Superlattice formation lifting degeneracy protected by non-symmorphic symmetry through a metal-insulator transition in RuAs
Hisashi Kotegawa, Keiki Takeda, Yoshiki Kuwata, Junichi Hayashi, Hideki Tou, Hitoshi Sugawara, Takahiro Sakurai, Hitoshi Ohta, Hisatomo Harima
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r APS/123-QED
Superlattice formation lifting degeneracy protected by non-symmorphic symmetrythrough a metal-insulator transition in RuAs
Hisashi Kotegawa , Keiki Takeda , Yoshiki Kuwata , Junichi Hayashi , HidekiTou , Hitoshi Sugawara , Takahiro Sakurai , Hitoshi Ohta , , and Hisatomo Harima Department of Physics, Kobe University, Kobe 658-8530, Japan Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan Research Facility Center for Science and Technology, Kobe University, Kobe, Hyogo 657-8501, Japan Molecular Photoscience Research Center, Kobe University, Kobe, Hyogo 657-8501, Japan (Dated: September 29, 2018)The single crystal of RuAs obtained by Bi-flux method shows obvious successive metal-insulatortransitions at T MI1 ∼
255 K and T MI2 ∼
195 K. The X-ray diffraction measurement reveals aformation of superlattice of 3 × × T MI2 , accompanied by a changeof the crystal system from the orthorhombic structure to the monoclinic one. Simple dimerizationof the Ru ions is nor seen in the ground state. The multiple As sites observed in nuclear quadrupoleresonance (NQR) spectrum also demonstrate the formation of the superlattice in the ground state,which is clarified to be nonmagnetic. The divergence in 1 /T at T MI1 shows that a symmetrylowering by the metal-insulator transition is accompanied by strong critical fluctuations of somedegrees of freedom. Using the structural parameters in the insulating state, the first principlecalculation reproduces successfully the reasonable size of nuclear quadrupole frequencies, ν Q forthe multiple As sites, ensuring the high validity of the structural parameters. The calculation alsogives a remarkable suppression in the density of states (DOS) near the Fermi level, although thegap opening is insufficient. A coupled modulation of the calculated Ru d electron numbers andthe crystal structure proposes a formation of charge density wave (CDW) in RuAs. Some lackingfactors remain, but it shows that a lifting of degeneracy protected by the non-symmorphic symmetrythrough the superlattice formation is a key ingredient for the metal-insulator transition in RuAs. I. INTRODUCTION
Metal-insulator transition derived by a drastic revo-lution in conductivity is an exotic phenomenon in con-densed matter physics. Except for a gap opening in-duced by strong electronic correlations, it is generally acooperative symmetry breaking brought by a couplingof the Fermi surface instability and degrees of freedomin solid, such as charge, spin, orbital, or multipole.[1–5]Symmetry of crystal is a key ingredient to understanda picture of metal-insulator transition. If material islow dimensional, typically composed of one-dimensionallinear chain, it generally possesses Fermi surface with agood nesting. It promotes a Peierls transition, opening agap at the Fermi level.[1] In case spins contribute to thePeierls transition, it is often characterized by a dimer-ization to produce a spin-singlet.[2] If material is highlysymmetric, on the other hand, the ions can be locatedunder high local symmetry, inducing the orbital degen-eracy or multipole degeneracy. A contribution of suchdegrees of freedom to a metal-insulator transition is adebate topic.[3–5]In 2012, Hirai et al. have reported that simple binaryRuP and RuAs undergo a metal-insulator transition.[6]They crystallize in the orthorhombic structure in thespace group of
P nma . The nearest-neighbor Ru ionsform a zig-zag chain along the a axis, while the secondand third nearest-neighbor Ru ions form a zig-zag lad-der along the b axis. This structure is neither a simplelow-dimensional one nor a high-symmetric one. Two suc-cessive metal-insulator transitions have been reported in the polycrystalline samples,[6] and this behavior is moreremarkable in RuP than in RuAs, and it disappears in theisostructural RuSb. For RuAs, the transition tempera-tures have been estimated to be 250 K and 190 K, whichare denoted as T MI1 and T MI2 in this paper. Interest-ingly, a Rh doping to RuAs and RuP strongly suppressesthe insulating state, and induces superconductivity.[6, 7]Intriguing question is what triggers the metal-insulatortransition of these materials. The previous band calcu-lation has suggested that the topology of Fermi surfaceis similar between RuAs and RuP, and that of RuSb dif-fers from two compounds.[8] RuAs and RuP possess thedegenerate flat bands near the Fermi level, which origi-nates mainly from the 4 d xy orbitals of Ru; therefore, itis expected that the splitting of the flat band is relatedwith the metal-insulator transition. Charge density wave(CDW) may be realized, but the nesting property of theFermi surface is not so clear, because they are not simplelow-dimensional materials. Photoemission measurementhas not detected a typical feature of a CDW transition forthe polycrystalline RuP,[9] that is, the charge distribu-tion of the Ru orbital is not clearly seen. Except for theCDW scenario, the contribution of pseudo-degeneracy ofthe d orbitals and a possibility of a spin-singlet forma-tion have been discussed,[7, 9] but a mechanism of themetal-insulator transition is still unsettled.Recently, physical properties of a single crystal of RuPmade by Sn-flux method have been reported.[10, 11] Thecrystal shows the clear successive transitions at 320 Kand 270 K, but the ground state of the single crystal ismetallic in contrast to the polycrystalline sample. Thestructural transition originating from the formation of asuperlattice has been confirmed at room temperature fora single crystal RuP,[6, 10] whereas the structure of thepolycrystalline sample at room temperature is still in theoriginal P nma .[6, 12] The formation of a superlattice isa key feature to reveal the origin of the metal-insulatortransition of these materials, but unfortunately inconsis-tency of the physical properties of RuP between singleand poly crystals complicates the problem. In this pa-per, we focus RuAs to investigate the origin of the metal-insulator transition. A single crystal of RuAs, whoseproperty is similar to the polycrystalline one, was suc-cessfully obtained using Bi-flux method.
II. EXPERIMENTAL PROCEDURE
To make the single crystal, the starting materials ofRu : As : Bi = 1 : 1 : 35 were sealed in a silica tube,and they were heated up to 1050 ◦ C, followed by a slowcooling with a rate of − ◦ C/h down to 600 ◦ C. After acentrifugation, small single crystals with a maximum longaxis of about 0.5 mm were obtained. The crystals madeby this procedure are denoted as ◦ C,and the cooling rate of − ◦ C/h. The size of crystals wassimilar between . We also triedSn-flux method, but it failed to yield single crystals ofRuAs. Very small single crystals of RuP are also obtainedusing Bi-flux method, but the resistivity does not showinsulating behavior, and the overall behavior resemblesthat of the single crystal made by Sn-flux method.[10]The electrical resistivity ( ρ ) of RuAs was measured us-ing a four-probe method, in which electrical contacts ofwire were made by a spod-weld method. The currentdirection could not be confirmed owing to the smallnessof the crystal, but it is expected to be perpendicular tothe a axis on the analogy of the Laue experiment forother crystals. The high pressure was applied by utiliz-ing an indenter-type pressure cell and Daphne7474 as apressure-transmitting medium.[13, 14] Magnetic suscep-tibility measurement was performed by utilizing a Mag-netic Property Measurement System (MPMS : QuantumDesign). X-ray diffraction measurements using a singlecrystal were made on a Rigaku Saturn724 diffractometerusing multi-layer mirror monochromated Mo-K α radia-tion. A small single crystal of 0 . × . × .
03 mmwas used for the measurement. The data were collectedto a maximum 2 θ value of ∼ ◦ with using the an-gle scans. For all structure analyses, the program suiteSHELX was used for structure solution and least-squaresrefinement.[15] Platon was used to check for missing sym-metry elements in the structures.[16] We also performednuclear quadrupole resonance (NQR) and nuclear mag-netic resonance (NMR) for RuAs using As nucleus witha nuclear spin of I = 3 /
2. Band calculations were ob- tained through a full-potential LAPW (linear augmentedplane wave) calculation within the LDA(local density ap-proximation).
III. RESULTS AND DISCUSSIONA. Resistivity, pressure effect, and magnetization
Figure 1(a) shows the temperature dependence of ρ fora single crystal RuAs. The ρ shows almost constant athigh temperatures down to T MI1 = 250 K, and possessesa clear kink at T MI1 , below which ρ starts to increase. Asharp transition appears at T MI2 = 190 K, followed by aclear insulating behavior down to the lowest temperature.As shown in the inset, the transition at T MI2 possesses ob-vious hysteresis similarly to the polycrystalline sample,[6]while hysteresis was not visible at T MI1 . The increase in ρ below T MI2 is much larger than that of the polycrystallinesample, indicating that a contribution from possible con-ductive impurities can be avoided in the measurementusing the single crystal. A fitting of the resistivity datainto a typical activation form of ρ ( T ) ∝ exp( E g / k B T )between 50 K and T MI2 = 190 K gives the energy gap of E g = 340 K. ρ deviates from the simple activation formbelow 50 K.
150 200 250 300 3500.20.30.40.5
150 200 250 3000.20.30.40.5 T MI2
RuAssingle crystal ( m c m ) T (K) T
MI1 (a) T MI1 T MI2 ( m c m ) T (K) T MI1 T MI2
T (K)(b) T MI1 T MI2 ( m c m ) T (K) FIG. 1. (color online) (a) Temperature dependence of ρ forRuAs at ambient pressure. The resistivity shows clearly twosuccessive metal-insulator transitions at T MI1 and T MI2 . Theinset shows the hysteresis behavior at T MI2 . (b) The pres-sure dependence of ρ for RuAs. Both transition temperaturesincrease with elevating pressure up to 3.34 GPa. Figure 1(b) shows the pressure variation of ρ for RuAsup to 3.34 GPa. Both T MI1 and T MI2 increase slightlywith increasing pressure. The rates were estimated tobe +3 . T MI1 and +0 . T MI2 , re-spectively. This tendency suggests that the stronger hy-bridization induced by a smaller volume stabilizes theinsulating state, consistent with that RuP is more insu-lating.
MI2
RuAs single crystal ( - e m u / m o l ) Temperature (K) T
MI1
FIG. 2. Temperature dependence of the magnetic suscepti-bility measured for many pieces of single crystals at 1 T. Twosuccessive transitions can be seen obviously. The T MI1 and T MI2 for
Figure 2 shows the temperature dependence of themagnetic susceptibility measured at 1 T on the cool-ing process. The overall behavior is similar to that ob-tained in the polycrystalline sample,[6] but the transi-tions become much sharper. The kink at T MI1 = 255K is continuous, while the discrete drop was observed at T MI2 = 200 K. The ground state is dominated by dia-magnetism as well as the polycrystalline sample.[6] Inthe metallic state, the susceptibility is temperature in-dependent, that is, Curie-Weiss like behavior is absent.Here, we used the single crystal T MI1 and T MI2 are slightly higher than those of
B. Structural analysis by X-ray diffractionmeasurement
TABLE I. Crystallographic data of RuAs for the metallic andinsulating phases.Temperature 293 K 170 KFormula RuAs Ru As Crystal system orthorhombic monoclinicSpace group
P nma (no.62) P /c (no.14) a (˚A) 5.724(3) 6.624(3) b (˚A) 3.3283(14) 18.974(7) c (˚A) 6.323(3) 8.759(4) β ( ◦ ) 90 100.843(6) V (˚A ) 120.46(10) 1082.8(8) Z R wR hk klh l (a) 293 K > T MI1 (b) 170 K < T MI2
FIG. 3. (color online) Single-crystal x-ray diffraction patternsfor RuAs at (a) 293 K and (b) 170 K. Reciprocal lattice vec-tors are shown for the orthorhombic
P nma symmetry. Thesuperlattice spots are seen below T MI2 . The new periodicitycan be regarded as 3 × ×
3, but the unit cell is found to bemonoclinic from the superlattice spots in the hk Next, we performed a structural analysis of RuAs us-ing a single crystal > T
MI1 and (b)170 K < T
MI2 . The crystal system above T MI1 was con-firmed to be orthorhombic as reported previously.[6, 17]In the insulating state below T MI2 , the superlattice spotsare clearly observed. They appear at the positions of0 k/ l/ kl plane and h/ l/ h l plane, while they are visible only at the positions of h + 1 / k + 2 / h + 2 / k + 1 / hk × ×
3, but the asymmetric arrangementof the superlattice spots for hk T MI2 is not orthorhombic but of mono-clinic; therefore, the size of the unit cell is smaller thanthat of the 3 × × T MI1 and T MI2 , on the other hand, the superlatticespots also appear (not shown), and it is likely to be in-commensurate, but a detailed structural analysis has notbeen performed successfully yet. Table I and II show the
FIG. 4. (color online) The crystal structure of RuAs in themetallic phase [(a) and (b): two unit cells are shown.], and inthe insulating phase [(c) and (d)]. The blue lines indicate theunit cell of each phase. The orthorhombic
P nma is changed tomonoclinic P /c at low temperatures, where new periodicitycan be regarded as 3 × × P nma , all the Ru ions areequivalent, and the zig-zag chain is formed by connecting thenearest-neighbor Ru ions, while two-type of chains appearin the ground state. The bond lengths of the neighboring Ruions are shown, but signatures of dimerization or trimerizationare not seen. (f) Liner-like chains of the Ru ions, which is aportion of the zig-zag ladder along the b axis in the P nma symmetry. The three-fold periodicity of the bond length isclearly observed. crystallographic data and the structural parameters forthe respective sites at 293 K and 170 K obtained by thepresent experiments and analyses described in the sec-tion of the experimental procedure. In the metallic stateabove T MI1 , the space group of
P nma and the latticeparameters are consistent with the previous reports forthe polycrystalline samples.[6, 17] As shown in Table II,the analysis suggests that a small amount of deficiencyof As is present ( ∼ P nma contains the equivalent 4 Ru and4 As atoms in the unit cell, as shown in Fig. 4(a). In theground state below T MI2 , the system transforms to themonoclinic structure in P /c , in which the inequivalent 9 Ru and 9 As sites exist, and totally 36 Ru and 36 Asatoms are included in the unit cell. Therefore, the unitcell in the insulating state is comparable to 9 unit cellsof the original structure in P nma . The c axis in P nma just corresponds to the b axis in P /c , whose length is 3times as long as the original lattice constant. As shownin the figure, the ab plane in P nma corresponds to the ac plane in P /c . The blue line in Fig. 4(d) indicates theunit cell of the monoclinic structure, while the red lineindicates the 3 × P nma , the Ru ions form the perfectzig-zag chain consisting of the equivalent sites along the a axis, while it slightly deforms in P /c . The chain1 iscomposed of an alternation of 6 different Ru sites, whilethe chain2 includes an alternation of 3 sites. The re-spective distances between the neighboring Ru ions areshown, but they are featureless and do not show a clearindication of a dimerization of the Ru ions. Absence ofa dimerization is obviously supported by an odd numberof Ru sites in the unit cell, excluding a possibility of aspin-singlet formation in the insulating state. As shownin Fig.4(f), on the other hand, the clear three-hold peri-odicity of the bond length can be seen along the original b axis, where the bonding built a liner chain with equalintervals of 3.328 ˚A in the metallic phase. In a linearchain, for example, the Ru1-Ru6 and Ru3-Ru6 bondingsshrink to ∼ . ∼ .
66 ˚A. This tendency is commonlyseen for all the bondings along the original b axis. Thiskey feature in the deformed structure will be discussed inthe final part, together with results of a band calculation. C. Nuclear quadrupole/magnetic resonance
We performed NMR/NQR measurements to investi-gate the microscopic state of RuAs. Figures 5(a) and(b) show the NMR spectrum measured at around 8 Tand the NQR spectrum measured at zero field, respec-tively. We used many pieces of small single crystals forboth measurements; therefore, the experimental condi-tion is similar to a measurement using polycrystallinesamples. Here, the NMR/NQR data using the crystal H ∼ ν Q = 39 . η = 0 .
2, which give the resonance frequency of ν res = 40 . TABLE II. Structural parameters of RuAs in the metallic and insulating phases. The equivalent isotropic atomic displacementparameter B eq and the occupancy are also shown.293 K site wyckoff x y z B eq (˚A ) occup.Ru 4c 0.00027 0.25 0.20272 0.59 1As 4c 0.19557 0.25 0.56909 0.36 0.988170 K site wyckoff x y z B eq (˚A ) occup.Ru1 4e -0.23004(7) 0.93147(2) 0.26397(5) 0.308(9) 1Ru2 4e 0.56805(6) 0.76233(2) 0.56793(5) 0.321(9) 1Ru3 4e 0.60492(7) 0.43577(2) 0.60076(6) 0.334(9) 1Ru4 4e 0.09791(6) 0.59599(2) 0.59745(5) 0.342(9) 1Ru5 4e -0.27167(7) 0.89775(2) 0.73385(5) 0.336(9) 1Ru6 4e 0.07992(6) 0.93010(2) 0.58449(5) 0.278(9) 1Ru7 4e 0.25102(6) 0.76444(2) 0.25156(4) 0.298(9) 1Ru8 4e -0.07116(6) 0.72837(2) 0.43422(6) 0.358(9) 1Ru9 4e 0.42160(6) 0.59933(2) 0.91880(4) 0.285(9) 1As1 4e -0.28917(8) 0.63657(3) 0.51665(6) 0.268(13) 0.986(3)As2 4e 0.63135(8) 0.69241(3) 0.81187(6) 0.231(14) 0.984(3)As3 4e 0.05282(8) 0.85291(3) 0.35787(6) 0.222(14) 0.985(3)As4 4e -0.05849(8) 0.80788(3) 0.65457(6) 0.254(14) 0.985(3)As5 4e 0.39884(8) 0.52525(3) 0.68557(6) 0.274(14) 0.986(3)As6 4e 0.97124(8) 0.47511(3) 0.65011(6) 0.242(14) 0.985(3)As7 4e 0.37374(8) 0.85257(3) 0.68016(6) 0.214(14) 0.987(3)As8 4e 0.28399(8) 0.68482(3) 0.48169(6) 0.239(13) 0.988(3)As9 4e -0.28604(8) 0.97992(3) 0.51817(6) 0.214(13) 0.988(3) around 40.0 MHz, which corresponds to ± / ↔ ± / P nma , whichis consistent with these observations. In the NQR spec-trum, the spectral width is quite narrow at a high tem-perature of 320 K, but it is significantly broadened justat T MI1 = 250 K. In the intermediate temperature rangebetween T MI2 and T MI1 , the NQR spectrum is stronglybroadened and almost disappears. The contrastive obser-vation of the NMR signal in the same phase, for whichthe Zeeman interaction is predominant, excludes a possi-bility that the fast relaxation weakens the NQR intensity.Therefore, the electric field gradient (EFG) parameters, ν Q and η are suggested to be distributed strongly in thisphase. This is in sharp contrast to the ground state be-low T MI2 = 190 K, where the sharp signals for the NQRmeasurement are suddenly recovered, and we observed 8resonance lines. From this result and the structural anal-ysis, it is clear that the ground state of RuAs is commen-surate. On the other hand, the broad and weak NQR in-tensity in the intermediate phase implies that the chargedistribution is incommensurate.Next, we checked the resonance frequencies at the in-equivalent As sites through a first principle calculationof the EFG using the structural parameters. The calcu-lation method of EFG has been explained elsewhere,[18]and it has been used successfully for many systems.[19–22] Here, the nuclear quadrupole moment for the As nu-cleus, Q = 314 × − m is utilized to convert EFG to ν Q .[23] Table III shows ν calQ , η cal , and the resultant reso- TABLE III. Calculated and experimental EFG parameters ofRuAs in the metallic and insulating phases.metallic phase293 K 290 Ksite ν calQ η cal ν calres ν expres error(MHz) (MHz) (MHz) (%)As 36.7 0.833 40.7 40.0 -1.8insulating phase170 K 180 Ksite ν calQ η cal ν calres ν expres error(MHz) (MHz) (MHz) (%)As6 25.68 0.551 26.95 27.6 +2.4As2 25.35 0.810 27.99 29.5 +5.1As7 35.39 0.508 36.89 38.0 +2.9As9 37.65 0.508 39.24 40.9 +4.1As1 40.70 0.837 45.20 47.0 +3.8As8 43.47 0.562 45.70 47.0 +2.8As3 47.13 0.317 47.91 49.7 +3.6As4 48.76 0.554 51.19 52.7 +2.9As5 54.71 0.869 61.22 62.9 +2.7 nance frequency ν calres estimated from the calculation, and ν expres observed experimentally. In the metallic state, thecalculated ν calQ is close to the experimental ν expQ = 39 . η cal is de-viated from the experimental η = 0 .
2. Since ν res is not so
10 20 30 40 50 60 70 805 6 7 8 9 10 11 single crystals As-NQR T MI2 T MI1
RuAs A s - N Q R I n t n s i t y ( a r b . un i t ) f (MHz)
320 K H = 0(b) As-NMR A s - N M R I n t en s i t y ( a r b . un i t ) H (T)
270 K f = 58.3 MHz(a) T MI2 T MI1
RuAssingle crystals
FIG. 5. (color online) (a) Field-swept NMR spectrum forRuAs measured at around 8 T. (b) NQR spectrum for RuAsmeasured at zero field. In the metallic state above T MI1 , theNMR spectrum obtained using many pieces of single crys-tals shows a typical powder pattern by assuming the uniqueAs site, as shown by the red curve. This is consistent withthe NQR spectrum observed at around 40.0 MHz. Below T MI1 , the broadened NMR spectrum and the suppression ofthe NQR intensity indicate the strong distribution of ν Q and η . In the ground state below T MI2 , the several peaks are ob-served at the NQR measurement, indicative of the formationof the superlattice. The blue lines indicate the resonance fre-quencies calculated using the structural parameters at 293 Kand 170 K. sensitive to η , ν res has a good consistency between thecalculation and the experiment within the small error,which is defined by ( ν expres − ν calres ) / ν expres . In the insulatingstate, ν calQ , η cal , and ν calres for all 9 As sites are calculatedand shown in ascending order of ν calres in the table. Theexperimental ν expres is also listed in ascending order. Inthe NQR spectrum shown in Fig. 5(b), we observed 8inequivalent signals; therefore, 1 site is missing. The in-tensity analysis in the wide frequency range is difficultto keep an accuracy, but the signal just below 50 MHzhas the largest intensity (area) and the broadest widthamong the 8 signals, indicating that 2 peaks are acci-dentally overlapped in the signal. This interpretation isstrongly supported by the calculation, in which the As1and As8 sites have the almost same resonance frequen-cies, which are slightly smaller than the subjected reso-nance frequency. In this context, the ν expres for all the Assites show the almost regular error of about +2 . ∼ . ν calres are shown by theblue lines in Fig. 5(b) for each phase. The present cal-culation reproduces excellently the EFG at the As sites,ensuring the high validity of the obtained structural pa-rameters as well as the reliability of the calculation. Si-multaneously, this result reveals that the ground state ofRuAs is nonmagnetic, because the spectral splitting by the internal field can be ignored. RuAssingle crystals As-NQR / T T ( s - K - ) Temperature (K) T MI1 T MI2 (a)
RuAssingle crystals As-NQR T MI1 ~T (b) T MI2 / T ( s - ) Temperature (K) / T ( s - ) T (K -1 ) FIG. 6. (color online) Temperature dependence of (a) 1 /T T and (b) 1 /T for RuAs. RuAs undergoes the insulating stateaccompanied by a strong development of some fluctuations.The T behavior below T MI2 indicates that the energy gap ofRuAs is anisotropic.
Figure 6(a) shows the temperature dependences of1 /T T for the single crystal RuAs. T was measured atthe peak of ∼
49 MHz in the insulating state, and at thesingle peak at ∼
40 MHz in the metallic state. Unfortu-nately, we could not measure T in the intermediate re-gion between T MI1 and T MI2 owing to the weak intensity.The 1 /T T shows a strong divergence toward T MI1 andobvious suppression below T MI2 . The divergence showsthat a symmetry lowering by the metal-insulator transi-tion is accompanied by strong critical fluctuations. Sincethe As nuclear spin is I = 3 /
2, both magnetic and elec-tric relaxations are possible for the origin of the diver-gence of 1 /T . The absence of Curie-Weiss like behav-ior in magnetic susceptibility suggests that the magneticcorrelations of ~q = 0 is weak in this system, but theconcerned wave vector is probably finite, because the su-perlattice of 3 × × /T T corresponds to a ~q -summed dynamical suscepti-bility. Therefore; the presence of magnetic correlationscannot be excluded experimentally at present. Figure6(b) displays the temperature dependence of 1 /T forRuAs. 1 /T in RuAs follows T behavior below T MI2 in contrast to a conventional exponential behavior. Onepossibility is that the relaxation at low temperatures isextrinsically dominated by a small amount of magneticimpurities. We cannot exclude this possibility becausethe Curie tail appears in the susceptibility at low tem-peratures. Another possibility is intrinsically that thedensity of states (DOS) near the Fermi energy, E F hasa linear energy dependence, that is, D ( E ′ ) ∼ | E ′ | , where E ′ = E − E F , unlike a simple full gap. The thermal ex-citation in this energy dependence gives T dependencein 1 /T . If this is the case, the band structure near E F isexpected to be like a semimetal. We cannot judge whichis correct, but an estimation of the energy-gap was triedfor a comparison by the same manner as that attemptedfor RuP.[7] Using 1 /T ∼ exp( − E g /k B T ) for the exper-imental data between T MI2 and 50 K, as shown in theinset of Fig. 6(b), we obtained E g = 308 K ±
30 K, whichis comparable to 340 K estimated from the resistivity inthe same temperature range. The energy gap of RuAsis several times smaller than 1250 K for RuP,[7] which isqualitatively consistent with a difference in the resistivitybetween two compounds.[6]
FIG. 7. (color online) The calculated energy dispersion andthe DOS of RuAs in the metallic phase in the orthorhombic
P nma space group. The four-fold degeneration is realizedalong axes shown by red lines in the Brillouin zone boundaryeven though the spin-orbit coupling is considered, becauseof the protection by the non-symmorphic symmetry. Twohole bands and two electron bands denoted by 61 −
64 crossthe Fermi level. The flat bands near E F are seen along thedegenerated Y − S , T − R , and S − R axes, producing the largeDOS at E F . In the lower panel, the black curve indicates thetotal DOS integrated in the whole k space. The red and greencurves indicate the partial DOS originating from the Ru-4 d and As-4 p orbital, respectively. FIG. 8. The Fermi surfaces of RuAs in the metallic phase inthe P nma space group. The 63 and 64 electron sheets arealmost degenerated and low dimensional.
D. Electronic structure calculation
Figures 7 (a) and (b) show the calculated energy dis-persion and the DOS for the metallic phase in the
P nma space group, and the Fermi surfaces are drawn in Fig. 8.In the energy dispersion, the flat bands near E F are seenalong the T − R , S − R and partially Y − S axes, and theyconstruct the peak structure in the DOS near E F . Thisfeature is consistent with the previous calculation.[8] Thespin-orbit coupling is taken into account in the presentcalculation, and the DOS is slightly modified and thepeak feature near E F became more remarkable. Theband splitting by the spin-orbit coupling can be seenalong the specific axes, such as S − X , Z − T , and Y − T ,where only two-fold spin degeneracy remains. However,the four-fold degeneracy is completely maintained, forexample, along the Y − S , T − R , and S − R axes, whichare on the Brillouin zone boundary, as indicated by redlines in Fig. 7(a), because it is protected by the non-symmorphicity of the P nma space group.[24] This fea-ture will be a common point to contribute an electronicstate of systems in the non-symmorphic
P nma spacegroup, for instance, it can be a key ingredient to interpreta magnetoresistance of the isostructural CrAs.[24] Thisprotection yields the almost degenerate Fermi surfacesat the Brillouin zone boundary in the metallic phase of
FIG. 9. (color online) The calculated energy dispersion in thevicinity of E F and the DOS of RuAs in the insulating phasein the monoclinic P /c space group. A gap-like feature islikely to appear in the DOS near E F . In the lower panel, theblack curve indicates the total DOS integrated in the whole k space. The red and green curves indicate the partial DOSoriginating from the Ru-4 d and As-4 p orbital, respectively.In the inset, the solid line with the hatching region indicatesthe total DOS for the insulating state, while the dotted lineshows the metallic state. Here, the DOS of the metallic phaseis multiplied by 9 to adjust the difference in the size of theunit cell. RuAs. The plate-like Fermi surfaces with a hollow in themiddle are seen in 63 and 64 electron bands, and theypartially degenerate because of the protected degeneracyalong the Y − S , T − R , and S − R axes. Interestingly, theflat bands near E F exist along the axes with the four-folddegeneracy protected by the crystal symmetry. This cer-tainly produces the peak structure in the DOS and makesthis phase unstable at low temperatures; therefore, thelifting of this degeneracy by a symmetry lowering fromthe non-symmorphic P nma is a key ingredient of themetal-insulator transition.We test a band calculation for the ground state inthe P /c space group, and the energy dispersion in thevicinity of E F and the DOS are shown in Fig. 9. Here,the Brillouin zone is that of the monoclinic structure. Wecan confirm a disappearance of the degenerate flat bands, but the present calculation did not produce a clear en-ergy gap, which is relatively small as estimated to be E g = 340 K ∼ E F ,and a switching of the electron bands and the hole bandsdoes not occur in the momentum space. As a result, avalley of DOS near E F approximates a gap-like feature,as shown in the inset of Fig. 9(b). The DOS at E F of ∼ ∼ ∼ .
03 eV in the LDA framework. In otherwords, inadequate consideration of Coulomb interactioncauses the underestimation of the gap. The energy gapin principle may open by increasing Coulomb interactionnumerically in the semimetallic electronic state, althoughthe energy shift of approximately 0 . TABLE IV. Calculated d -electron numbers at each Ru site inthe insulating phase. insulating phasesite d -electron a difference fromnumber the average (%)Ru1 5.301 +0.038Ru2 5.305 +0.113Ru3 5.303 +0.075Ru4 5.310 +0.208Ru5 5.301 +0.038Ru6 5.291 -0.151Ru7 5.290 -0.170Ru8 5.304 +0.094Ru9 5.286 -0.245 Another important point is why the superlattice of3 × × P nma space group, and it canbe insulating with maintaining the size of the unit cell.For example, the simple dimerization along the zig-zagchain (along the a axis in P nma ), which does not changethe size of the unit cell, can lift this degeneracy, but thisis not realized. To check a relationship between the struc-
FIG. 10. (color online) The arrangement of the Ru ions inthe metallic state (upper left) and the insulating state (upperright and lower). In the metallic phase, the Ru ions formthe zig-zag ladder along the b direction. In a lower structure,the number indicates each Ru site. The Ru6, Ru7 and Ru9sites, where the calculated electron numbers are fewer, areshown by green spheres. In the bc plane of the original P nma structure, a linear alignment of those sites is realized. In thelower structure, the shorter Ru-Ru bonding of less than 3.21˚A are drawn. tural modulation and the electronic state, we evaluatedthe d -electron number of each Ru site in the insulatingstate, which was obtained in the band calculation, andthey are shown in Table IV. The average number of d electrons at all the Ru sites is 5.299, which correspondsto Ru . . The differences from the average number ateach Ru site are also listed in the table. The d electronnumbers at the Ru6, Ru7, and Ru9 sites are obviouslyfewer than those of other sites. An arrangement of theseRu ions in the crystal structure is shown in Fig. 10, wherethe Ru6, Ru7, and Ru9 sites are drawn by green spheresand the As sites are eliminated. An upper right struc-ture is the ac plane in the P /c space group, which isequivalent to that in Fig. 4(d) and a lower figure showseach layer normal to the ac plane. These layers are the bc plane in the original P nma space group, and it consists ofthe zig-zag ladders. As shown in the upper left structure,the zig-zag ladder was constructed by the equivalent Rusites in the metallic phase, and it deforms in the insulat-ing state. The shorter Ru-Ru bondings, whose length isless than 3.21 ˚A, are shown in the lower figure. As al-ready shown in Fig. 4, some bondings obviously extend,making a clear three-hold periodicity along the original b axis. The Ru6, Ru7, and Ru9 sites possess 4 shorterbondings in the layer, while other sites have 3 shorterbondings. This difference is likely to induce the distribu-tion of the d electron numbers. Interestingly, the Ru6, Ru7, and Ru9 sites align in a straight line in this layer,indicative of a formation of a stripe-type charge mod-ulation. Reflecting the original zig-zag chain along the a axis in the P nma space group, which is perpendicu-lar to these layers, the direction of the stripe changesalternatively layer by layer. This apparent coupling ofthe structural and electronic modulation suggests a for-mation of commensurate CDW in the ground state ofRuAs. It is conjectured that the 3 × × IV. SUMMARY
In summary, the several experiments have been per-formed for the single crystals of RuAs obtained suc-cessfully using Bi-flux method. It shows clear succes-sive metal-insulator transitions at T MI1 ∼
255 K and T MI2 ∼
195 K alike the polycrystalline sample. This en-ables us to escape from an awkward problem on the sharpdifference between the poly- and single- crystals of RuP.The X-ray structural analysis and the NQR spectrumfor RuAs demonstrate the nonmagnetic superlattice of3 × × d electron number suggests a formation of a stripe-typeCDW, where the direction of the stripe alternates layerby layer. A direct observation of this electronic mod-ulation is an important issue, and a verification of theorbital state at each Ru site is also an interesting sub-ject. RuAs is not a simple low-dimensional material butpossesses the Fermi surface instability caused by a non-symmorphicity of the P nma space group, resulting in thetransition to the insulating state with the characteristicstructural and electronic modulation.
ACKNOWLEDGEMENT
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