Andreev bound states at a cuprate grain boundary junction: A lower bound for the upper critical field
M. Wagenknecht, D. Koelle, R. Kleiner, S. Graser, N. Schopohl, B. Chesca, A. Tsukada, S. T. B. Goennenwein, R. Gross
aa r X i v : . [ c ond - m a t . s up r- c on ] S e p Wagenknecht et al./ZBCA-Hc2 – vers.01
Andreev bound states at a cuprate grain boundary junction: A lower bound for theupper critical field
M. Wagenknecht, ∗ D. Koelle, and R. Kleiner
Physikalisches Institut – Experimentalphysik II, Universit¨at T¨ubingen,Auf der Morgenstelle 14, D-72076 T¨ubingen, Germany
S. Graser and N. Schopohl
Institut f¨ur Theoretische Physik, Universit¨at T¨ubingen,Auf der Morgenstelle 14, D-72076 T¨ubingen, Germany
B. Chesca
Department of Physics, Loughborough University,Loughborough, Leics LE11 3TU, United Kingdom
A. Tsukada
NTT Basic Research Laboratories, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243, Japan
S. T. B. Goennenwein and R. Gross
Walther-Meissner-Institut, Bayerische Akademie der Wissenschaften,Walther-Meissner Str. 8, D-85748 Garching, Germany (Dated: October 31, 2018)We investigate in-plane quasiparticle tunneling across thin film grain boundary junctions (GBJs)of the electron-doped cuprate La − x Ce x CuO , in magnetic fields up to B = 16 T, perpendicularto the CuO layers. The differential conductance in the superconducting state shows a zero biasconductance peak (ZBCP) due to zero energy surface Andreev bound states. With increasingtemperature T , the ZBCP vanishes at the critical temperature T c ≈
29 K if B = 0, and at T = 12 Kfor B = 16 T. As the ZBCP is related to the macroscopic phase coherence of the superconductingstate, we argue that the disappearance of the ZBCP at a field B ZBCP ( T ) must occur below theupper critical field B c ( T ) of the superconductor. We find B ZBCP (0) ≈
25 T which is at least afactor of 2.5 higher than previous estimates of B c (0). PACS numbers: 74.25.Dw, 74.25.Op, 74.50.+r, 74.45.+c
Determining the magnetic field − temperature ( B − T )phase diagram of high- T c cuprates has been the focus ofinterest since the discovery of these materials. In con-trast to the case of conventional type II superconduc-tors, where the B − T phase diagram basically consistsof the Meissner phase, the Shubnikov phase and the nor-mal state, the phase diagram of high- T c cuprates is ex-tremely rich, exhibiting a variety of vortex phases andalso a pseudogap region. However, particularly the tran-sition between the superconducting state and the normalstate, and thus the relation between the superconductingand the pseudogap states, is hard to determine, not onlydue to the extremely large values of the upper criticalfield B c in the case of hole-doped cuprates, but also be-cause of the presence of vortex liquid phases as well asstrong fluctuation effects, leading to nonzero resistance intransport experiments long before B c has been reached.In order to evaluate similarities and differences totheir hole-doped counterparts, many investigations havebeen performed within the past years on electrondoped materials like the single layer T’ cuprates [1] ∗ Electronic address: [email protected] with composition Ln − x Ce x CuO ( Ln = La, Pr, Nd).Pr − x Ce x CuO (PCCO) and Nd − x Ce x CuO (NCCO)have been studied extensively, while there is less datapublished for La − x Ce x CuO (LCCO). The precise de-termination of the phase diagram of these materials iscertainly of fundamental interest.In terms of B c , for PCCO and NCCO thin films nearoptimal doping, resistive measurements [2] or an analysisof the vortex Nernst signal [3, 4, 5] revealed B c (0) val-ues in the range of 7-10 T. For optimally doped LCCOan analysis of the vortex pinning strength yielded B c (0)around 9 T [6]. However, the various methods appliedto determine the upper critical field often yield incon-sistent results, see e. g. the discussion in [2]. In thispaper we show that an analysis of Andreev bound states(ABS) causing a zero bias conductance peak (ZBCP) inthe conductance spectra of cuprate grain boundary junc-tions (GBJs) yields a new lower bound for B c which isat least a factor of 2.5 above previous estimates.ABS result from the constructive interference of An-dreev reflected electron like and hole like quasiparticles.If the quasiparticles experience a sign change of the su-perconducting order parameter upon reflection, the ABSappear at the Fermi energy, giving rise to the ZBCP [7].ABS-caused ZBCPs have been observed both in hole-doped [8, 9, 10, 11, 12] and electron-doped [13, 14, 15, 16]cuprates, where the sign change is due to the d x − y sym-metry of the order parameter [17]. This type of ZBCPcan be observed with GBJs [11, 16] as well as for normalmetal/superconductor junctions [8, 9, 11, 12, 13, 14, 15]or junctions between a conventional superconductor anda d -wave superconductor [18].We note here that ZBCPs in the quasiparticle tunnelspectrum of superconductors can have other reasons thanthe formation of ABS, most prominent being the scat-tering of quasiparticles at magnetic impurities situatedin the tunnel barrier, as described by the Appelbaum-Anderson model [19, 20]. Such competing mechanismscan be identified, however, e. g. by analyzing the tem-perature and magnetic field depencence of the ZBCP.A ZBCP caused by ABS relies on the phase coherenceof the elementary excitations above the Cooper pairingground state. It thus should vanish when the macro-scopic phase coherence is lost, i. e., at the transition be-tween the superconducting state and the normal state.Such ZBCPs thus allow, at least in principle, to deter-mine B c or at least to give a reasonable lower bound,provided that the ZBCPs do not vanish far below B c ,e. g. due to the formation of a vortex liquid or othereffects like a (field induced) shift of ABS to larger en-ergy. As we will see below, in the geometry used in ourexperiments an unsplitted ZBCP is clearly visible abovethe irreversibility line, allowing its use as a probe of thesuperconducting state in high magnetic fields.The 900 nm thin films for our study were depositedby molecular beam epitaxy with ozone as the oxidationgas [21] on SrTiO (STO) symmetric ( α = − α , seeinset of Fig. 2) [001]-tilt bicrystal substrates with a to-tal misorientation angle ( α + α ) of 24 ◦ and 30 ◦ . Allfilms in this study had a Ce doping of x ∼ .
08 (slightlyunderdoped, T c ≈
29 K). The samples were patternedby photolithography and Ar ion milling with junctionwidths ranging from 40 µ m to 400 µ m [31]. Transportdata were collected with a current bias four point probeat 5 K ≤ T ≤
40 K and magnetic fields B ≤
16 T appliedparallel to the thin film c-axis. dI ( V ) /dV -characteristicswere measured with a lock-in amplifier (modulation fre-quency 1-5 kHz, I ac = 1 − µ A) and subsequently cal-ibrated with the numerical derivative of simultaneouslyrecorded I ( V )-curves. Unless indicated otherwise, thedata shown below are all for the same 24 ◦ GBJ.Fig. 1 shows resistivity ρ ( T ) of a bridge structure notcrossing the grain boundary, for 0 T ≤ B ≤
10 T. Similaras for thin films of PCCO [22] and LCCO [23], the on-set of T c decreases with increasing B and the transitionwidth is broadened. For B > T down to 5 K, and for larger fields we alsoobserve an upturn in ρ ( T ), as already reported previously[22, 24]. We determine ”transition temperatures” wherethe resistance of the (extrapolated) linear part of ρ ( T )[cf. dashed line in Fig. 1] has dropped to, respectively10, 50 and 90 per cent of its normal state value, givenby the intersection of the dashed line with the parabolicfit for ρ ( T ) above 35 K. The corresponding ”transition ( c m ) T (K)6 T 0 T10 T 7 T10% ( c m ) T (K)
FIG. 1: (color online) ρ ( T ) of a LCCO thin film for 0 T ≤ B ≤
10 T (in steps of 1 T). Dashed lines and full circles onthe 6 T curve indicate determination of temperatures wherethe resistance has dropped to, respectively 10, 50 and 90 percent of its normal state value (grey line). These values definethe critical fields B , B and B . The inset shows ρ ( T ) at B = 0 up to 200 K with a parabolic fit (grey line). temperatures” or, respectively, transition fields B , B and B , are shown further below in the B − T diagramof Fig. 4. Although the resistive transition broadens sig-nificantly, these fields do not differ strongly at a giventemperature and tend to extrapolate to a zero tempera-ture value around 7 T, suggesting that B c (0) is of thisorder. However, as we will discuss below, ZBCPs can beseen in much higher fields, suggesting e. g. superconduc-tivity below 12 K at 16 T.Fig. 2 (a) shows quasiparticle tunneling spectra (QTS)for a 24 ◦ GBJ, as obtained at 5 K for B up to 16 T. At B = 0, a clear gap structure, that is a suppression in thequasiparticle density of states (QDOS), is observed, withsymmetric coherence peaks at voltages V gap = ± ± B > V gap the conductance increaseslinearly with voltage, cf. upper inset in (b), and is al-most independent of the applied field up to 6 T [32]. Forfields above 6 T the differential conductance strongly de-creases due to the onset of resistance in the film adding inseries to the grain boundary resistance. This additionalresistance has been subtracted in Fig. 2 (b), where onecan see that the conductance in the subgap region in-creases monotonically with increasing field. The lowerleft inset in Fig. 2 (b) shows the integral over the tun-nel conductance, taken between -15 mV and 15 mV. Theintegral is field-independent, showing that the density ofstates is conserved.In the QTS of our samples we also observe a ZBCP,consistent with the previous study on optimally dopedthin film LCCO GBJs [16]. At T = 5 K the ZBCP per-sists up to the highest fields achievable with our setup, d I/ d V ( m A / V ) (a) V (mV) d I/ d V ( m A / V ) (b) B (T) I n t eg r a l ( a r b . un i t s ) FIG. 2: (color online) Quasiparticle conductance spectra ofa 24 ◦ LCCO thin film GBJ at T = 5 K for 0 T ≤ B ≤
16 Tin (steps of 2 T). Graph (a) shows conductance as measured.In (b) the resistance of the leads appearing above 6 T hasbeen subtracted. The inset in (a) shows an enlargement ofthe low bias region at 16 T. The upper inset in (b) shows thezero field conductance on a larger voltage scale at T = 5 K(black line) and at T = 32 K (grey line), where the ZBCP hasdisappeared. The lower left inset shows the integral over theconductance curves taken for voltages between -15 mV and+15 mV. The lower right inset in (b) illustrates the geom-etry of the bicrystal GBJ. Vortices are indicated by circles,screening currents by arrows. i. e. 16 T. The ZBCP can already be seen clearly in theuncorrected data, as shown in the inset of Fig. 2 (a). Wesaw similar ZBCPs in 15 out of 19 samples both on 24 ◦ and 30 ◦ substrates.Fig. 3 shows the evolution of the ZBCP as a functionof T at B = 16 T (a), and as a function of B at T = 13 K(b). Data are shown by thick black lines. The thin linesrepresent parabolic fits to the background quasiparticleconductance at low voltages. From the figures we seethat, at B = 16 T the ZBCP disappears between 11 Kand 12 K, while at T = 13 K it disappears between 13 Tand 14 T [33].As the ZBCP disappears reproducibly for a given T or B while increasing B or T , respectively, we can fol-low the disappearance of the ZBCP in a B − T phasediagram, which is shown in Fig. 4. Full symbols showthe ”critical” field B ZBCP where the ZBCP area A ZBCP has reached zero for two different samples (squares: 30 ◦ -4 -2 0 2 41718192021 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4-4 -2 0 2 41718192021 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 d I/ d V ( m A / V ) (a) B = 16 T constant
10 K
11 K
12 K ( b ) d I/ d V ( m A / V ) V (mV) 11 T
12 T
13 T
T = 13 K constant 14 T
FIG. 3: (color online) Quasiparticle conductance dI ( V ) /dV of a 24 ◦ LCCO thin film GBJ in the vicinity of zero biasshowing the disappearance of the ZBCP (a) at constant field B = 16 T for different T and (b) at constant temperature T = 13 K for different B . Thin lines are parabolic fits to thequasiparticle conductance outside the ZBCP. GBJ, circles: 24 ◦ GBJ). We determined A ZBCP by inte-grating the difference of the measured quasiparticle spec-tra and the parabolic background conductance [c. f. Fig.3] in the range ± A ZBCP ( B ) | T = const and A ZBCP ( T ) | B = const decreases nearly linearly with increas-ing B and T , respectively[34], the intersection of the lin-ear fits with the A ZBCP = 0 axis defines B ZBCP (withvertical and horizontal error bars, respectively, in Fig.4). This procedure also allows to determine B ZBCP for
B >
16 T from A ZBCP ( B ) | T = const (see inset of Fig. 4). B ZBCP increases monotonically with decreasing T , ex-trapolating to B ZBCP ( T = 0) ≈
25 T. The black andgrey lines show B c ( T ), obtained from microscopic cal-culations (with T c = 29 K and B c (0) = 25 T), assumingeither a 2D Fermi cylinder (black line) [25] or a 3D Fermisphere (grey line) [26]. These lines may be considered asa lower bound for the true B c of our samples. Note that B c (0) = 25 T is at least a factor of 3.5 larger than thezero temperature extrapolation of B .So far we have argued that the observation of theZBCP extends the superconducting regime to magneticfields that are much higher than anticipated. We nextshould discuss why we see a uniform ZBCP at all at largefields, without evidence for a splitting. A pronouncedsplitting would occur due to circulating currents if a sin-gle vortex were present near one side of the grain bound-ary [27]. On the other hand, in the case of a symmetricstatic vortex configuration, the screening currents thatflow along the grain boundary are of equal strengths butopposite direction (cf. arrows in lower right inset in Fig.2b). In this situation the shifts of the ABS (forming fastcompared to the time scale of vortex fluctuations) shouldcancel and no splitting is expected. In the case of a vor-tex liquid, which is likely to be present in the high fieldregion we discuss here, the screening currents on the twosides of the GBJ will fluctuate, but are likely to have zero B ( T ) T (K) 5 K6 K8 K10 K12 K Z B C P a r ea ( a . u . ) B (T)
FIG. 4: (color online) Magnetic field vs. temperature phasediagram showing the fields B (open squares), B (opendiamonds) and B (open triangles), as determined from ρ ( T )curves of Fig. 1, together with the field B ZBCP where theZBCP in the quasiparticle tunnel spectrum disappears. Fullcircles: 24 ◦ GBJ, full squares: 30 ◦ GBJ. The black and thegrey lines correspond to B c ( T ), calculated for a 2D Fermicylinder and a 3D Fermi sphere, respectively. The inset showsthe ZBCP area vs. B for different temperatures. Lines arelinear fits, which, by extrapolation to zero ZBCP area, definevalues of B ZBCP for
B >