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[PhysRevB.109.014518.pdf](https://mdr.nims.go.jp/filesets/fed6f485-7f13-459b-85a9-6e219d235b88/download)

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[Taichi Terashima](https://orcid.org/0000-0001-9239-0621), Hideaki Fujii, [Yoshitaka Matsushita](https://orcid.org/0000-0002-4968-8905), [Shinya Uji](https://orcid.org/0000-0001-9351-6388), Yuji Matsuda, [Takasada Shibauchi](https://orcid.org/0000-0001-5831-4924), [Shigeru Kasahara](https://orcid.org/0000-0002-6007-9617)

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[Transport evidence for twin-boundary pinning of superconducting vortices in FeSe](https://mdr.nims.go.jp/datasets/27b786a5-dcf7-4046-8f58-eb00fae1b763)

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Transport evidence for twin-boundary pinning of superconducting vortices in FeSePHYSICAL REVIEW B 109, 014518 (2024)Transport evidence for twin-boundary pinning of superconducting vortices in FeSeTaichi Terashima ,1,* Hideaki Fujii,2 Yoshitaka Matsushita ,3 Shinya Uji ,1 Yuji Matsuda,4Takasada Shibauchi ,5 and Shigeru Kasahara 6,†1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Tsukuba 305-0003, Japan2Department of Physics, Okayama University, Okayama 700-8530, Japan3Research Network and Facility Services Division, National Institute for Materials Science, Tsukuba 305-0047, Japan4Department of Physics, Kyoto University, Kyoto 606-8502, Japan5Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan6Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan(Received 1 November 2023; revised 3 January 2024; accepted 5 January 2024; published 29 January 2024)We provide bulk transport evidence for twin-boundary pinning of vortices in FeSe. We measure interlayerresistance in FeSe in magnetic fields and find that, as the field is rotated in the ab plane, the flux-flow resistivityis suppressed when the field direction is parallel to twinning planes. The width of the associated dip in theresistance vs in-plane field direction curve varies as T 1/2B−3/4, consistent with the creation of kinked vorticesnear the parallel field geometry.DOI: 10.1103/PhysRevB.109.014518I. INTRODUCTIONTwin boundaries in superconductors are known to affectbehavior of superconducting vortices by suppressing or en-hancing superconductivity near them. A famous example isflux pinning by twin boundaries in YBa2Cu3O7−δ (YBCO)single crystals [1–3]. It was reported that the flux-flow re-sistivity was largely suppressed when the magnetic field wasparallel to the twinning planes.Most iron-based superconductors, unless sufficientlydoped, undergo a tetragonal-to-orthorhombic structural phasetransition as cooled from room temperature. Accordingly,crystals are twinned below the transition temperature Ts.The twin boundaries are parallel to high-temperature tetrag-onal (100) or (010) planes. Scanning SQUID and mag-netic force microscopy studies on Ba(Fe1−xCox )2As2 andBaFe2(As1−xPx )2 have reported that twin boundaries enhancesuperfluid density and repel vortices [4–6]. By contrast, scan-ning tunneling microscopy studies on FeSe have shown thattwin boundaries in FeSe suppress the superconducting gapand superfluid density and pin vortices [7,8]. The twin-boundary pinning of vortices in FeSe has also been confirmedin a scanning SQUID study [9]. Fe(Se, Te) is a prime candi-date in a search for Majorana fermions [10,11] and these twinboundaries may be used to arrange vortices as desired in quan-tum computing applications where vortices carrying Majoranafermions are manipulated [12]. Therefore, twin-boundary pin-ning properties in FeSe may be of interest. In this work, weprovide bulk transport evidence for twin-boundary pinning ofvortices in FeSe and show that temperature and magnetic-field*TERASHIMA.Taichi@nims.go.jp†kasa@okayama-u.ac.jpvariation of pinning properties can be described by a theorypreviously developed for YBCO [13].II. EXPERIMENTSHigh-quality single crystals of FeSe were grown by achemical vapor transport method [14]. Figure 1 shows theexperimental setup: four samples were mounted on a rotationplatform of the two-axis rotator probe. To measure interlayerresistance Rc, a current and a voltage contact were spot-welded on each (001) plane and then reinforced by silverconducting paste. Notice that the [100]t direction, where thesubscript t refers to the room-temperature tetragonal cell, iseasily recognized from the surface morphology [Fig. 1(b)].The twin boundaries run along the [100]t and [010]t direc-tions. The polar θ and azimuthal φ angles of the appliedmagnetic field were defined with respect to the platform asshown in Fig. 1(c). To remove possible Hall voltage con-tamination, measurements were performed at a positive field+B and at a negative one −B for each field direction andthe symmetrized voltage was used to calculate Rc, i.e., Rc =[V (+B) + V (−B)]/2I , although the antisymmetric voltage[V (+B) − V (−B)] was on average less than 1% of the sym-metric one. In the following, we concentrate on samples 3 and4, on which high-quality data were obtained (for samples 1and 2, see Appendix A). For these samples, the orientation ofthe crystal axes were confirmed by x-ray diffraction measure-ments after all the resistance measurements were finished.III. RESULTS AND DISCUSSIONFigure 2 shows the temperature dependence of the in-terlayer resistance Rc for samples 3 and 4. While thetemperature dependence of the in-plane resistance is metal-lic from room temperature [15], the measured interlayer2469-9950/2024/109(1)/014518(6) 014518-1 ©2024 American Physical Societyhttps://orcid.org/0000-0001-9239-0621https://orcid.org/0000-0002-4968-8905https://orcid.org/0000-0001-9351-6388https://orcid.org/0000-0001-5831-4924https://orcid.org/0000-0002-6007-9617https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.109.014518&domain=pdf&date_stamp=2024-01-29https://doi.org/10.1103/PhysRevB.109.014518TAICHI TERASHIMA et al. PHYSICAL REVIEW B 109, 014518 (2024)FIG. 1. Sample platform and samples. (a) Two-axis rotationplatform at θ = 90◦ and φ = 0◦. The diameter of the platform is12.4 mm. Four samples 1–4 are mounted, for each of which the[100]t direction is indicated by pink arrows. (b) Blow-up of sample4. The [100]t direction is readily determined from the morphologyof the cleaved surface. (c) The polar θ and azimuthal φ angles of theapplied field were defined with respect to the platform.resistance curves exhibit a nonmetallic temperature de-pendence, i.e., dRc/dT < 0, near room temperature. Thestructural transition temperature Ts, superconducting transi-tion temperature Tc, and residual resistivity ratio at T = 10 Kare 87.6 K, 8.5 K, and 8.7 for sample 3 and 89.4 K, 9.0 K,and 15 for sample 4, respectively. The interlayer resistivityat T = 10 K is estimated to be 0.50, 1.8, and 0.57 m� cm forsamples 2, 3, and 4, respectively, which is roughly comparableto a value of ∼1 m� cm reported in [16]. For comparison, thein-plane resistivity at T = 10 K is roughly 15 μ� cm [15,17].Therefore, the resistivity anisotropy is estimated to be morethan 30.Figure 3 shows the field dependence of the interlayer resis-tance Rc at T = 8 K for samples 3 and 4. The black curves arefor B ‖ c, whereas the green and brown ones are for in-plane50403020100Rc (m)300250200150100500T (K)121086420Rc  (m)#3#4FIG. 2. Interlayer resistance Rc vs temperature for samples 3and 4.1.00.80.60.40.20.0Rc (m)1086420B (T)sample #4 B // c  (B // [100]t)76543210Rc (m)6543210B (T)sample #3 B // c (B // [100]t) (a)(b)FIG. 3. Magnetoresistance of samples 3 and 4 at T = 8 K forthree field directions, B ‖ c and B⊥c with φ = −4 and −58◦. φ =−4◦ corresponds to B ‖ [100]t for sample 3 (a), while φ = −58◦does for sample 4 (b). Notice different horizontal scales for (a) and(b), which is the main reason for the apparent broad transitions insample 3 (a).fields. For sample 3, the resistance in the superconductingtransition region is smaller at φ = −4◦ (green) compared toφ = −58◦ (brown), while for sample 4 it is smaller at φ =−58◦ (brown). Looking at the pink arrows in Fig. 1(a), wenotice that φ = −4◦ and −58◦ correspond to B ‖ [100]t forsamples 3 and 4, respectively, as far as the naked eye can see.Figures 4 and 5 show detailed field-orientation dependenceof the interlayer resistance in the superconducting transitionregion and in the normal state. Figure 4(a) shows the interlayerresistance of sample 3 measured in the transition region atB = 2.2 T and T = 8 K as a function of θ and φ compared tothat in the normal state at B = 6 T and T = 8 K. The currentdensity is 0.46 A/cm2. We also performed measurements withthe current density of 0.15 A/cm2 but observed no appreciablechange. The transition-region data show three distinct dips.Considering a slight misalignment of the sample, we pickedup the minimum resistance at each φ as the resistance for thein-plane field and plotted it as a function of φ in Fig. 4(b).The dip positions correspond to the field directions parallel to[010]t , [100]t , and [01̄0]t within experimental accuracy. Thebackground variation of the resistance outside the dip regionsmay be ascribed to inhomogeneous current distribution, i.e.,the current is not exactly along the c axis everywhere inthe sample. We also note that, to allow two-axis rotation,014518-2TRANSPORT EVIDENCE FOR TWIN-BOUNDARY PINNING … PHYSICAL REVIEW B 109, 014518 (2024)4.03.53.02.52.0Rc (m)-90 -60 -30 0 30 60 90 (deg)N (-2 m )SCB // [100]t[010]t[0-10]t(a)(b)FIG. 4. Interlayer resistance Rc of sample 3 in magnetic fields.(a) Resistance as a function of φ and θ measured at B = 2.2 T andT = 8 K in the superconducting transition region (SC) compared tothat at B = 6 T and T = 8 K in the normal state (N). The latter isoffset by −1 m�. (b) Resistance for in-plane fields as a function of φfor the superconducting transition region (SC) and normal state (N).The normal state curve is offset by −2 m�.electrical wires are not fixed and hence that small pickupof electromotive force induced by wire vibration due to accurrent is inevitable.Figure 5(a) shows the interlayer resistance of sample 4measured in the transition region at B = 6 T and T = 8 K asa function of θ and φ compared to that in the normal state atB = 6 T and T = 9 K. The current density is 0.51 A/cm2. Theresistance for the in-plane field is shown as a function of φ inFig. 5(b). The dip positions correspond to the field directionsparallel to [100]t , and [01̄0]t within experimental accuracy.Figure 6(a) shows the resistance of sample 3 for in-planefield as a function of φ measured at different temperaturesand hence different field strengths. The dip sharpens as thetemperature is lowered and hence the field is increased. Wedetermined the full width at half maximum (FWHM) of theφ ∼ 0 dip for each of the three curves in Fig. 6(a) (for details,see Appendix B) and plotted it against T 1/2B−3/4 in Fig. 6(b).We see a nice linear relation between the two quantities.Our observations can qualitatively be explained as follows:when B ‖ [100]t (or [010]t ), some vortices are trapped by twinboundaries. Because I ‖ c, the direction of the Lorentz force is0.650.600.550.500.450.40Rc (m)-90 -60 -30 0 30 60 90 (deg)N (-0.15 m )SCB // [100]t[0-10]t(a)(b)FIG. 5. Interlayer resistance Rc of sample 4 in magnetic fields.(a) Resistance as a function of φ and θ measured at B = 6 T andT = 8 K in the superconducting transition region (SC) compared tothat at B = 6 T and T = 9 K in the normal state (N). The latter isoffset by −0.15 m�. (b) Resistance for in-plane fields as a functionof φ for the superconducting transition region (SC) and normal state(N). The normal state curve is offset by −0.15 m�.[010]t ([100]t ), i.e., perpendicular to the boundaries. However,as long as the twin-boundary pinning force is stronger than theLorentz force, the vortices do not move and hence do not con-tribute flow resistance. Because the vortex spacing l is muchsmaller than the twin-boundary spacing d as explained below,only a portion of vortices is trapped by the twin boundariesand hence we observe a resistance drop, not zero resistance.The inequality l � d is justified as follows: for a trian-gular vortex lattice in isotropic superconductors, the vortexspacing is given by a� = 1.074(�0/B)1/2, where �0 is theflux quantum. Considering the coherence length anisotropy ofξab/ξc ∼ 4 [18], the in-plane vortex spacing l is estimated tobe l = √ξab/ξca� ∼ 66–30 nm for B = 2.2–10.8 T. On theother hand, photoemission electron microscopy (PEEM) [19]and STM [12] observations of twin boundaries in FeSe sug-gest that a typical twin-boundary spacing can be assumed tobe d ∼ 300 nm.As already noted at the beginning of this article, vor-tex pinning due to twin boundaries was previously studiedin the high-transition-temperature cuprate superconductorYBCO [1–3]. The present data are reminiscent of [20], where014518-3TAICHI TERASHIMA et al. PHYSICAL REVIEW B 109, 014518 (2024)3.53.02.52.0Rc (m)-90 -60 -30 0 30 60 90 (deg)T = 8 K, B = 2.2 TT = 7 K, B = 8.2 TT = 6.4 K, B = 10.8 TI = 3 mA1086420FWHM (deg)1.51.00.50.0T1/2B-3/4 (K1/2T-3/4)(a)(b)FIG. 6. Temperature and field dependence of the resistance dip.(a) Interlayer resistance Rc of sample 3 for in-plane fields as afunction of φ for three different temperatures and fields as indi-cated. The black horizontal lines indicate FWHM for the φ ∼ 0 dips.(b) FWHM plotted against T 1/2B−3/4. The solid line indicates thelinear relation between the two quantities.the interlayer resistance of YBCO in the superconductingtransition region was measured as a function of in-plane fielddirection and resistance drops were observed for field direc-tions parallel to the twin boundaries.Blatter et al. gave a first theoretical description of thetwin-boundary pinning in YBCO [13]: the authors argued thatthe twin boundaries attract the vortices due to the suppressedorder parameter and hence that each vortex deforms to adjustitself to the twinning planes. Accordingly, as long as the angle�φ between the twin boundary and applied field is small,each vortex follows the twin boundary over some distance,then proceeds to the next boundary, and follows the bound-ary again, resulting in a kinked vortex. Assuming l � d andtaking into account the interaction between the vortices, thecritical angle (�φ)∗ where the vortices are released from thetwin boundaries and get straight is given by(�φ)∗  [π ln(κ√�)2√32�εlεl]1/2[ld]3/2, (1)where κ and � are the Ginzburg-Landau parameter and themass anisotropy ratio (mc/mab), respectively. εl and �εl arethe line tension of a vortex and its reduction when it is trappedin the twin boundary, respectively. Because �εl ∝ t (1 − t )and εl ∝ (1 − t ), where t is a reduced temperature T/Tc,�εl/εl ∝ T . Because l ∝ B−1/2, the temperature and field de-pendence of the critical angle is given by (�φ)∗ ∝ T 1/2B−3/4.Figure 6(b) confirms this relation, demonstrating the kinked-vortex scenario.Finally, we mention a recent work [21], where the magnetictorque in FeSe was measured as a function of the in-planefield angle in the mixed state. The authors reported that theirreversible torque showed a peak when the field was parallelto the orthorhombic a or b axis, which corresponds to 〈110〉t .Although the peak suggests the enhanced pinning for this fielddirection, the reported direction differs from ours (〈100〉t )by 45◦.IV. CONCLUSIONWe have shown from bulk transport measurements thattwin boundaries in FeSe pin vortices. The width of the as-sociated dip in Rc(φ) curves vary as T 1/2B−3/4 as expectedfrom the Blatter theory developed for YBCO [13]. In thecase of YBCO, the initial slope of the upper critical fieldBc2 was so high that the temperature range where resistancedip measurements like the present ones could be performedwas very limited. In this study, by virtue of the relatively0.70.60.50.40.3Rc (m)-90 -60 -30 0 30 60 90 (deg)N (-0.4 m )SCB // [100]t[010]t[0-10]t(a)(b)FIG. 7. Interlayer resistance Rc of sample 2 in magnetic fields.(a) Resistance as a function of φ and θ measured at B = 2.2 T andT = 8 K in the superconducting transition region (SC) compared tothat at B = 6 T and T = 8 K in the normal state (N). The latter isoffset by −0.3 m�. (b) Resistance for in-plane fields as a functionof φ for the superconducting transition region (SC) and normal state(N). The normal state curve is offset by −0.4 m�.014518-4TRANSPORT EVIDENCE FOR TWIN-BOUNDARY PINNING … PHYSICAL REVIEW B 109, 014518 (2024)small initial slope of Bc2 in FeSe, we could demonstrate thisrelation for a meaningful temperature range. The knowledgeabout the twin-boundary vortex pinning that we acquired inthis study may be useful in improving superconducting wiresand devices. Further, it may be of use to future topologicalquantum computing.ACKNOWLEDGMENTSThis work was supported by Grant-in-Aid for ScientificResearch on Innovative Areas “Quantum Liquid Crystals”(Grants No. JP19H05824 and No. JP22H04485), Grant-in-Aid for Scientific Research(A) (Grants No. JP21H04443,No. JP22H00105, and No. JP23H00089), Grant-in-Aid forScientific Research(B) (Grant No. JP22H01173), Grant-in-Aid for Scientific Research(C) (Grant No. JP22K03537), andFund for the Promotion of Joint International Research (GrantNo. JP22KK0036) from Japan Society for the Promotion ofScience. MANA is supported by the World Premier Interna-tional Research Center Initiative (WPI), MEXT, Japan. T.T.acknowledges H. Kitano for valuable comments.APPENDIX A: SAMPLES 1 AND 2The output voltage from sample 1 was very noisy, probablybecause of bad electrical contacts and/or wires, and hence nomeaningful data were obtained. For sample 2, Rc(φ, θ ) datawere successfully recorded at T = 8 K and B = 2.2 T, andan Rc(φ) curve with dips, which is similar to that for sample3, was obtained (Fig. 7). However, at higher magnetic fields,the out-of-phase component of the lock-in output increasedlargely, likely because of wire vibration, and hence no reli-able data were obtained at higher magnetic fields and lowertemperatures.3.02.82.62.4Rc (m)-40 -20 0 20 40(a)(b)(c) (deg)T = 8 K, B = 2.2 T3.43.23.02.8Rc (m)-20 -10 0 10 (deg)T = 7 K, B = 8.2 T2.62.42.22.01.8Rc (m)-20 -10 0 10 (deg)T = 6.4 K, B = 10.8 TFIG. 8. Estimation of the FWHM of the φ ∼ 0 dip in sample 3is illustrated for (a) T = 8 K and B = 2.2 T, (b) T = 7 K and B =8.2 T, and (c) T = 6.4 K and B = 10.8 T.APPENDIX B: FWHM ESTIMATIONTo estimate the FWHM of the φ ∼ 0 dip in sample 3, weassumed a linear background as shown in Fig. 8.[1] W. K. Kwok, U. Welp, G. W. Crabtree, K. G. Vandervoort, R.Hulscher, and J. Z. 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