## Introduction

Band topology and strong electron correlations represent two of the most active research themes in quantum materials1, with much attention now focused on the search for physics arising from their coexistence. To date, however, few examples of correlated topological materials are known to exist2,3,4,5. Among these, iridium oxides have emerged as one of the most promising material platforms on which to investigate the interplay between the spin-orbit and electron-electron interactions6,7,8, due to the comparable energy scales of spin-orbit coupling (Λ), Coulomb repulsion (U), and electron bandwidth (W)9.

The Ruddlesden-Popper series Srn+1IrnO3n+1, for example, exhibits a plethora of intriguing properties, such as spin-orbit-coupled Mottness10, pseudogap phenomenology11,12,13,14, odd-parity hidden order15, and metal-insulator transitions16,17,18,19. The spin-orbit-coupled Jeff = 1/2 and Jeff = 3/2 bands, resulting from crystal-field splitting of the eg and t2g orbitals, are often treated as the starting point for their understanding7. In single-layer Sr2IrO4 (n = 1), the electron bandwidth of the half-filled Jeff = 1/2 band is such that U/W > 1, resulting in a spin-orbit-coupled Mott insulator. With increasing n, electron hopping (and thereby W) increases while at the same time U is reduced. Consequently, bilayer Sr3Ir2O7 is found to be only weakly insulating16, while the infinite-layer end member SrIrO3 is itinerant, though its semimetallic ground state and low carrier concentration appear at odds with theoretical expectations of a metallic state with a half-filled Jeff = 1/2 band and a large Fermi surface. Recently, the semimetallicity of SrIrO3 was proposed to have a topological origin20,21,22.

SrIrO3 crystallizes in two polymorphs: an ambient-pressure monoclinic phase and a high-pressure orthorhombic phase, which is also stabilized under epitaxial strain17,18. Three-dimensional (3D) Dirac points are created at the zone boundary of the non-symmorphic lattice by glide symmetry and are protected against gapping caused by spin-orbit coupling. This feature, coupled with their perceived proximity to a Mott transition, makes them attractive candidates for realizing a correlated topological semimetallic state. Until now, however, studies of their intrinsic electronic structure and properties have been restricted due to the fact that orthorhombic SrIrO3 (o-SIO3) can only be synthesized in thin-film form at ambient pressure9,17,18,19,23,24,25), whereas monoclinic SrIrO3 (m-SIO3), which can be synthesized in bulk form, has thus far remained largely unexplored.

Here, we report the determination of the full Fermi surface of m-SIO3 via the observation of Shubnikov-de Haas oscillations in high-quality single crystals. A number of small pockets are detected, in excellent agreement with first-principles density-functional theory (DFT) calculations. According to DFT, the electronic band structure of m-SIO3 is found to be highly sensitive to atomic displacements, though the presence of linear (Dirac) band-crossings at the A- and M-points in the first Brillouin zone remains robust. Significantly, the experimentally determined effective masses are found to be substantially enhanced compared to the DFT band mass, signifying the presence of strong electron correlations. We find a good overall agreement between the theoretically derived angular dependence of the quantum oscillation frequencies with the experimental observation, indicating that correlation effects play only a minor role in determining the Fermi surface topology of m-SIO3. Further evidence for strong correlation effects is provided by the observation of a linear-in-temperature (T) component in the low-T resistivity, as well as an unusually large Kadowaki–Woods ratio. Overall, this study demonstrates that m-SIO3 is a rare iridate topological semimetal displaying signatures of both a correlated Fermi liquid and a non-Fermi liquid ground state, possibly linked to its proximity to a Mott transition. The availability of high-quality single crystals and the sensitivity of its electronic structure to small perturbations make m-SIO3 a promising platform on which to explore correlation-driven physics in a topological system.

## Results and discussions

### Shubnikov-de Haas oscillations

Figure 1a shows field-dependent resistivity ρxx(B) curves measured at T = 0.36 K and two angles θ = 70 and 83 relative to the [001]-axis (see inset to Fig. 1a for experimental alignment). Prominent Shubnikov-de Haas (SdH) oscillations emerge above 20 T (most evident in the θ = 83 trace). By plotting the field-derivative dρxx/dB in Fig. 1b, the full oscillatory signals become visible for both angles. The oscillation waveform at θ = 83, which consists of four oscillatory components as revealed by the fast Fourier transform (FFT) spectrum, is dominated by the FSdH = 650 T component. At θ = 70, all four constituent frequencies, with distinct peaks at FSdH = 75, 422, 653, and 907 T, can be tracked over a range of temperatures, as shown in Fig. 1c, thereby enabling a more reliable determination of the corresponding quasiparticle effective masses m*. Each frequency FSdH is related to an extremal cross-sectional area (Ak) of the Fermi surface perpendicular to the field direction via the Onsager relation FSdH = (/2πe)Ak. By fitting the T-dependence of the oscillation amplitude AFFT(T) at θ = 70 using the Lifshitz-Kosevich expression for the thermal damping term26$${R}_{T}=X/\sinh X,$$ where X = 14.69 m*T/B, we obtain m* values associated with each frequency ranging from 1.9 to 4.8 me. Such high masses are exceptional for a Dirac semimetal.

### DFT calculations

In order to understand the origin of the observed SdH oscillations, we performed DFT band structure calculations using the generalized gradient approximation with effects of spin-orbit coupling included (GGA+SOC). Figure 2 shows the calculated band structures using the structural parameters reported in27, refined at room temperature (RT), and those found on our own single crystals, refined at low temperature (LT; 13 K) (see Supplementary Methods). The RT band structure agrees well with a previous report22, with linear band-crossings near the Fermi energy ϵF at the M- and A-points. The LT band structure, however, reveals a markedly different picture, though notably the linear band-crossings at M- and A-points are still preserved.

The effects of SOC on each band structure are illustrated in Fig. 2c, d. The inclusion of SOC leads to a separation of the low-lying bands near ϵF by up to ~ 0.3 eV, while the degeneracy at the M- and A-points remains unaffected. The resultant Fermi surfaces from the two GGA+SOC band structures, shown in Fig. 2e, f, show a number of notable differences, which we attribute to the extreme sensitivity of the electronic structure of m-SIO3 with respect to the precise atomic positions—known to be a challenging issue for iridates25,28—rather than to a structural phase transition. The different types of samples used for the structural refinements—polycrystalline powder in Ref. 27 and crushed single crystals in our study—can cause minute structural differences and, in turn, lead to differences in the corresponding band structures. Nevertheless, the linear band-crossings near ϵF at the M- and A-points are found to be a robust feature independent of such structural details, confirming their protection by the underlying nonsymmorphic lattice symmetry.

In order to identify the appropriate Fermi surface model from the DFT calculations, we compare in Fig. 3 the angular dependence of the observed quantum oscillation frequencies FSdH(θ) with the predictions emerging from each model. As shown in Fig. 3a, the four distinct frequency branches disperse differently with angle θ and range from 50 to 2000 T. Overall, we find a better agreement between the experiment with the LT-SOC model (referred to as the LT model hereafter), which reproduces the close tracking between F1 and F2, the rapid increase in FSdH as θ → 0, as well as the moderate variation of F3 with respect to θ. This observation implies all the observed pockets originate from the metallic bulk. While the apparent divergence of frequencies F1,2 as B approaches [001] suggests a possible surface state originating in the (100) plane, we can exclude such a possibility by examining its precise angle dependence. For a surface orbit, the SdH frequency is expected to follow a $$1/\cos \phi$$ dependence as B is tilted at an angle ϕ away from the surface normal in which the orbit is hosted. As shown in Supplementary Fig. 3, by plotting $${F}_{1,2}\cos \phi$$ as a function of ϕ, where ϕ = 90 − θ denotes the tilt angle between B and [100], we find $${F}_{1,2}\cos \phi$$ deviates strongly from a constant value as ϕ exceeds 30, inconsistent with expectations for a surface origin. We therefore conclude that there is no surface contribution to the observed SdH frequencies. We note that the LT model underestimates the FSdH for the F1,2 branch as θ → 90, indicating the electron pocket at M-point is less elongated in reality than that illustrated in Fig. 2f, possibly due to subtle atomic displacements and/or correlation effects.

Nevertheless, despite the technical challenges associated with DFT calculations for this complex oxide, the overall agreement between the experimentally observed SdH frequencies and the theoretical expectations from the LT model suggests that the full Fermi surface of m-SIO3 has been determined by our study. The Dirac points lie ≈ 15 and 50 meV below the Fermi level at the M- and A-points, respectively, at which the band dispersion remains linear (see Fig. 2d).

### Signatures of strong electronic correlations

Having established the appropriate Fermi surface model, we proceed to quantify the extent of electron correlation in m-SIO3 by comparing the measured effective masses m* with the calculated band masses mb. Here we use the definition $${m}_{{{{\rm{b}}}}}={\hslash }^{2}(d{A}_{k}/dE){| }_{{\epsilon }_{{{{\rm{F}}}}}}$$, namely the change of area enclosed by the cyclotron orbit in k-space with respect to the change in energy at the Fermi level, to describe the band mass of quasiparticles with an arbitrary dispersion ϵ(k). As shown in Table 1, we find a substantial mass renormalization factor m*/mb for all frequencies, ranging from 1.4 to 4.5, signifying strong electron correlations. We note that m*/mb is larger for the hole pocket (F3) compared to the electron pockets with linear band-crossings, possibly reflecting the different impact of correlation effects on the conventional and Dirac-like bands.

The inclusion of U up to 3 eV in our calculations leads to a considerable modification in the Fermi surface topology, as shown in Supplementary Fig. 4. The best agreement with experiment, however, is found when U = 0, indicating that the influence of electron correlations cannot be effectively captured for complex iridates using the GGA+SOC+U approach23. A more accurate accounting of correlation effects will likely require the implementation of computationally demanding dynamical mean-field theory calculations, which will be the subject of a future investigation. Nevertheless, the remarkable agreement between the LT model and experiment demonstrates that correlation effects play only a minor role in determining the Fermi surface topology, as found for related systems such as o-SIO323 and the topological semimetal ZrSiS29.

The anomalous nature of the electronic state in m-SIO3 is revealed through its transport and thermodynamic properties at low temperatures. ρxx(T) below 15 K follows an unusual T + T2-dependence, as revealed by the finite intercept in dρxx/dT at T = 0 (Fig. 4a, b). The T-linear term A1 = 0.1 μΩ cm K−1, though small, persists down to the lowest temperatures, possibly indicating the presence of low-energy critical fluctuations. By contrast, the specific heat and magnetic susceptibility of m-SIO3, shown in Fig. 4c, d, are more characteristic of a paramagnetic Fermi-liquid state. Using the coefficient of the T2 term A2 = 0.048 μΩ cm K−2 and the electronic specific heat coefficient γ0 = 4.47 (7) mJ mol−1 K−2, the corresponding Kadowaki-Woods ratio (RKW) is found to be $${A}_{2}/{\gamma }_{0}^{2}\approx$$ 2400 μΩ cm K2 mol2 J−2 or $${A}_{2}/{\gamma }_{V}^{2}\approx$$ 3.5 μΩ cm K2 cm6 J−2, where γV is the volume form of γ030. These values, though high relative to other correlated metals30,31,32, are nonetheless consistent with theoretical estimates derived for a 3D Fermi surface30 (see Supplementary Discussion for details), implying that electron-electron scattering dominates the transport behaviour at low T. Recently, it has been shown that the strength of electron interactions correlates with RKW in the most general case32, and overall consistency in our analysis indicates that electron-electron scattering is responsible for the large RKW and the highly renormalized m* in m-SIO3, possibly due to the SOC-renormalized bandwidth and/or proximity to a quantum critical point33,34.

The topological character of the electronic bands in m-SIO3 is examined by extracting the phase factor of the SdH oscillations (see Supplementary Fig. 5). While we find a nontrivial phase factor ≈ π, as expected for a topologically nontrivial band, recent theoretical findings have suggested that the phase factor in quantum oscillations can comprise multiple contributions and therefore cannot be considered as a conclusive evidence for a nontrivial band topology35. Nonetheless, we emphasise that the topological non-trivial character for the electron band in m-SIO3 is further supported by the good agreement between the DFT calculations—with their topologically-protected Dirac points at M and A—and the observed quantum oscillation angular dependence.

Recently, transport signatures of Dirac quasiparticles have been reported in a closely-related iridate CaIrO336,37. The resultant Fermi surface areas and effective masses, however, were found to be small (FSdH = 3.2 − 11.2 T and m* = 0.12 − 0.31 me), suggesting that the Fermi level in CaIrO3 is much closer to the Dirac point and that electron correlations are considerably weaker than in m-SIO3. A recent photoemission experiment on o-SIO3 thin films, on the other hand, found an electron-like band with linear dispersion and parabolic hole-like bands with heavy quasiparticle masses m* = 2.4 − 6.0me23, largely in agreement with our findings on m-SIO3. Collectively, these findings identify SIO3 as a rare example of a topological semimetal with enhanced electron correlations, possibly induced through proximity to a Mott instability9. The extreme sensitivity of its low-energy electronic structure to atomic displacement, highlighted by the DFT calculations, further identifies m-SIO3 as a viable platform on which to explore the Mott transition in a topological semimetal, by tuning the relative strength of the electronic bandwidth and Coulomb repulsion via doping or via structural tuning parameters such as hydrostatic pressure or uniaxial strain.

## Methods

### Crystal growth and characterization

Single crystals of m-SIO3 were grown using the flux method described in Ref. 38. Low-temperature structural refinement using X-ray diffraction (XRD) was performed at 13 K (see Supplementary Methods for details).

### Measurements

Electrical resistivity measurements were performed on Hall bars of (600 × 100 × 60) μm3 in size, cut from pristine crystals, with an ac current of 3 mA applied along the bar identified as the crystallographic axis [100] by Laue XRD. Magnetic fields up to 35 T were generated using a Bitter magnet at the High Field Magnet Laboratory (HFML) in Nijmegen, the Netherlands. Zero-field resistivity measurements were performed using a Cryogenic Free Measurement System by Cryogenic Limited; specific heat and magnetic susceptibility measurements were performed using a Physical Properties Measurement System and a Magnetic Properties Measurement System XL, respectively, by Quantum Design Inc.

### Band structure calculations

DFT band structure calculations were carried out using ab-initio VASP code39 with energy cut-off set to 400 eV and Brillouin zone sampled by the 9 × 9 × 5 Monkhorst-Pack k-point mesh. We used WANNIER90 package40 to construct the corresponding tight-binding (TB) Hamiltonian and ensure that the resulting VASP and TB electronic band structures are identical near the Fermi level. The visualization of Fermi surfaces was done using XCrysDen code41 and the oscillation frequency expected from the DFT Fermi surface model was calculated using the SKEAF code42.