efficient parameters to tune the positions of Weyl nodes in CeAlSi. At ambient pressure, a magnetism-facilitated anomalous Hall/Nernst effect (AHE/ANE) is uncovered. Angle-resolved photoemission spectroscopy (ARPES) measurements demonstrated that the Weyl nodes with opposite chirality are moving away from each other upon entering the ferromagnetic phase. Under pressure, by tracing the pressure evolution of AHE and band structure, we demonstrate that pressure could also serve as a pivotal knob to tune the positions of Weyl nodes. Moreover, multiple pressure-induced phase transitions are also revealed. These findings indicate that CeAlSi provides a unique and tunable platform for exploring exotic topological physics and electron correlations, as well as catering to potential applications, such as spintronics.

In general, to attain Weyl states, space-inversion (SI) or TR symmetry should be broken, and there are a few cases in which SI and TR symmetries are simultaneously broken [1][2][3][4] .For the nonmagnetic LaAlPn, SI symmetry is naturally broken, and the system hosts two types of Weyl states (type-I and type-II) 31,32 .
Moreover, a spin Hall angle that is comparable to MTe2 (M = W, Mo) has been predicted in LaAlPn 50- 54 .More intriguingly, pressure-induced superconductivity and robust topology against pressure up to 80. 4 GPa have been uncovered in LaAlPn 55 .In contrast to LaAlPn, both SI and TR symmetries are broken in the magnetic siblings, i.e., RAlPn (R = Ce, Pr, Nd, Sm, Pn = Si, Ge), rendering them rare cases for studying novel topological properties with the simultaneous breaking of SI and TR symmetries 21,29,36,39,49,56 .
CeAlSi is a ferromagnetic Weyl semimetal with noncollinear magnetic ordering, and electrical transport measurements revealed an anisotropic AHE, a loop-shaped Hall effect (LHE) in the ferromagnetic state, and a nontrivial Berry phase 41 .Previous ARPES experiments in the paramagnetic phase unveiled surface Fermi arcs and linearly dispersing conical features that correspond to the Weyl cones, further demonstrating the existence of Weyl fermions 42 .The flat band stemming from Ce 4f electrons was also detected near Fermi level (EF), indicating that electron correlations may also play a role 42 .Scanning superconducting quantum interference device (sSQUID) and magneto-optical Kerr effect (MOKE) microscopy on CeAlSi found the presence of nontrivial chiral domain walls that contributed to the topological properties [43][44][45] .According to DFT calculations, the Weyl nodes in CeAlSi arise from the SI symmetry breaking, and the TR symmetry breaking with the inclusion of magnetism just shifts the positions of Weyl nodes in the Brillouin zone (BZ) as the ferromagnetism acts as a simple Zeeman coupling 30,41 , which lacks experimental verification.Upon compressing CeAlSi up to ~ 3 GPa, it was proposed that the electronic structure and magnetic structure of CeAlSi remain nearly unchanged, but the AHE and LHE are suppressed 45 .Nevertheless, the evolution of band structure and topology under higher pressure has not been elaborated 40,45  suggest that CeAlSi provides a unique and tunable platform to study novel topological states, the interplay between magnetism and topology, and topological properties with electron correlation effect.

Anomalous magneto-transverse transport in CeAlSi
CeAlSi crystallizes in the tetragonal structure with the space group I41md (No. 109), as shown in Fig. 1(a) 32,41 .High-quality single crystals of CeAlSi are synthesized through a flux method 32,41 .The largest natural surface is the ab plane [Supplementary Fig. 2(a)].CeAlSi possesses in-plane (the ab plane) noncollinear ferromagnetic ordering below ~ 10 K defined according to magnetization, which is also evident in resistivity [Fig.1(c)] 41 .Figure 1 According to the Mott relation, the thermoelectric signals are proportional to the derivative of the conductivities at EF 10 , which also applies to the anomalous Hall conductivity and anomalous Nernst conductivity 10,57 .Therefore, thermoelectric transport is exquisitely sensitive to the band structure and the anomalous contributions near EF.To further address the anomalous transverse transport in CeAlSi, we performed thermoelectrical transport measurements.Figure 1(g) and Supplementary Fig. 3(b) show the Nernst and magneto-Seebeck signals at selected temperatures, respectively.For Nernst signal, a spinelike profile near zero field can be seen, which maybe comes from conventional contributions as reported in Cd3As2 58 .However, for CeAlSi, the spinelike feature only appears when system enters the ferromagnetic state, implying magnetism may adjust the band structure of CeAlSi.The fieldindependent anomalous components in Nernst are evident at high fields and low temperatures.To further analyze the ANE, an empirical approach is adopted 58 : Here,    and    represent conventional and anomalous contributions, respectively.arctan (   /  ) ~    /  ] when the system enters into the regime of magnetic fluctuations, and then the ANA reaches ~ 9.5% at 7.8 K.The anomalous Nernst conductivity −xy is also calculated, which shows similar behavior, as displayed in Supplementary Fig. 3(e).We obtain the contour plots of    , −xy and dM/dH in Fig. 1(h).As mentioned above, magnetization displays a nonlinear dependence at low temperatures, and this is more evident in the dM/dH plot.Above 15 K, the magnetization is linear, while    and −xy already arise, which means that the AHE and ANE do not scale with the magnetization, and they root in topology rather than magnetism.When the system is in the vicinity of the temperature where magnetic fluctuations start to play a role,    and −xy are significantly enhanced, implying magnetism interacts with topology, and the interplay between them facilitates the anomalous magneto-transverse transport in CeAlSi.In MTMs, the coupling between magnetic configuration and external magnetic field could produce various intermediate magnetic or topological states, and hence the variation of AHE may come from these states [23][24][25][26][27][28] .
However, for CeAlSi, it was proposed that the angle between the noncollinear spins does not change with applied magnetic field up to 8 T 41 .Therefore, the enhancement of anomalous transverse transport in CeAlSi is supposed to arise from the shift of the positions of Weyl nodes rather than intermediate states.

Effect of magnetism on the electronic structure of CeAlSi revealed by ARPES
In order to directly uncover the intricate effect of ferromagnetism on the electronic properties of CeAlSi, we now conduct high-resolution ARPES measurements.In Fig. 2(a), the f-electron behavior contributed by Ce is illustrated by the resonant ARPES measurements at the N edge of the Ce element.
The resonant enhancement at ~ − 0.30 eV, corresponding to the Ce 4f 1 7/2 final state 59 , is revealed at the Ce 4d → 4f resonant photon energy of 121 eV.The core-level photoemission spectra in Fig. 2(b) show the characteristic peaks of Al-2p and Si-2p orbitals, where the coexistence of main peaks and shoulders is similar to the case in PrAlSi and SmAlSi 60 .Besides, it is also evidenced that the position of  band with respect to EF has also been adjusted via magnetism.Such an evolution of  band dispersion indicates that magnetism tune the bulk band structure of CeAlSi as well as the positions of Weyl nodes.The behavior of  is compatible with the traditional Zeeman splitting 61 , while the evolution of split  could have a more complicated origin, further studies considering the correlation effects of 4f electrons would be required.The marked temperature evolutions of  and  bands in the energy and momentum imply the intertwined magnetism and itinerant electrons.The current observations are in sharp contrast to the temperatureindependent electronic structures in ferromagnetic PrAlSi and antiferromagnetic SmAlSi, where the coupling between the spin configuration of 4f states and the conduction electrons has been suggested to be negligible 60 .Moreover, based on the previous results of magnetic RAlPn materials 38,39,42,60 , the  band is of surface origin, while the origin of  band is debated because it can be reproduced by either bulk 60 or surface 39 band calculations.With the presence of the large kz-broadening effect, we deduce that the observed  band could be contributed by both the bulk and surface features.This might be a cause of its unusual magnetic behavior.Therefore, the revealed strong interplay between the magnetism and the itinerant electrons both in the bulk and on the surface demonstrates that, among the several RAlPn compounds established thus far, CeAlSi could be the most promising platform that hosting the magnetic tunability of bulk Weyl nodes and surface Fermi arcs.The pressure evolution of TC is roughly consistent with previous reports 40,45 .Above 15.9 GPa, the resistivity shows metallic behavior.Figure 3(c) shows the Hall resistivity at 2 K at various pressures.

Pressure evolution of anomalous Hall effect and pressure-induced phase transitions in CeAlSi
With increasing pressure to 3.2 GPa, the Hall resistivity decreases slightly, followed by a slight enhancement at 5.6 GPa.Surprisingly, when the pressure reaches 8.5 GPa, the slope of the Hall resistivity changes sign abruptly, indicating a pressure-induced Lifshitz transition (discuss later).We obtain the anomalous Hall resistivity by subtracting the ordinary contribution.Upon increasing pressure,    initially decreases, which is consistent with the previous study 45 .However, beyond 1.8 GPa,    increases, reaching a maximum at 5.6 GPa.At 8.5 GPa, a sign change from positive to negative accompanied by a slight reduction in    implies that the dominant carriers change from hole to electron.Upon further compression,    decreases monotonically and then cannot be resolved above 32.5 GPa.The pressure-dependent AHA and the absolute value of anomalous Hall conductivity |   | are also calculated, as plotted in Fig. 3(g), which have a similar evolution as    in Fig. 3(d).
The anomalous Hall angles are ~ 9.0% and ~ 9.7% for 0.6 GPa and 5.6 GPa, respectively.To further shed light on the intrinsic AHE for pressurized CeAlSi, the anomalous Hall conductivity as a function of the longitudinal conductivity is summarized in Supplementary Fig. 5.For the intrinsic AHE, the anomalous Hall conductivity is independent of the longitudinal conductivity (|   |vs.  ~ constant) 10,62 .Clearly, the data adhere to the universal law both at high and ambient pressures, verifying the intrinsic nature of the AHE in CeAlSi.
The contour profiles of the derivative of the normalized resistivity with respect to temperature, the pressure evolutions of the Hall coefficient (RH), and the resistivity at 2 K are plotted in Figs.3(e-f).As may be seen, the pressure-induced Lifshitz transition seems to correspond to the evolution of magnetism.To further shed light on the transition, we calculated the magnetic moments under pressure via DFT calculations, yielding 0.8364B, 0.9657B, 0.6811B, and 0.00256B for 0, 10, 20, and 40 GPa, respectively, which is overall consistent with the experimental data.Thus, the enhancement of TC under low pressure derives from the pressure-driven enhancement of magnetic moments.Under higher pressure, the magnetic moments decrease gradually, and then disappear, leading to a magnetic phase transition from the ferromagnetic to a paramagnetic state.Since we demonstrate that magnetism has a strong impact on the evolution of band structure at ambient pressure, thus the pressure evolution of magnetic moments provides a strong hint that the Lifshitz transition arises from the coupling between the electronic band structure and magnetic configurations.
To obtain more information about the pressure-induced phase transitions, we investigate the pressure evolution of the crystal structures and electronic band structures.extracted from Rietveld refinements.The ratio of a/c is plotted in the lower panel of Fig. 4(c).As can be seen, in addition to the structural phase transition, there are two anomalies at ~ 10 GPa and ~ 20 GPa, which correspond with the pressures where the Lifshitz transition and the transition from the magnetic state to a paramagnetic state in resistivity appear, respectively.The band structures at several selected pressures are calculated, which remain overall unchanged (Supplementary Fig. 6), except that the hole pockets along the -X line become smaller with pressure and then transform to electron pockets at ~ 10 GPa [Figs.4(d-i)], which confirms the pressure-induced Lifshitz transition in CeAlSi.
This also implies that the pockets along the -X line dominate the transport behavior (the Hall coefficient under pressure changes from positive to negative) in CeAlSi.Since there is no distinct anomaly in the calculated band structures for 10 GPa and 20 GPa, the structural anomalies probably arise from magnetostriction/magnetoelastic effects that are altered by pressure 45,47 .At 0 GPa, the Weyl nodes along the -X line are located 74 meV above EF, whereas they shift to −57 meV and −78 meV below EF for 10 GPa and 20 GPa, respectively.This indicates that pressure tunes the crystal structure of CeAlSi, which consequently has an effect on the evolution of the Weyl nodes as well as in turn AHE.
Based on our calculations, we found that pressure does not change the classification of Weyl nodes, but just shifts the positions of Weyl nodes as observed in magnetism scenario (Supplementary Table 1).

Discussion
Previous high-pressure studies on CeAlSi revealed a monotonic decline of AHE and LHE with pressure up to 2.7 GPa, while the negligible pressure effect on the magnetic structure and electronic band structure implies the importance of the nontrivial domain walls for the anomalous transport behavior of CeAlSi 43,45 .Under pressure, the anomalous Hall resistivity of CeAlSi is significantly enhanced compared with that at ambient pressure.Considering that the dimensions of the sample (Supplementary Fig. 1) we used are comparable to the size of one single magnetic domain 41,44 , the magnetic texture as well as the topological properties can be affected by the domain-wall landscapes or other effects, for example, magnetostriction/magnetoelastic effects 43 .As a consequence, in addition to the tuning of the positions of Weyl nodes via pressure, the contributions to AHE from the landscapes of domain walls need to be elaborated further.Nevertheless, the pressure evolution of AHE together with band calculations provide compelling evidence for the tunability of positions of Weyl nodes via pressure.
The local 4f-moments of Ce 3+ in CeAlSi interact within the lattice, leading to a noncollinear ferromagnetic ordering 41 .ARPES experiments suggest that Ce 4f electrons could play a role in CeAlSi, although the band deriving from Ce 4f electrons is ~ 0.3 eV below EF 42 .Supplementary Fig. 8 shows the semilogarithmic plots of the resistivity above 13.2GPa.The resistivity at 15.9, 17.9 and 19.8 GPa decreases to a minimum, and then shows a −lnT dependence, characteristic of Kondo systems 63 .Below ~ 5 K, the divergence from logarithmic increase suggests the spin-compensated state or the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between magnetic impurities may play a role 64,65 .The pressure evolution of magnetic moments and AHE indicates that pressure may also tune the electron correlation effect in CeAlSi.Therefore, the amplified quantum fluctuations in CeAlSi may be recognized as the origin of novel topological states of matter and various quantum phase transitions 66 .
In Additionally, the domain-wall landscapes, magnetostriction/magnetoelastic effects, or electron correlation effect may also play a significant role in the transport behavior under pressure.These results suggest that ferromagnetic CeAlSi could serve as a fertile and tunable platform to explore novel topological states, and the interplay among magnetism, topology, and electron correlations.
During the preparation of this manuscript, we noticed that the anomalous Nernst effect with different results from ours in CeAlSi has been reported by other workers 67 .

Methods
For the growth of CeAlSi single crystals, a self-flux method was adopted, as described in the literature 32 .The as-grown single crystals were characterized by x-ray diffraction (XRD) measurements [Supplementary Fig. 2].The details of sample preparation for electrical and thermoelectrical transport measurements, high-pressure electrical transport and XRD measurements, ARPES measurements, and first-principles calculations can be found in the Supplementary Information.
. Since ferromagnetism is proposed to serve as an efficient parameter to tune the positions of Weyl nodes, therefore how and to what extent the Weyl nodes in CeAlSi evolve with pressure remains elusive.In this work, by resorting to electrical and thermoelectrical transport, ARPES, high-pressure techniques, and band calculations, we systematically study the band structure and topological properties of CeAlSi.At ambient pressure, both ANE and AHE in CeAlSi are unveiled.They arise in the paramagnetic state, and then are enhanced when temperature approaches the ferromagnetic transition temperature (TC), indicative of the interaction of magnetism and topology.The anomalous Hall conductivity (   ) and the anomalous Nernst conductivity (   ) follow the Mott relation, and the latter is the derivative of the former at EF 10,57 .When EF crosses the Weyl points,    reaches a maximum, while    peaks when EF shifts away from the Weyl points 57 .Since the TR symmetry breaking due to the inclusion of ferromagnetism in CeAlSi does not change the classification and the quantity of Weyl nodes but just shifts their positions, the enhancement of AHE/ANE may arise from the shift of the positions of Weyl nodes.The magnetic tunability of both the bulk and surface band structure of CeAlSi is unambiguously evidenced by our ARPES experiments, further illuminating that the Weyl node positions can be adjusted by magnetism.Under pressure, an enhancement and a sign change of AHE take place.Based on band calculations, we found that pressure has similar effect on Weyl nodes as magnetism.In addition, multiple pressure-induced phase transitions are discovered, i.e., a pressure-induced Lifshitz transition at ~ 10 GPa, a magnetic transition from the ferromagnetic state to a paramagnetic state beyond ~ 20 GPa, and a structural phase transition at ~ 40 GPa.These results (b) displays the calculated electronic band structure and associated Berry curvature.Figure1(d)shows the Hall resistivity of CeAlSi at different temperatures.There is a turning point at ~ 2.5 T, above which the Hall resistivity profile with a positive slope displays a linear dependence.The turning point in Hall resistivity persists up to ~ 10 K, and then broadens and shifts to higher fields.Above ~ 100 K, the Hall resistivity displays linear behavior.Figure1(e) shows the magnetization at different temperatures.The magnetization above 15 K displays a linear dependence, evidencing that CeAlSi is in the paramagnetic state.When temperature decreases below 15 K, the system approaches the regime of magnetic fluctuations, and nonlinear components start to contribute.To obtain the anomalous contributions in Hall resistivity, we subtract the linear background by adopting the expression,   =  0  +   41,45  .A unusual loop-shaped Hall effect (LHE), a hysteresis produced during the upward and downward scan of fields, is also verified in our sample [Supplementary Fig.2(c)], as reported in previous studies41,45 .The anomalous Hall resistivity at different temperatures is plotted in Supplementary Fig. 3(a).The anomalous Hall conductivity [   =    /(   2 +   2 ) ] and anomalous Hall angle [ AHA ≡ arctan (   /  ) ~    /  ,   =   /(  2 +   2 ) shown in Supplementary Fig. 2(d)] are also calculated, as shown in Fig. 1(f).The AHE (AHA) arises below ~ 100 K, and then ascends with temperature approaching the regime of magnetic fluctuations.When the system enters into the ferromagnetic state, the anomalous    and AHA not vary much.
0  ,    , , and B0 denote the amplitude of the conventional semiclassical contribution, the amplitude of the anomalous contribution, carrier mobility, and the saturation field above which a plateau appears.From the fit, the amplitude of the anomalous Nernst signal (|   |/) is extracted for low temperatures, as shown in the inset of Fig. 1(g).Upon decreasing temperature below ~ 31 K, the ANE appears and attains a plateau below 15.3 K.There is an abrupt enhancement of the anomalous Nernst angle [ANA ≡

Figure 2 (
c) presents the bulk and (001)projected surface BZs with high-symmetry points of the RAlPn family.It has been found that the ARPES intensity suffers from the large kz-broadening effect in this series of compounds reflected in the observation of similar band structure in a wide vacuum-ultraviolet photon energy range38,42,60 .The ARPES spectra would reflect the electronic states integrated over a certain kz region of the bulk BZ, therefore we use the projected 2D BZ (Γ ̅ ,  ̅ ,  ̅ ) hereafter.As shown in Fig.2(d), the overall Fermi surface (FS) topology of CeAlSi shares many similarities with those of the magnetic RAlPn compounds like PrAlSi 60 , SmAlSi39,60 , and PrAlGe38 , including the inner () and outer squarelike pockets around Γ ̅ , the dumbbell-like pockets () around  ̅ , and the ripple-shaped FS contours across the BZ boundaries.By a closer look, we notice that there are band splittings of the  and  FSs.The splitting of  FS has been previously observed in PrAlSi and SmAlSi60 , while the split  FS has not been reported before in other RAlPn materials.To study whether the band splittings are related to ferromagnetism as well as the magnetic impact on the electronic structures of CeAlSi, we then perform temperature-dependent ARPES measurements on another sample.As shown in Figs.2(e) and 2(f), compared to the other FS contours, the evolution of the  and  FSs crossing over Tc is clearly revealed.In the paramagnetic phase [Fig.2(e)], the splitting of  vanishes and the momentum splitting scale of  increases.In Figs.2(g) and 2(h), we present the near-EF band dispersions across Tc measured along cuts #a and #b [illustrated in Fig. 2(d)], respectively.It can be seen that the ferromagnetism has sizeable effect on the band structure of CeAlSi, like causing the splitting of  band [Fig.2(g)] and reducing the splitting of  band at EF [Fig.2(h)].

Figure 3 (
Figure 3(a) displays the resistivity profiles at various pressures.Under pressure, TC increases monotonically with pressure up to 13.2 GPa [Figs.3(a) and 3(b)], beyond which it cannot be resolved.

Figure 4 (
a) displays the high-pressure XRD profiles.Under pressure, the crystal structure with the space group of I41md persists up to 39.3 GPa.Upon further compression, a new diffraction peak situated at ~ 10.9 arises, indicative of a structural phase transition.The emerged high-pressure phase coexists with the I41md phase up ~ 60 GPa. Figure 4(c) shows the pressure evolution of lattice constants with respect to 1 GPa [Fig.4(b)] summary, we systematically studied the band structure and topological properties of the ferromagnetic Weyl semimetal CeAlSi through anomalous magneto-transverse transport, ARPES, and band calculations, demonstrating that the positions of Weyl nodes can be tuned via magnetism and pressure.At ambient pressure, the enhancement of AHE and ANE across TC stems from the shift of the positions of Weyl nodes.The essential role of magnetism in tuning both the bulk and surface band structure of CeAlSi is demonstrated by our ARPES experiments, distinguishing CeAlSi, which has a novel possibility for controlling the Weyl node positions by magnetism, from other magnetic RAlPn siblings established thus far.Under pressure, multiple phase transitions are discovered.High-pressure band calculations reveal that pressure could shift the positions of Weyl nodes, which agrees with the transverse transport measurements.

Figure captions Figure 1 |
Figure captionsFigure 1 | Anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in CeAlSi.a The schematic structure of CeAlSi with a noncentrosymmetric structure (space group of I41md).b Band structure and associated Berry curvature.c Longitudinal resistivity (xx) in zero field.Zero-fieldcooling (ZFC) and field-cooling (FC) magnetization as a function of temperature for CeAlSi with the magnetic field applied along the c axis.The ferromagnetic transition temperature (TC) is ~ 10.1 K defined according to magnetization.d Transverse Hall resistivity (yx) different temperatures with the magnetic field applied along the c axis. e Field dependence of magnetization at various temperatures with the magnetic field applied along the c axis.Inset shows the low-field data.f Anomalous Hall conductivity (  A ) at various temperatures.Inset displays the anomalous Hall angle (AHA).g Nernst signal normalized to the temperature at different temperatures.Inset shows the temperature dependence of the amplitude of anomalous Nernst signal normalized to the temperature (|  A |/), and the anomalous Nernst angle (ANA).h Contour plots of the   A , −xy (see Supplementary Note 3 for more details) and the derivative of magnetization (dM/dH).The background color represents the magnitude of their values.

Figure 2 |
Figure 2 | ARPES measurements of CeAlSi.a Angle-integrated photoemission spectra of CeAlSi with Ce N edge on-resonant (121 eV) and off-resonant (116 eV) photons, respectively.b Core-level photoemission spectra of CeAlSi recorded at h = 160 eV.c Sketches of 3D BZ and (001)-surface BZ for the noncentrosymmetric I41/md space group structure.d Constant-energy ARPES image of CeAlSi (h = 40 eV, CR + polarization, T = 1.4 K, sample no.S1) obtained by integrating the photoemission intensity within EF ± 20 meV.Cuts #a and #b indicate the locations of the band dispersions in g and h, respectively.e, f Constant-energy maps at EF of CeAlSi (h = 40 eV, CR + polarization, sample no.S2) taken above (13 K) and below (1.5 K) Tc, respectively.The red solid curves in d-f represent the (001)projected BZs. a (= 4.26 Å) is the in-plane lattice constant of CeAlSi.g Second derivative intensity plots of CeAlSi measured along cut #a above and below Tc, respectively.The black arrows indicate the splitting of  band below Tc. h Same as g recorded along cut #b.The red solid curves are guides to the eye for the split  bands.

Figure 3 |
Figure 3 | Pressure-induced phase transitions in CeAlSi.a Temperature dependence of longitudinal resistivity at different pressures.b Low-temperature resistivity normalized to the data at 50 K.With

Figure 4 |
Figure 4 | Pressure evolution of the crystal structure and band structure of CeAlSi.a X-ray diffraction (XRD) pattern of CeAlSi at room temperature up to 60 GPa.The ambient-pressure structure with the space group of I41md persists to ~ 39.3 GPa, beyond which a new diffraction peak emerges (marked with a dashed line and asterisk), indicating that a pressure-induced structural phase transition occurs.0 represents that the pressure inside the sample chamber is released to zero, indicating that the emerging new structural phase is unstable at ambient pressure.b The Rietveld refinement of the XRD pattern at 1.0 GPa.The refined value is RP = 2.23% with weighted profile RWP = 1.60%.The upper panel in (c) shows the pressure-dependent normalized parameters a/a0, c/c0 and V/V0 extracted from powder diffraction refinements.The lower panel in (c) shows the pressure evolution of the a/c ratio.d-fBandstructures of CeAlSi along the -W-X line for 0 GPa, 10 GPa, and 20 GPa, respectively.g-i Calculated 3-dimensional (3D) Fermi surfaces for 0 GPa, 10 GPa, and 20 GPa, respectively.The violet and dark yellow color represent electron pockets and hole pockets, respectively.At 10 GPa, pressure drives hole pockets (the red dashed circle as marked in g) into electron pockets, demonstrating the pressure-induced Lifshitz transition observed in Hall resistivity under pressure.