Proceedings of the 29th International Conference on Low Temperature Physics (LT29)
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Proc. 29th Int. Conf. Low Temperature Physics (LT29)
JPS Conf. Proc. 38, 011041 (2023)
https://doi.org/10.7566/JPSCP.38.011041

Andreev Bound States and Doppler Shift in
La1.85Sr0.15CuO4/Au Junctions
Hironori Teshima1 , Kang Donguhn1 , Takashi Sakamori1 , Rikizo Yano1 , Yuya Hiramatsu1 ,Shun Tamura1 , Keiji Yada1 , Yukio Tanaka1 , Takao Sasagawa2 , Satoshi Kashiwaya11

Department of Applied Physics, Nagoya University, Furocho, Chikusa, Nagoya, Aichi 464-8603,
Japan
2
Laboratory for Materials and Structures, Tokyo Institute of Technology 4259 Nagatsuta,Midori-ku, Yokohama, Kanagawa 226-8503, Japan
E-mail: s.kashiwaya@nagoya-u.jp(Received July 28, 2022)
The formation of Andreev bound states (ABSs) at surfaces is one of the peculiar properties speciﬁc tounconventional superconductors. Although a large number of experimental data on the observationof the ABSs have been presented at the surfaces of YBa2 Cu3 O7−δ , the results of La1.85 Sr0.15 CuO4(LSCO) are limited. Here we study the formation of the ABSs and their magnetic ﬁeld (MF) responses at the surfaces of LSCO by using the in-situ electrodes formation technique. The conductance spectra of the LSCO/Au junctions change from broad zero-bias peaks to narrow zero-bias
peaks by increasing the exposure duration of the cleaved surfaces to the vacuum during the junction
fabrication. This trend is qualitatively consistent with the barrier height dependence of the theoretical formula of tunneling conductance spectrum for d x2 −y2 -wave superconductors. The origin of thedistributed amplitudes of the MF responses of the conductance spectra is discussed by taking into
account the junction shape dependence of the Doppler shift.
KEYWORDS: Andreev bound state, Zero-bias conductance peak, Doppler shift

1.

Introduction

One of the most peculiar features of the superconductors preserving an unconventional pair potential with ﬁnite phase variation in momentum space is the formation of Andreev bound states (ABSs)
at surfaces and boundaries. The appearance of the ABSs can be detected by the tunneling conductance spectra of normal/insulator/superconductor (N/I/S) junctions as the conductance peaks inside
the superconducting energy gap. The width of the zero bias conductance peak (ZBCP) is exceedingly
narrow for N/I/S junctions of (110) oriented surfaces of d x2 −y2 -wave superconductors due to the formation of the dispersion-less zero-energy ABSs [1–4]. Therefore, the N/I/S junctions of d x2 −y2 -wave
superconductors are ideal probes to test the Doppler shift that the quasiparticles in superconductors
experience the energy shift in the applied magnetic ﬁeld (MF) [5]. A similar energy shift has widely
been studied as the Volovik eﬀect; the density of states at the Fermi level is enhanced in the MF by
the circulating current near vortex cores when the pair potential has nodes [6]. Previous studies on
the observation of the ZBCP and their MF response in cuprates are mainly performed at (110) oriented surfaces of YBa2 Cu3 O7−δ (YBCO), and their results of the MF responses are rather distributed[7–10, 12]. Compared with a large number of reports on YBCO, the results on La1.85 Sr0.15 CuO4(LSCO) are limited because of the diﬃculty in high-quality tunneling barrier at LSCO surfaces[13–17]. Therefore, here we examine a simple method of fabricating N/I/S junctions with variousbarrier heights using LSCO and investigate the MF response of conductance spectra to clarify theproperties of the Doppler shift on the tunneling conductance spectra. Also, we numerically analyze
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the amplitude of energy shift by considering the junction shape dependence of the Doppler shift. We
present a possible explanation for the distributed results on the energy shift amplitude detected invarious experiments.

Fig. 1. (a) Experimental conductance spectra obtained in the LSCO/Au junctions as the function of exposure
duration (T e ). The curves are shifted for clarity. The arrows show the appearance of the two dips by increasing
the exposure period. The inset shows an optical microscopy image of an LSCO/Au junction. (b) Temperaturedependence of ∆ obtained in the LSCO/Au junction of T e =0 min. The red circles show the experimental data,and the dotted line shows the BCS theory of ∆=13 meV. (c) Temperature dependence of ∆ obtained in theLSCO/Au junction of T e =30 min. The blue circles show the experimental data, and the dotted line shows theBCS theory of ∆=12.8 meV.

2.

Junction fabrication

The optimally doped single crystals of LSCO used in the present study were grown by a ﬂoatingzone method, and their T c onset and T c zero are 41K and 37K, respectively. Careful treatment is required in the fabrication process because the surfaces of LSCO are easily degraded to non-conductivein the air. Since the deposition of a high-quality insulating layer is extremely diﬃcult, we apply thedegraded layer to the insulating layer of the tunneling junction by tuning the degradation condition. A
similar method has been successfully used in Al-based tunneling junctions and Josephson junctions,in which the oxidized layers in low pressured O2 atmosphere are applied for high-quality insulating
layers. Referring to this method, we developed a fabrication method for the N/I/S junction as follows.
First, we molded the single crystals into thin pellets with a sub-millimeter thickness. The c-axis of
the crystals was perpendicular to the wide surface. Next, the pellets were stored in a vacuum chamber with a pressure ∼1 Pa, and then cleaved the pellets in a vacuum. Then, the counter electrodes(Au) were deposited in-situ after the cleaved surfaces were exposed to the low vacuum for a certain2

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duration. We expect the barrier potential of the insulator can be tuned by changing the exposure duration. Finally, the cleaved pellets were taken out of the chamber and ﬁxed on SrTiO3 substrates toget electrical contacts (see the inset of Fig. 1). The conductance spectra were measured by the conventional three-terminal method with Physical Properties Measurement System (PPMS, Quantum
Design Japan, Inc.). Although the orientation of the boundary is perpendicular to the CuO2 plane,
we cannot certify that the boundary is along (110). Since the junction boundaries are dominated bysevere unevenness, various interface orientations are contained intrinsically in a single junction.

3.

Experimental conductance spectra

Figure 1 shows experimental conductance spectra obtained in the LSCO/Au junctions as thefunction of the exposure duration (T e ). The broad zero-bias peak with excess conductance is detected
when the exposure duration is relatively short (T e = 0, 10 min). The amplitude of the order parameter∆ estimated by the dip energy in the conductance of approximately 13meV is consistent with previous works. The temperature dependences of ∆ for T e =0 min and T e =30 min shown in Fig. 1(b) and1(c) follow BCS theoretical curves. These facts certify that the conductance peaks originate from superconductivity. By increasing the exposure duration, the excess conductance is gradually suppressedwith the appearance of the two dips beside the peak marked by arrows in Fig. 1(a), and the widths andthe heights of zero-bias peaks are reduced. Small zero-bias peaks inside the gap are observed for T e= 30 min. A seriously suppressed superconducting gap is detected for T e = 40 min. The conductanceshapes for T e = 0 min and T e = 30 min are similar to those reported in [10] and [8], respectively.
This fact suggests that the spectral shape diﬀerence in previous reports can mostly be attributed to thesurface quality.
Next, we discuss the consistency between experimental data and the theory of conductance spectra of d x2 −y2 -wave superconductors. The amplitude of barrier height is introduced by Z (Z ≡ Hb /ℏk2F ,Hb : amplitude of δ-potential, kF : Fermi wave length) parameter in the theory [3, 4]. When Z is small,the conductance spectra are dominated by Andreev reﬂection with large excess conductance [18].
The shape of the broad zero-bias peak reﬂects the distribution of the gap amplitude of d x2 −y2 -wave
pair potential [3]. This feature is consistent with experimental results of the broad zero-bias peak ofT e = 0 min. By increasing Z, the sharp ZBCP with dips inside the gap appears to reﬂect the formationof the ABSs. This feature is consistent with experimental results of the narrow zero-bias peak withthe two dips detected in the T e = 30 min junction. The Z dependence of theoretical curves is qualitatively consistent with those observed in experiments by varying the exposure duration. Therefore,
we conclude that controlling the barrier potential by tuning the exposure duration is successfully accomplished. On the other hand, the peak height of T e = 30 min is seriously suppressed compared tothat theoretically expected to (110) surface of d x2 −y2 -wave superconductors. One origin for the suppression is that the orientation of the junction was not controlled to (110) as stated above, and theaverage of various orientation components reduced the conductance peak height. Another is that thecurrent fabrication process could produce impurities near the interface; the peak height is suppressedby impurity scattering near the boundaries [19].

4.

Magnetic ﬁeld responses

The energy shift of quasiparticles in superconductors in the applied MF is known as the Dopplershift. The shift can be detected in tunneling conductance spectra as peak shift or broadening. According to the theory [5], the amplitude of energy shift is 2.3 meV/T for YBCO by assuming typicalvalues (∆=17 meV, the coherence length ξ=1.4 nm, the penetration depth λ=800 nm), and 1.3meV/Tfor LSCO (∆=11 mV, ξ=3.26 nm, λ=300 nm). Figure 2 shows the MF responses of conductancespectra obtained in the present experiments when the MF was applied parallel to the c-axis of the3Proceedings of the 29th International Conference on Low Temperature Physics (LT29)
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Fig. 2. Magnetic ﬁeld responses of conductance of LSCO/Au junctions with (a) T e =0 min, (b) T e =10 min,(c) T e =20 min. The peak broadening is obtained for (c) as plotted by black dotted lines that follow the conductance bends. The curves in (c) are shifted for clarity.

crystals. When T e is small (0 min, 10 min), the ZBCPs were relatively robust to the MF, while thetwo side peaks located ∼4-5 meV were severely suppressed. Since the two side peaks are sensitive tothe MF, we attribute the origin to the proximity eﬀect and the multiple Andreev reﬂection due to thehigh transmissivity of the junction [20]. On the other hand, the ZBCP detected in T e =20 min junction
showed the peak broadening when the MF was applied, as plotted by the black dotted line in Fig.
2(c). Assuming that the Doppler shift induces the broadening, the amplitude of the Doppler shift wasapproximately 0.06 meV/T. These observations indicate that the amplitudes of the Doppler shift are
far smaller than those expected theoretically. In fact, the amplitude of the Doppler shifts reported inprevious reports are rather distributed; 0.7 meV/T [7], 1.2 meV/T [11], 0.5 meV/T [9], no-splitting[12]. The fact that ﬁnite Doppler shift was observed only for the relatively high-barrier junction isinconsistent with the tunneling core model [21]. We believe that the distributed results in cuprates
indicate the requirement for further analyses of the Doppler shift experimentally and theoretically.

5.

Simulation of the Doppler shift

We discuss a possible origin for the distributed amplitudes of the Doppler shift. Theoretically, theenergy shift is introduced into the conductance formula as the ﬁnite vector potential eﬀect. Although
the shift has been evaluated in the uniform vector potential in the previous studies [5, 22, 23], theuniformity is not valid to get the consistency with experimental data because the vector potential depends on the shape and the position of the junction. Therefore, we solved the London equation with aﬁnite element method by assuming a realistic junction shape and calculated the conductance spectra.
We assumed a plate-shaped d x2 −y2 -wave superconductor, and the junction electrodes were formed at
diﬀerent positions at the side face as shown in Fig.3 (a). The orientation of the side face was assumed
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to be (110) in the calculation. The obtained conductance spectra under the MF shown in Fig.3 (b)show strong position dependence. The splitting amplitude decreased as the electrode position approached the edge of the superconductor. Similar position dependence appears when the junction
surface has unevenness. Therefore, we conclude that we should consider details of the junction shapewhen analyzing the amplitude of the Doppler shift. More details will be presented elsewhere.

Fig. 3. (a) Schematic illustrations of the junction shape used in the calculation. We assume a d x2 −y2 -wave
superconductor with a plate (height = 0.3 µm, width, depth = 5.0 µm, λab = 100 nm, λc = 1500 nm), and thesizes of the N/I/S junction electrodes are 200 × 200 nm2 . The positions of electrodes A, B, C, and D are 2.5,1.24, 0.2, and 0.1 µm apart from the edge, respectively. (b) Calculated normalized conductance spectra for eachjunction position shown in (a). The dotted line is the normalized conductance in the zero ﬁeld. The curves A-Dshow the calculated conductance spectra under the 0.1µ0 H0 MF parallel to the c-axis (µ0 H0 = ϕ0 /λξπ2 , ϕ0 ismagnetic ﬂux quantum). ∆0 is the maximum of the amplitude of d x2 −y2 -wave pair potential.

6.

Summeries

We developed a simple method to fabricate LSCO/Au junctions with various barrier heights. The
development of conductance spectra as the function of exposure duration was qualitatively consistent
with theoretical conductance spectra for d x2 −y2 -wave superconductors with various barrier heights.
The magnetic ﬁeld responses due to the Doppler shift were suppressed than those expected theoretically. We propose a possible origin accounting for the variety of the Doppler shift’s amplitude interms of the junction shape eﬀect based on the numerical simulation of conductance spectra.
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Acknowledgements
The authors would thank Dr. Toshimitsu Ito (AIST) and Dr. Yasuko Ozaki (AIST) for assistingin determining the crystal orientation of LSCO.
This study was supported by KAKENHI (Grant Nos. 18H01243, 20H00131, 20H01857, 21H01009,21H04652, 21H05236, 21K18181 and 21K13854). The single crystal growth was supported by Collaborative Research Projects in MSL-Tokyo Tech., Japan.
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