Quantum oscillations in monoclinic SrIrO3: non-trivial topology and strong electron correlations ina three-dimensional Dirac semimetal

Yu-Te Hsu,1, ∗ Danil Prishchenko,2 Maarten Berben,1 Matija Culo,1 Steffen Wiedmann,1 Emily C. Hunter,3

Paul Tinnemans,4 Tomohiro Takayama,5 Vladimir Mazurenko,2 Nigel E. Hussey,1, 6, † and Robin S. Perry7, 8, ‡

1High Field Magnet Laboratory (HFML-EMFL) and Institute for Molecules and Materials,Radboud University, Toernooiveld 7, 6525 ED Nijmegen, Netherlands

2Department of Theoretical Physics and Applied Mathematics,Ural Federal University, 620002 Ekaterinburg, Russia

3School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Mayfield Road, Edinburgh EH9 2TT, United Kingdom

4Department of Solid State Chemistry, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen5Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

6H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom7London Centre for Nanotechnology and Department of Physics and Astronomy,

University College London, London WC1E 6BT, United Kingdom8ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Harwell, OX11 0QX, United Kingdom

(Dated: May 11, 2021)

We report the observation of Shubnikov-de Haas oscillations in bulk single crystals of monoclinic SrIrO3

in magnetic fields up to 35 T. Analysis of the oscillations reveals a Fermi surface comprising multiple smallpockets with effective masses up to five times larger than the calculated band mass. Phase analysis of the oscil-lations indicates non-trivial topological character of the dominant orbit while ab-initio calculations reveal robustlinear band-crossings at the Brillouin zone boundary. These collective findings, coupled with knowledge of theevolution of the electronic state across the Ruddlesden-Popper iridate series, establishes monoclinic SrIrO3 as atopological semimetal on the boundary of the Mott metal-insulator transition.

Band topology and strong electron correlations representtwo of the most active research themes in quantum materi-als [1], with much attention now focused on the search fornovel physics arising from their coexistence. To date, how-ever, very few examples of correlated topological materialsare known to exist [2–5]. Among these, iridium oxides (iri-dates) have emerged as one of the most promising materialplatforms on which to investigate the interplay between spin-orbit and electron-electron interactions [6–8], due to the com-parable energy scales of spin-orbit coupling (Λ), Coulomb re-pulsion (U ) and electron bandwidth (W ) [9].

The Ruddlesden-Popper series Srn+1IrnO3n+1, for exam-ple, exhibits a plethora of intriguing properties, such as spin-orbit-coupled Mottness [10], pseudogap phenomena [11–14],odd-parity hidden order [15], and metal-insulator transitions[16–19]. The spin-orbit-coupled Jeff = 1/2 and Jeff = 3/2bands, resulting from crystal-field splitting of the eg and t2g

orbitals, are often treated as the starting point for their un-derstanding [7]. In single-layer Sr2IrO4 (n = 1), the elec-tron bandwidth of the half-filled Jeff = 1/2 band is suchthat U/W > 1, resulting in a spin-orbit-coupled Mott insula-tor. With increasing n, electron hopping (and thereby W ) in-creases while at the same time U is reduced. Bilayer Sr3Ir2O7

(n = 2), for example, is only weakly insulating [16]. Theinfinite-layer end member SrIrO3 in turn is found to be itiner-ant, though its semimetallic ground state and low carrier con-centration appear at odds with theoretical expectations of a

∗ yute.hsu@ru.nl† nigel.hussey@ru.nl‡ robin.perry@ucl.ac.uk

metallic state with a half-filled Jeff = 1/2 band and a largeFermi surface (FS).

SrIrO3 crystallizes in two polymorphs: an ambient-pressure monoclinic phase and a high-pressure orthorhom-bic phase, which is also stabilized under epitaxial strain[17, 18]. Recently, the semimetallicity of both polymorphswas proposed to have a topological origin [20–22]. Three-dimensional (3D) Dirac points are created at the Brillouinzone boundary of the non-symmorphic lattice by glide sym-metry and are protected against gapping caused by spin-orbitcoupling. This feature, coupled with their perceived prox-imity to a Mott transition, makes them attractive candidatesfor realizing a correlated topological semimetallic state. Un-til now, however, studies of their intrinsic electronic structureand properties have been restricted due to the fact that or-thorhombic SrIrO3 (o-SIO3) can only be synthesized in thin-film form [9, 17–19, 23–25]), while monoclinic SrIrO3 (m-SIO3), which can be synthesized in bulk form, has thus farremained largely unexplored.

Here, we report the determination of the full FS of m-SIO3

via the observation of Shubnikov-de Haas (SdH) oscillationsin high-quality single crystals. A number of small pock-ets are detected, in excellent agreement with first-principlesdensity-functional theory (DFT) calculations. According toDFT, the electronic band structure of m-SIO3 is found to behighly sensitive to atomic displacements, though the linear(Dirac) band-crossings at the A- and M-points in the first Bril-louin zone remain robust even in the presence of strong spin-orbit coupling. The excellent agreement between the exper-imentally determined FS and DFT confirms that these cross-ings are topologically protected. The topological characterof m-SIO3 is further revealed through the appearance of a

arX

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105.

0374

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May

202

1

2

non-trivial phase factor in the quantum oscillations. In ad-dition, the corresponding quasiparticle effective masses m∗

are found to be substantially enhanced compared to the DFTband mass. This, coupled with the observation of a linear-in-temperature (T ) component in the low-T resistivity and anenhanced Kadowaki-Woods ratio, indicates the presence ofstrong correlations. Overall, this study establishes m-SIO3

as a correlated semimetal with a symmetry-protected Diracpoint. The availability of high-quality crystals, the sensitivityof its electronic structure to small perturbations and its prox-imity to a Mott state makem-SIO3 an ideal platform on whichto explore the physics of the Mott transition in a system withtopological character.

Single crystals of m-SIO3 were grown using the fluxmethod [26] and cut into Hall bars of dimension (600×100×60) µm3. Electrical resistivity measurements were then per-formed in magnetic fields (B) up to 35 T with an ac current of3 mA applied along the [100] crystallographic a-axis. Com-plementary specific heat and magnetic susceptibility mea-surements were performed using a Physical Properties Mea-surement System by Quantum Design Inc. Finally, to assistwith the DFT band structure calculations, low-temperature (T= 13 K) structural refinement was carried out using X-raydiffraction (for full details, see Supplemental Material).

Figure 1(a) shows the field-dependent resistivity ρxx(B)curve at T = 0.36 K and θ = 83 relative to the [001]-axis(see inset to Fig. 1(a) for the experimental alignment). ClearSdH oscillations emerge above 20 T. By plotting the field-derivative dρxx/dB in Figure 1(b), the full oscillatory sig-nal becomes visible. The fast Fourier transform (FFT) spec-trum of the SdH oscillations measured at θ = 70 (an angleat which all frequencies are best-resolved) is plotted in Fig.1(c). Four distinct peaks at FSdH = 75, 422, 653, and 907 Tare clearly resolved. Each frequency FSdH is related to anextremal cross-sectional area (Ak) of the FS perpendicular tofield direction via the Onsager relation FSdH = (~/2πe)Ak.By fitting the temperature dependence of the oscillation am-plitude AFFT(T ) using the Lifshitz-Kosevich expression forthe thermal damping term [27] RT = X/ sinhX, where X= 14.69 m∗T/B, we obtain m∗ values associated with eachfrequency ranging from 1.9 to 5.8 me. Such high masses areunusual for a Dirac semimetal.

In order to understand the origin of the observed SdH os-cillations, we employed ab-initio VASP code [1] to performDFT band structure calculations using the generalized gradi-ent approximation with effects of spin-orbit coupling included(GGA+SOC; see Supplementary Material for details). Fig-ure 2 shows the calculated band structures obtained with struc-tural parameters refined at room temperature (RT) as reportedin [28], and at low-temperature (LT; 13 K) performed on ourown crystals. The RT band structure agrees well with a pre-vious report [22], with linear band-crossings near the Fermienergy EF at the M- and A-points. The LT band structure,however, reveals some marked differences..

The effects of SOC on the band structures are illustrated inFig. 2(c,d). The inclusion of SOC leads to a separation of thelow-lying bands near EF by up to ∼ 0.3 eV, though the de-generacy at the M- and A-points remain unchanged. The re-

Bθc

ba

0 10 20 30

60

64

68

0 500 1000 1500 20000

1

2

3

4

0 500 1000 1500 20000

1

2

3

4

4.5 K 3.2 K 2.4 K 1.3 K 0.87 K 0.46 K 0.36 K

(a)

0 1 2 3 4 5 60.0

0.5

1.0

654 T, 1.90 (3) 907 T, 2.81 (3) 422 T, 5.8 (7) 75 T, 2.0 (4)

Anorm

(arb

. uni

ts)

T (K)

FSdH, m*/me

xx (µΩ

cm

)

B (T)

T = 0.36 K = 83°

(b)

(c)

(d)

10 20 300.0

0.2

0.4

dxx

/dB

(µΩ

cm

T-1

)

B (T)

AFFT

(arb

. uni

ts)

F (T)

= 70°

653

FIG. 1. Shubnikov-de Haas oscillations in m-SIO3. (a) Electricalresistivity ρxx measured up to 35 T. Crystal structure (in conven-tional unit cell) and experimental alignment are shown in the inset.B is rotated within the a-c plane, with θ denoting the angle betweenB and [001]. (b) Field-derivative of data shown in (a). Prominentoscillations onset above 15 T. (c) Fourier spectrum of the SdH os-cillations measured at θ = 70 and indicated temperatures, after asmooth background is removed by polynomial subtraction. Four dis-tinct peaks are resolved using a field window of 18 T < B < 35 T.(d) Extraction of m∗ (see text) reveals an enhanced m∗ for all FSdH.

sultant FS from the two GGA+SOC band structures are shownin Fig. 2(e,f). While both models indicate an electron pocketat the A-point, the location and character of the other pocketsstrongly depend on the structural details. The extreme sen-sitivity of the calculated band structures with respect to theprecise atomic positions is known to be a challenging issuefor iridates [25], and the large number of inequivalent atomsinm-SIO3 further increases the technical difficulty. Neverthe-less, the linear band-crossings nearEF at the M- and A-pointsare found to be a robust feature independent of the structuraldetails, confirming their protection by the underlying latticesymmetry.

In order to identify the correct FS model from the DFT cal-culations, we compare in Fig. 3 the angular dependence ofthe observed SdH frequencies FSdH(θ) with the predictionsemerging from each model. As shown in Fig. 3(a), the fourdistinct frequency branches disperse differently with angle θand range from 50 T to 2000 T. While both models predictfour branches at most angles and an electron-pocket associ-ated with the highest frequency branch (Fig. 3(b, c)), we findbetter overall agreement with the LT-SOC model (referred toas the LT model hereafter). Importantly, the close tracking be-tween F1 and F2, the rapid increase in FSdH as θ → 0, andthe moderate variation of F3 with respect to θ are all well-reproduced in the LT model.

The rapid increase of F1,2 as B is tilted away from [100]may suggest a surface state located within the (100) plane.For such an orbit, the SdH frequency should follow a 1/ cosφ

3

-1.5

-1

-0.5

0

0.5

1

K Y M A K Q E A

E -

EF (

eV)

Γ Υ Μ Α Γ Q E A

(b)GGA + SOC LT structure

(this work)

RT - SOC

(e)

Α

Ε Q Υ

ΜΓ

LT - SOC

(f)

(d)

Γ Υ Μ Α Γ

0

0.40.2

-0.2

0

0.2

-0.2

0.4 LT (SOC)

LT (no SOC)(c)

Γ Υ Μ Α Γ

0

0.40.2

-0.2

0

0.40.2

-0.2

RT (SOC)

RT (no SOC)

-1.5

-1

-0.5

0

0.5

1

K Y M A K Q E A

E -

EF (

eV)

RT structure (Qasim et al.)

(a)GGA + SOC

Γ Υ Μ Α Γ Q E A

E -

EF

(eV

)

1.0

0

0.5

-0.5

-1.0

-1.5

FIG. 2. Electronic structure of m-SIO3 calculated by density-functional theory. (a, b) Band structures obtained using room-temperature (RT)lattice parameters [28] and low-temperature (LT) lattice parameters. High-symmetry points in the first Brillouin zone are labeled in (f). (c,d) Comparison of the RT and LT band structures with and without SOC near the Fermi energy EF. Bands that give rise to electron and holeFermi pockets are highlighted in cyan and yellow, respectively. Note band-crossings at the M- and A-points are found in both GGA+SOCresults despite the overall differences. (e, f) Corresponding Fermi surface model of the RT and LT band structures (GGA+SOC).

-90 -45 0 45 90-90 -45 0 45 900

500

1000

1500

2000

F SdH

(T)

(°)-90 -45 0 45 90

(°)

DFT-LT

(°)

DFT-RTS1S2

DFTLT-SOC

(a) (b) (c)

F1

F2

F3

F4

DFTRT-SOC

FIG. 3. Angular dependence of the observed and calculated quantumoscillation frequencies. (a) FSdH(θ) measured in two crystals S1and S2. Four distinct branches can be identified, labeled as F1 to F4.(b, c) FSdH(θ) expected from the LT and RT Fermi surface modelsas shown in Fig. 2, with the electron and hole-pockets color-codedaccordingly. Note that the y-axis for all panels is the same.

dependence as B is tilted away from the surface. We ex-amine this possibility by plotting F1,2 cosφ versus φ, whereφ = 90 − θ denotes the tilt angle between B and [100], asshown in Supplemental Material Fig. S2. We find F1,2 cosφdeviates strongly from a constant value as φ exceeds 30, in-consistent with expectations for a surface state. We thereforeconclude that all the observed pockets arise from the metallicbulk. Despite the technical challenges associated with DFTcalculations for this complex oxide, the remarkable agree-ment in the experimentally observed angular dependence ofSdH frequencies and the theoretical expectations from the LTmodel suggests that the full FS ofm-SIO3 has been accuratelydetermined by our study.

Having established the FS, we proceed to quantify thestrength of electron correlations in m-SIO3 by comparing themeasured m∗ with the calculated band masses mb. As shownin Table I, we find a substantial mass renormalization factorm∗/mb for all frequencies, ranging from 1.4 to 5.4. We notethatm∗/mb is larger for the hole pocket (F3) compared to theelectron pockets with linear band-crossings, possibly reflect-ing the different impact of correlation effects on the conven-tional and Dirac-like bands.

Further insights into the anomalous nature of the elec-tronic state in m-SIO3 can be gleaned from its transportand thermodynamic properties at low temperatures. Asshown in Supplemental Material Fig. S4, ρxx(T ) = ρ0 +A1T + A2T

2 below 15 K, where A1 = 0.1 µΩ cm K−1

and A2 = 0.048 µΩ cm K−2. The persistence ofthe T -linear term down to the lowest temperatures indi-cates the presence of low-energy (quantum) critical fluctu-ations. Given the electronic specific heat coefficient γe =4.47 (7) mJ mol−1 K−2, the Kadowaki-Woods ratio (RKW) isfound to beA2/γ

2e ≈ 2400 µΩcm K2 mol2 mJ−2 orA2/γ

2V ≈

3.5 µΩcm K2 cm6 mJ−2, where γV is the volume form of γe

[29]. These values, though high relative to other correlatedmetals [29, 30], are nonetheless consistent with theoretical es-timates derived for a 3D FS [29] (for details, see Supplemen-tal Material). This implies that enhanced electron interactionsareenhanced electron interactions are indeed responsible forthe large RKW [31] and highly renormalized m∗ in m-SIO3,presumably due to the SOC-renormalized bandwidth and/orproximity to a quantum critical point [32].

To examine the topological character of the electronicbands in m-SIO3, we extract the phase factor associated withthe dominant SdH oscillations. The Lifshitz-Kosevich expres-

4

TABLE I. FS parameters found by experiment and DFT calculations (LT model). l, m∗, and mb represents quasiparticle mean free path,effective mass, and DFT band mass, respectively. All parameters are extracted at θ = 70. Note that a reliable extraction of l associated withF4 is precluded by the dominating influence of the higher-frequency oscillations. The parameters marked by † are an average over the multiplesmall orbits (< 30 T) predicted by the DFT that cannot be resolved experimentally.

FSdH (T) FDFT (T) l (nm) m∗ (me) mb(me) m∗/mb

F1 907 462 30 ± 2 2.81 ± 0.03 1.46 1.9F2 653 410 39 ± 3 1.90 ± 0.03 1.36 1.4F3 422 318 26 ± 3 5.8 ± 0.7 1.07 5.4F4 75 15† - 2.0 ± 0.4 1.04† 1.9†

0.03 0.04 0.05-0.04

-0.02

0.00

0.02

0.04

0 10 20 300.00

0.01

0.02

0.03

0.04

0.05

0.0 0.5 1.0

( = 1.10 ± 0.15 π)

Δxx

(µΩ

cm

)

1/B (T-1)

F2 = 653 T

Experimental dataSimulation F1 + F2 + F3

(a)Max.Min.

1/B

(T-1

)

N

N0 = 0.54 ± 0.09

(b)

FIG. 4. Phase factor of the dominant oscillation orbit. (a) SdH wave-form measured at θ = 70 (grey) and the simulation with three con-stituent frequencies F1,2,3 (black). The dominant contribution withF2 = 653 T is separately shown in blue, which is largely in-phasewith the measured waveform, with a non-trivial phase factor φ ≈ π.(b) Landau fan plot for the dominant F2 oscillations. The magneticfields which correspond to the maxima in ∆ρxx are assigned with N= integer (see text for details). A finite interceptN0 ≈ 0.5 is found inthe 1/B → 0 limit, highlighted in the inset, indicating a non-trivialtopological character. Error margins in φ and N0 reflect the standarddeviations found by varying the frequency input F2 by ± 3 T.

sion for SdH oscillations is given by [33]

∆σxx = A0B1/2RTRDRS cos

[2π

(F

B− 1

2+

λ

2π+ δ

)](1)

where A0 is a constant; RD = e−B0/B is the scatteringdamping term; RS is the spin damping term (assumed to be1); F is the SdH oscillation frequency; λ is the phase off-set, and δ is an additional factor equals to + 1

8 (− 18 ) for a

minimal (maximal) 3D Fermi surface cross-section. Sinceρxx ρyx in m-SIO3 (see Supplemental Material Fig. S1),σxx = ρxx/(ρ

2xx + ρ2

yx) ≈ 1/ρxx and Eq. 1 can be rewrittenas

∆ρxx = A′0B1/2RTRD cos

(2π(F/B) + φ

)(2)

where φ = λ + 2πδ. We fit the SdH waveform measured atθ = 70 using Eq. 2 with the experimental frequencies as in-

puts and A′0, B0, and φ as free parameters (see SupplementalMaterial for details). Note that A′0 and B0 only determine theoscillation amplitude and play no role in determining φ. Themeasured waveform is well-reproduced by a superposition ofthe three constituent oscillations, as shown in Fig. 4(a). Wefind the dominant oscillations with F2 = 653 T has a finitephase factor φ = (1.10± 0.15)π and is largely in-phase withthe measured waveform. This observation enables the extrac-tion of the zeroth Landau level index N0 by plotting the se-quence of 1/BN corresponding to the N -th maximum in ρxx(N -th minimum in σxx), known as the Landau fan plot. N0

is found to be 0.54 ± 0.09 as shown in Fig. 4(b). We notethat this analysis is limited to the F2 orbit since the other twoorbits have diminished amplitudes comparable to the noisefloor, thereby preventing a reliable extraction of the associatedphase factors. Nevertheless, we find that φ ≈ π and N0 ≈ 0.5for the F2 oscillations are highly reproducible with respect tothe fitting details (see Supplemental Material Fig. S5) and aretherefore robust features of the F2 orbit.

Conventionally, a phase factor φ ≈ π is interpreted as themanifestation of a finite geometric (Berry) phase and used asan evidence for a topologically non-trivial band [34]. How-ever, it has been recently proposed that λ comprises contri-butions from multiple origins, including orbital magnetic mo-ment, Zeeman coupling as well as geometric phase and can,in general, take a continuous value between 0 and 2π [35].Equally, it has been pointed out that under certain symmetry-imposed conditions, λ is quantized and can indeed be used toidentify the topological character of electronic bands [35, 36].In the case of m-SIO3, the nonsymmorphic lattice symmetryconstrains λ to be either 0 or π, and a finite λ = π is ex-pected for a Dirac band [35]. Our observation of a finite φ(= λ + 2πδ) ≈ π and N0 ≈ 0.5 thus provide strong evidencefor the non-trivial topological character of the associated elec-tronic band. This conclusion is further supported by the ob-served robustness of linear crossings from the DFT calcula-tions against strong spin-orbit coupling and lattice displace-ment, which is validated by the overall agreement betweenour experimental observations and theoretical calculations.

Transport signatures of Dirac quasiparticles in the closely-related iridate CaIrO3 were reported recently [37, 38] thoughthere, m∗ = 0.12 − 0.31 me, suggesting that electron corre-lations are considerably weaker in CaIrO3 than in m-SIO3. Arecent photoemission experiment on o-SIO3 thin films foundan electron-like band with linear dispersion and parabolichole-like bands with heavy quasiparticle masses m∗ = 2.4 −

5

6.0 me [23], largely in agreement with our findings on m-SIO3. Collectively, these findings identify SIO3 as a rareexample of a topological semimetal with enhanced electroncorrelations, presumably induced through proximity to a Mottinstability [9]. The extreme sensitivity of its low-energy elec-tronic structure to atomic displacement, highlighted by theDFT calculations, further identifies m-SIO3 as a viable plat-form on which to explore the Mott transition in a topologi-cal semimetal by tuning the relative strength of the electronicbandwidth and Coulomb repulsion via doping or via struc-tural tuning parameters such as hydrostatic pressure or uniax-ial strain.

We gratefully acknowledge useful discussions with A. Rostand and D. F. McMorrow. We would like to thank G. Sten-ning and D. Nye for help with the instruments in the Ma-terials Characterisation Laboratory at the ISIS Neutron andMuon Source, Kuang-Yu Samuel Chang and Roos Leenen fortechnical assistance with the DFT calculations, and SebastianBette for XRD characterizations. We acknowledge the sup-port of the HFML-Radboud University (RU)/Netherlands Or-ganisation for Scientific Research (NWO), a member of theEuropean Magnetic Field Laboratory. This work is part ofthe research program Strange Metals (Grant 16METL01) ofthe former Foundation for Fundamental Research on Matter,which is financially supported by the NWO and the EuropeanResearch Council (ERC) under the European Unions Hori-zon 2020 research and innovation programme (Grant Agree-ment No. 835279-Catch-22). We gratefully acknowledge sup-port from the UK Engineering and Physical Sciences researchcouncil, grant EP/N034694/1. The work of D. P. and V. M.was supported by Act 211 Government of the Russian Feder-ation, contract 02.A03.21.0006.

SUPPLEMENTAL MATERIAL

A. Structural parameters of monoclinic SrIrO3

Monoclinic SrIrO3 (m-SIO3) crystallizes in a distortedhexagonal perovskite structure (space group C2/c, no. 15)with nine inequivalent atoms in the unit cell. We performedlow-temperature powder X-ray diffraction (PXD) at 13 K oncrushed crystals from the same growth batch as described inthe main text. Figure S1 shows the experimental and calcu-lated spectra from our PXD measurements. The structural pa-rameters found from the published room-temperature refine-ment [28] and our low-temperature results are summarized inTable S1 and used as input for the DFT calculations.

20 25 30 35 40 45 50 55 60

2θ (˚)

100

0

20

40

60

80

20

0

-20

Experimental dataCalculationBackground

FIG. S1. Powder X-ray diffraction spectrum measured at 13 K onmonoclinic SrIrO3 from this work. The lattice parameters inferredfrom the calculation are shown in Table A. The difference betweenthe experimental and calculated spectra is shown in the lower panel.

B. Details of DFT calculations

Electronic structure calculations are carried out using ab-initio VASP code [39, 40], which is based on the densityfunctional theory in the plane-wave basis realization, withexchange-correlation part treated within GGA-PBE approx-imation. Effects of spin-orbit coupling (SOC) are included.Energy cut-off is set to 400 eV, while Brillouin zone is sam-pled by the 9 × 9 × 5 Monkhorst-Pack k-point mesh. Weuse WANNIER90 package [41] to construct the correspond-ing tight-binding (TB) Hamiltonian and ensured that the re-sulting VASP and TB electronic band structures are identicalnear the Fermi level. Smooth Fermi surfaces are generated us-ing fine 101 × 101 k-point mesh. The visualization of Fermisurfaces was done using XCrysDen code [42]. The oscilla-tion frequency expected from the DFT Fermi surface model iscalculated using the SKEAF code [43].

C. Hall resistivity and two-carrier analysis

Figure S2 shows longitudinal ρxx and Hall ρyx resistivitymeasured simultaneously at θ = 0 (B ‖ [001]). ρyx shows

6

TABLE S1. Structural parameters of monoclinic SrIrO3 from room-temperature refinement [28] and low-temperature refinement (this work).Length and angle parameters (x, y, z) correspond to the lattice constants (a, b, c) and (α, β, γ), respectively.

x y z x y zQasim et al. [28] this work

length (A) 5.60401(29) 9.6256(4) 14.1834(7) 5.58756 9.59604 14.17321angle () 90 90.232(4) 90 90 93.312 90

Sr1 0 0.0092(10) 0.25 0 0.0065(8) 0.25Sr2 0.0122(10) 0.6667(8) 0.0957(4) 0.0115(6) 0.6641(6) 0.09781(24)Ir1 0 0 0 0 0 0Ir2 0.9820(8) 0.6660(5) 0.84698(29) 0.9783(4) 0.66681(27) 0.84500(12)O1 0 0.4981(13) 0.25 0 0.4921(28) 0.25O2 0.2411(14) 0.2649(7) 0.2630(5) 0.198(7) 0.287(4) 0.2763(29)O3 0.8112(13) 0.4077(8) 0.0474(5) 0.815(4) 0.4117(23) 0.0352(14)O4 0.9407(13) 0.1344(9) 0.4087(5) 0.936(4) 0.188(3) 0.3979(16)O5 0.3238(18) 0.4204(8) 0.1058(6) 0.355(5) 0.4229(25) 0.0965(16)

pronounced non-linearity, characteristic of a multiband sys-tem. We estimate the carrier density and mobility using thetwo-carrier model:

ρxx =1

e

(nhµh + neµe) + (neµeµ2h + nhµhµ

2e)B2

(nhµh + neµe)2 + µ2hµ

2e(nh − ne)2B2

ρyx =B

e

(nhµ2h − neµ

2e) + µ2

hµ2e(nh − ne)B2

(nhµh + neµe)2 + µ2hµ

2e(nh − ne)2B2

(3)

where ne(nh) and µe(µh) are the density and mobility forthe electron-like (hole-like) carrier, respectively. Note that thetwo-carrier fits show a clear deviation from the experimentaldata; therefore the extracted parameters should be interpretedas order-of-magnitude estimates.

0 10 20 30

60

65

70

75

xx (µΩ

cm

)

B (T)

T = 0.36 K = 0°

yx (µΩ

cm

)ne= 4.6 x1020 cm-3

nh= 2.4 x1020 cm-3

e = 135 cm2 V-1 s-1

h = 185 cm2 V-1 s-1

-3

-2

-1

0

FIG. S2. Longitudinal resistivity ρxx and Hall resistivity ρyx mea-sured at 0.36 K and θ = 0. Dotted lines are the simultaneous fitsmade to the experimental data using Eq. S1, with the resultant fittingparameters as shown.

D. Possibility of a surface origin for F1 and F2

We examine the possibility of a surface origin for F1,2,which appears to diverge as B rotates from [100] to [001].

Figure S3 shows F cosφ versus φ for F1 and F2, with φ =90 − θ′ denotes the tilt angle between B and [100]. Herewe allow a small offset δθ applied to θ (i.e. θ′ = θ + δθ)that minimizes F at φ = 0, to account for the possible smallmisalignment in experimental setup (δθ < 10). For a simplesurface state with a two-dimensional Fermi surface withoutwarping, F (φ) is expected to follow F/ cosφ thus F cosφ isexpected to be a constant. We find F cosφ strongly deviatesfrom a constant value as |φ| exceeds 30

for both F1 and F2,

with a marked asymmetry between positive and negative φ.These observations argue against a surface origin for F1 andF2 and indicate they arise from the metallic bulk.

-90 -60 -30 0 30 60 900

300

600

900

S1 S2

Fcos

(°)

[100] [001][001]

F1

F2

FIG. S3. F cosφ as a function of φ, which denotes the tilt anglebetween B and [100], for F1 and F2. The corresponding alignmentto crystallographic axes are shown on the top axis.

7

E. Oscillation waveform simulation and phase factorextraction

1. SdH waveform simulation

In the presence of multiple oscillation components, theoverall SdH waveform is a superposition of the individualcontributions [27]:

∆ρxx =∑i

∆ρxx,i

=∑i

(A′

0RTRD)iB1/2 cos

[2π

(Fi

B

)+ φi

],

(4)

where RD = e−B0/B is the scattering damping term and idenotes the constituent component. We decompose the mea-sured oscillation waveform by 1) fitting the experimental datawith the dominant component using (F,m∗) found from FFTanalyses and (A′0, B0, φ) as free fitting parameters; 2) sub-tracting the fitted waveform from the experimental data; 3)repeating for next dominant component. As shown in Fig. S4,the experimental data is well-reproduced by the superpositionof the three constituent oscillations (FSdH = 653, 907, and422 T) with the associated damping term B0. The carriermean-free-path is estimated using

l =π~kF

eB0, (5)

where kF =√

2eF/~ is the Fermi wavevector. The resultsare summarized in Table I in the main text.

20 25 30 35

0.00

0.05

0.10

Δxx

(µΩ

cm

)

B (T)

T = 0.36 K = 70°

422 T (B0 = 91 ± 9 T)

907 T (B0 = 116 ± 8 T)

654 T (B0 = 75 ± 5 T)

654 T + 907 T + 422 T

Experimental data

653

653

FIG. S4. Oscillatory resistivity ∆ρxx measured at T = 0.36 K andθ = 70. The experimental data (black) is well reproduced by thesuperposition (grey) of the constituent components (shown in color).

2. Reliability of phase factor extraction

We examine the robustness of the non-trivial φ extractedfor the dominant oscillations and summarize the findings inFig. S5. Although three components (F1,2,3) contribute to thewaveform, the experimental oscillation amplitude is largely

accounted for by the dominant component F2 (dashed anddotted lines in Fig. S5(a)). Moreover, the F2 oscillations arein-phase with the experimental waveform to a very high de-gree, facilitating a reliable extraction of the associated φ ≈ π.Without the inclusion of a finite φ, the simulated F2 oscil-lations are largely out-of-phase with the experimental data(Fig. S5(b)) such that no linear combinations of the remainingoscillation components with any phase factor can reproducethe experimental waveform. The impact of a variation in theinput frequency and fitting range are also examined as shownin Fig. S5(d, e). A non-trivial φ ≈ π is consistently found overa reasonable range of frequency input and field window. Wenote that the same analyses cannot be made robustly for theother contributing frequencies, given their diminished ampli-tudes compared to the noise floor. Nevertheless, we concludethat the phase factor φ and zeroth Landau level index N0 ex-tracted for the dominant F2 oscillations is robust and leaveslittle doubt for the true value of the associated φ.

650 652 654 6560

1

2

0 300 600 900 12000.0

0.5

1.0

-0.03

0.00

0.03

0.03 0.04 0.05

-0.03

0.00

0.03

25 27 29 31 33 35650

652

654

656

0.0

0.5

1.0

N0

= 1.10 ± 0.15 πN0 = 0.54 ± 0.09

(π)

F (T)A

(arb

. uni

ts)

F (T)

F2 = 653.3 ± 0.6 T18 T < B < 35 T

Experiment653 T fit ( = 1.09 ± 0.01 π)

e-B0/B e-B0/B + noise floor

Δxx

(µΩ

cm

)(a) (c)

(d)

(e)

653 T simulation( = 0)

1/B (T-1)

(b)

Bmax (T)

F 2 (T

)

0

1

2

(π)

FIG. S5. (a) Experimental SdH waveform compared with the dom-inant F2 component fitted with a finite phase factor. Dashed anddotted lines illustrate the amplitude envelopes described by an ex-ponential decay (Dingle damping term), with and without the noisecontribution, respectively. (b) Simulation of F2 oscillations withφ = 0. (c) Fourier spectrum of the oscillations shown in (a) over18 T < B < Bmax = 35 T (open symbols) and a Gaussian fit for thedominant peak (solid line), yielding F2 = 653.3 ± 0.6 T. (d) φ andN0 found by fitting the experimental waveform over the field range18 T < B < 35 T with a varied F2 input over F2 ± 3 T, i.e. 5σ asfound in (c). Colour shadings illustrate the error margins of φ andN0 given by their standard deviations. (e) φ and F2 found with vary-ing Bmax for the fitting range. For each Bmax, the Gaussian-fittedF2 within the same field window is used as input to find φ.

8

0 2 4 60.0

0.2

0.4

0.6

0 50 100 150 2000

20

40

60

0 5 10 15

50

55

60

0 150 3000

200

400

600

10-1 100 101 102 103 104 105 106

10-3

10-2

10-1

100

101

102

103

0 50 100 150 200

0.8

1.0

1.2

T (K)

dxx

/dT

(µΩ

cm

K-1

)

C/T

(mJ

mol-1

K-2

)

T 2 (K)

γe = 4.47 (7) mJ mol-1 K-2

A2 = 0.048 µΩ cm K-2

B

xx (µΩ

cm

)

0 + A2T2

0 + A1T

T (K)

(x = 0.05)(x = 0.95)

A2 (µΩ

cm

K-2

)

2e (mJ2 mol-2 K-4)

UBe13

CeCu6CeCu2Si2

LiV2O4

UPt3CeB6

UAl2

Tl2Ba2CuO6

La1.7Sr0.3CuO4

Sr2RuO4

LaxSr1-xTiO3

CaVO3

LaxSr1-xTiO3

V2O3

Na0.7CoO2

KFe2As2LiFeAs

monoclinic SrIrO3

D

m (x

10-3

em

u m

ol-1

)

T (K)

A

0 = 8.7 (2) x10-4 emu mol-1

B = 2 T

C

(a) (b)

(c)

(d)

FIG. S6. (a) Zero-field resistivity ρxx below 15 K (top) and its temperature-derivative dρxx/dT below 6 K (bottom). The T -linearity ofdρxx/dT with a finite intercept at T = 0 indicates ρxx follows the form: ρxx(T ) = ρ0 + A1T + A2T

2. Purple dashed line overlaying theexperimental data is the fit using this functional form, with the T -linear and T 2-components shown in red and blue, respectively. Inset to toppanel shows ρxx(T ) up to 300 K. (b) Specific heat plotted as C/T versus T 2 and fitted with C/T = γe + βT 2 below 10 K (blue line). (c)Magnetic susceptibility χm measured with B = 2 T applied along [001]. χm is largely T -independent down to ≈ 50K, with a constant χ0 asmarked by the gray band. Below 50 K, χm shows a small upturn, likely associated with an impurity contribution that follows a Curie-Weissbehavior. (d) Transport coefficient A2 plotted against γ2

e , known as the Kadowaki-Woods plot, for selected correlated oxides (diamonds), ironpnictides (hexagons), heavy fermion materials (circles) ([29–31] and references therein), and monoclinic SrIrO3 (elongated diamond). Redline corresponds to A2/γ

2e = 10 µΩ cm mol2 K2 mJ−6, known to describe well for many heavy fermion materials.

F. Low-temperature physical properties

1. Transport and thermodynamic data

Figure S6 shows experimental data of zero-field resistivity,specific heat, and magnetic susceptibility measured on singlecrystals from the same growth batch as described in the maintext. Collectively, they show that the electronic ground stateof m-SIO3 is a paramagnetic semimetal which can be largelydescribed as a Fermi-liquid, albeit with a small T -linear com-ponent to its low-temperature resistivity. From the transportcoefficient of the T 2-resistivity (A2) and the electronic contri-bution to specific heat (γe), we calculate the Kadowaki-Woodsratio RKW = A2/γ

2e = 2402 µΩ cm mol2 K2 mJ−6, which is

among the highest values found for a large selection of corre-lated materials [29–31]. We further calculate the Wilson ratioRW using

RW =π2k2

B

3µ0µ2B

χP

γe(6)

where χP is the Pauli susceptibility and µB is the Bohr mag-neton. Assuming χP = χ0 −χcore = 9.5× 10−4 emu mol−1

with the core contribution χcore = −0.8 × 10−4 emu mol−1

[44], we find a large RW ≈ 15 for m-SIO3. We note, how-ever, if the van Vleck contribution χVV is taken into account,

which can be as large as 10−4 emu mol−1 for iridates [45],RW may be substantially reduced, although still expected tobe greater than RW = 1 of a free electron gas.

2. Theoretical estimate of the A2 coefficient

For a single-band 3D Fermi surface, it has been derived [29]that the transport coefficient A2 is related to the volume formSommerfeld coefficient γV by

A2/γ2V =

108π4~e2k2

B

a

k6F

γV =Z

VucNAγe

(7)

where a is the geometric mean of the lattice constants; Vuc

and Z are the volume and the number of formula units perunit cell, respectively; and NA is the Avogadro’s number. Us-ing the Z = 12 and Vuc = 762 A3 for m-SIO3 [28], we findthat the corresponding A2 coefficient for the individual Fermipocket F2, F3, and F4 are 0.023, 0.51, and 1.9 µΩ cm K−2, re-spectively. Assuming the resistivity adds in parallel and there-fore 1/A2 = 1/ΣiA2i, the overall A2 is 0.022 µΩ cm K−2.This theoretical estimate of A2 shows an order-of-magnitude

9

agreement with the experimental value of 0.048 µΩ cm K−2 and demonstrates the overall consistency of our analysis.

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