superconductor junction with a long-split gate

Superlattices and Microstructures, Vol. 25, No. 5/6, 1999 Article No. spmi.1999.0754 Available online at http://www.idealibrary.com on

A superconductor/semiconductor/superconductor junction with a long-split gate H IDEAKI TAKAYANAGI , E TSUKO T OYODA , TATSUSHI A KAZAKI NTT Basic Research Laboratories, Atsugi-shi, Kanagawa 243-0198, Japan (Received 24 March 1999)

Measurements of superconducting and normal transport in a superconductor/semiconductor/superconductor junction with a long-split gate show that when the two-dimensional electron gas in the semiconductor is put into the pinched-off state by applying a gate voltage, the two superconducting electrodes couple through a long and narrow channel with a small number of modes. Multiple Andreev reflections the focusing of Andreev-reflected holes are observed in this situation, but the supercurrent decreases quickly as gate voltage is increased and it disappears when the channel is long and narrow. A sharp conductance peak due to the coherent motion of the electrons and holes in the narrow channel is also observed. c 1999 Academic Press

Key words: Andreev reflection, superconductor/semiconductor junction, gate control.

1. Introduction Superconducting and normal transport in a superconductor/normal metal/superconductor (SNS) junction have been studied in junctions having a channel that is either wide and short or narrow and short [1]. A junction coupled with a long and narrow channel is also very interesting [2], but such a junction has not been studied experimentally, because of the difficulty of fabricating such a structure. We have therefore fabricated a semiconductor-coupled junction with a long-split gate and measured the transport in the narrow and long channel sandwitched by superconductors. Gate-fitted semiconductor-coupled Josephson junctions have provided many interesting results, such as the quantization of the critical current in a superconducting quantum point contact (SQPC) [3], Fabry–P´erot interference of the critical current [4], operation of a Josephson field effect transistor [5], mesoscopic fluctuations of the critical current [6], and controlled reentrant behavior of the conductance [7]. Gate control is a very powerful tool for the study of quantum transport because the electron state in the semiconductor can be changed systematically by adjusting the gate voltage. In this paper we report the changes in junction characteristics—the zero-bias resistance, the differential resistance as a function of bias voltage, and the critical current—that are induced by changing the gate voltage. The observed conductance enhancement is also discussed with regard to the coherent motion of the electron and the hole. 0749–6036/99/050993 + 12 $30.00/0

c 1999 Academic Press

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Long split gate Lg

A

B

Split gate

W Nb

Nb Nb L

Nb

InAs (2DEG)

InAlAs/InGaAs Heterostructure

5KV X20,000

1 µm

InP Substrate Fig. 1. A, Cross-sectional view of the junction. B, SEM photograph of the junction.

2. Junction structure and characteristics 2.1. Junction configurations Figure 1A, is a schematic cross-sectional view of the fabricated junction. We used an InAs-inserted In0.52 Al0.48 As/In0.53 Ga0.47 As heterostructure as the semiconductor. The two-dimensional electron gas (2DEG) was well confined in the 4 nm-thick InAs channel. The mobility µ and the carrier density NS of the 2DEG at 4.2 K were measured to be 31, 000 cm2 V−1 s−1 and 2.4 × 1012 cm−2 . The 2DEG was sandwitched between two superconducting Nb electrodes and both a supercurrent and normal current flowed through it. The junction width W was 40 µm and the distance L between Nb electrodes was 2 µm (Fig. 1B). The details of the fabrication processes were almost the same as those of the fabrication processes for a shortgated junction [5, 8]. The measured µ and NS values give a mean free path ` of 0.8 µm, the Fermi wavelength λF of 16 nm, and the Fermi velocity vF of 9.8 × 105 ms−1 . Given that L = 2 µm and ` = 0.8 µm, it is evident that the channel transport was in the quasiballistic regime. The junction had a long-split gate (length L g = 1.6 µm) and the geometrical split width was about 0.2 µm. When negative gate voltage was applied to the split gate and the state of the 2DEG was the pinched-off state, the channel width L W was defined by the depletion layer around the gate electrode. Because the 0.2 µm split width was relatively wide, the channel could not completely closed by applying a gate voltage (the minimum L W generated by gate voltage was about 0.05 µm). 2.2. Junction characteristics Figure 2A, shows the differential resistance–bias voltage characteristics (d V /d I –V ) measured at 4.2 K and 0.05 K. The energy gap 1 of Nb is 1.5 meV, but it is found from the figure that the energy gap in the junction was about 1 meV. In a superconductor/normal metal/superconductor (SNS) junction, multiple Andreev reflection (MAR) between two SN interfaces occurs when the elastic or inelastic scattering in the normal region is negligible [9]. MAR results in the subharmonic energy gap structures which appear on the current–voltage characteristics of the junction at V = 21/ne(n = 1, 2, 3). The d V /d I –V curve derived from measurements at 4.2 K showed only a structure of n = 1 because the channel transport was in the quasiballistic regime (` < L) and the elastic scattering was negligible. As shown in the figure, the curve derived from the measurements at the lower temperature has a second structure (n = 2).

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A

B 1.2 Normalized peak height

Differential resistance (Ä)

17 4.2 K

16 15

0.05 K

14 13 12 11 –6

–4

–2

0

2

Bias voltage, V (mV)

4

6

1 ∼ 1.5 meV

1.0

1 ∼ 1 meV

0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

5

6

Temperature (K)

Fig. 2. A, Differential resistance–bias voltage characteristics for two temperatures when gate voltage is zero. The curve for 4.2 K is shifted by 2 . For the measurements at 0.05 K, a small magnetic field was applied in order to suppress the supercurrent. B, Height of the peak structure around V = 0 as a function of temperature. The peak height is normalized by that at the lowest temperature.

On the d V /d I –V curve for T = 0.05 K a sharp peak around V = 0 is indicated by an arrow in the figure. The height of this peak gradually increased as temperature decreased, and the height of this peak is plotted as a function of temperature in Fig. 2B. The peak height for another junction which used the same heterostructure but had a larger energy gap (1 ≈ 1.5 meV) is also shown in the figure. The behavior of the peak height for the junction discussed here is very similar to that of the peak height for the junction with the larger energy gap. Moreover, the ratio of the energy gaps of the two junctions (1 meV/1.5 meV) is similar to the ratio of the temperatures at which the corresponding peak structures disappeared: 4.2 K/6 K (see the figure). Although the physical origin of the peak structure is not yet known, the similarity between the two ratios indicates that the structure is due to superconductivity in the S/2DEG/S junction. The d V /d I –V curve at a low value of V was about 20% lower than that at a value of V greater than 21/e. This indicates that the barrier strength Z of the S/2DEG interface is about 0.65 and the transmission probability of the interface 0 = 1/(1 + Z 2 ) is about 0.7 [10]. These Z and 0 values are large enough to provide good electrical contact between the 2DEG and the Nb electrodes. The supercurrent surprisingly observed in this junction with a long L of 2 µm discussed later is a result of the good contact at the interface.

3. Gate control of the junction characteristics 3.1. Zero-bias resistance A zero-bias resistance R0 = (d V /d I )V =0 is shown in Fig. 3A, as a function of Vg . This figure indicates that the pinched-off state of the 2DEG starts to appear when Vg is about −1.1 V and that two superconducting electrodes couple with each other through only the narrow channel when Vg < −1.1 V. The zero-bias conductance G 0 (= 1/R0 ) in the pinched-off state of the 2DEG is plotted in Fig. 3B. Some step-like structures are seen but are not clear. This is because of the transport properties of the narrow channel (i.e. L > `). When a magnetic field of 860 Gauss was applied perpendicularly to the 2DEG, G 0 in units of 2e2 / h was reduced by 1.5 to 3. Andreev reflection increases the conductance in a superconductor/normal metal junction and a magnetic field destroys the retro property of Andreev reflection. This increases the resistance. The conductance increase due to Andreev reflection will be discussed again in Section 3.2. A magnetic field of 860 Gauss was large enough to prevent superconductivity from influencing the conductance in the junction. The G 0 − Vg curve with a magnetic field shows that there is ten modes at Vg = −1.13 V

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A

Zero-bias resistance, R0 (Ä)

T = 0.05 K

1000

100

10 –1.5

–1

–0.5

0

Gate voltage, Vg (V)

[t] Zero-bias resistance, G0 (2e2/h)

11

A

10 9 B=0

8 7 6 B = 860 Gauss

5 4 –1.5 –1.45 –1.4 –1.35 –1.3 –1.25 –1.2 –1.15 –1.1 Gate voltage, Vg (V)

Fig. 3. A, Zero-bias resistance R0 as a function of gate voltage. R0 was measured under zero magnetic field. B, Zero-bias conductance in the pinched-off state of the 2DEG as a function of gate voltage measured under two magnetic fields.

and six modes at −1.25 V in the narrow channel (i.e. the number of subbands in the channel is ten and six for each vales of the gate voltage). 3.2. Differential resistance–bias voltage characteristics It is interesting to study the d V /d I –V characteristics as Vg changes. It is clearly seen in Fig. 4A, that the d V /d I –V curve becomes shallower as the absolute value of Vg increases. This indicates that the conductance increase due to Andreev reflection becomes smaller as the scattering in the 2DEG underneath the gate electrodes increases. This flattening of the d V /d I –V curve continued until the curve became almost flat at a Vg of about −1.0 V. Then, as shown in Fig. 4B, d V /d I stopped decreasing with decreasing V and began increasing with decreasing V . But this behavior changed again after the absolute value of Vg exceeded 1.1 V when the pinched-off state of the 2DEG started to appear (see Fig. 4B). As shown in Fig. 4C, the bump structure of d V /d I –V curve gradually became lower and the curve was almost flat when Vg ≈ −1.2 V as

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997

1.15 T = 0.05 K

Normalized dV/dI

1.1 1.05 1 0.95 0.9 0.85 0.8 –6

–4

–2

0

2

4

6

Bias voltage (mV)

[t] B

1.5

Normalized dV/dI

1.4 1.3 1.2 1.1 1 0.9 –6

–4

–2 0 2 Bias voltage (mV)

4

6

Fig. 4. A, Differential-resistance d V /d I as a function of bias voltage V for Vg = 0, −0.5 V, and −0.8 V (from bottom to top). d V /d I is normalized by its value at a high bias voltage. B, d V /d I –V characteristics for Vg = −1.1, −1.15, and −1.35 V (from top to bottom). C, d V /d I –V characteristics for Vg = 0 and −1.2 V. The curve for Vg = −1.2 V is shifted by 0.1. Subharmonic-gap structures are seen on both curves. D, Top view of the junction. Andreev reflection leads to the reflected holes being focused in the narrow channel.

shown in Fig. 4C. And as shown in Fig. 4B, the bump became a dip (i.e. a conductance-enhanced structure) when Vg = −1.35 V. The d V /d I –V behavior after the pinched-off state appears can explained as follows. After the 2DEG underneath the gate electrode was pinched off, there was only a narrow channel. The reflected electrons due to the normal reflection at the SN interface then did not return to the narrow channel but the reflected holes due to Andreev reflection returned to it because of the retro property (see Fig. 4D). When the holes return to the other electrode through the narrow channel, the measured resistance decreases. The d V /d I –V characteristics in Fig. 4B, show that the focusing effect of the Andreev-reflected holes was enhanced as the channel became narrower. This focusing effect was measured in a junction with a short split gate, which is called a superconducting quantum point contact (SQPC) because the 1D channel generated by the split gate shows the quantized critical current [11].

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1.2

C

Normalized dV/dI

1.1

1.0 0.9

0.8 –6

–4

–2 0 2 Bias voltage (mV)

4

6

D

Normal reflection

e h Gate

Nb Andreev reflection

Fig. 4. continued

Looking again at Fig. 4C. The d V /d I –V characteristics for Vg = −1.2 V clearly showed the subharmonic energy-gap structures up to n = 2 as illustrated by arrows in the figure. This indicates that the electron and hole came and went several times without energy dissipation through a narrow and long channel in the quasiballistic transport regime. A clear dip structure can also be seen around zero-bias voltage. This structure is not due to a supercurrent because the supercurrent disappeared when Vg was about −0.85 V (see Section 3.3). This sharp enhancement of the conductance with a narrow critical voltage (≈0.25 mV) will be discussed in Section 4. 3.3. Superconducting critical current As shown in Fig. 5, the current–voltage (I –V ) characteristics were measured as a function of gate voltage Vg at a low temperature. The figure shows that the junction showed a very high controllability of the maximum supercurrent (the critical current IC ) by Vg . Indeed, Fig. 6 shows that IC decreases quickly as Vg increases and disappears for Vg < −0.85 V while the zero-bias junction normal resistance R0 increases slowly (R0 increased from 15.6  to 40 ). This IC behavior is very different from that found in a short split-gated junction (SQPC) where IC still showed a small amplitude after Vg exceeded −1 V [3]. This junction has two parallel channels for the supercurrent. The first is the 2DEG underneath the gate and

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3 T = 0.05 K

Current (µA)

2 1 0 –1 –2 –3 –40

–20

–0 20 Voltage (µV)

40

Fig. 5. Current–voltage characteristics of the junction. From top to bottom, gate voltage Vg is 0, −0.2, −0.4, −0.5, −0.6, and −0.8 V.

A

B

50 0.2 40 IC (µA)

R0 (Ä)

0.15 30

0.1 0.05

20

0 –0.85

10 –0.8

–0.6

–0.4

–0.2

0

–0.8

–0.75

–0.7

Vg (V)

Vg (V) Fig. 6. A, Critical current IC and junction normal resistance R0 versus gate voltage measured at 0.05 K. B, IC as a function of Vg in the region where IC becomes almost zero.

the second is the long narrow channel generated by the split gates. The fact that there was no supercurrent when Vg < −0.85 V indicates two things. The first is that the 2DEG underneath the gate became gradually diffusive as the absolute value of Vg increased and that supercurrent could not flow through the 2DEG when Vg < −0.85 V. This behavior can be explained by proximity effect theory in the dirty limit case ξT > `, where ξT = (~D/2πkB T )1/2 is the coherence length and D is the diffusion constant in the 2DEG [13]. The second thing indicated is that supercurrent could not flow through a long, narrow channel. If we assume that the critical current IC is proportional to the junction width W , an IC of about 5 nA should be measured when the number of the modes in the semiconductor channel is 10. As discussed in Section 3.1, we confirmed that the channel survived at a Vg higher than −1 V and a Vg of about −1.13 V provided a

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10-mode channel. The IC may not be proportional to W , but no adequate explanation for the absence of the supercurrent is known. Mesoscopic fluctuations of the critical current were observed when the 2DEG in a S/2DEG/S junction was in the dirty limit [6]. The critical current exhibited mesoscopic fluctuations as a function of gate voltage (i.e. the Fermi energy of the 2DEG). This is because the physical origin of the fluctuations of the IC is the same as that of universal conductance fluctuations (UCF). Figure 6B shows IC as a function of Vg in the regime where the 2DEG became very dirty. The fluctuations of the IC that are evident in the figure may therefore also be explained by mesoscopic fluctuations.

4. Conductance enhancement due to coherent Andreev reflection Figure 7A shows the differential conductance–bias voltage (d I /d V –V ) characteristics measured when Vg = −1.25 V. A sharp peak can be seen around zero bias voltage. This peak is the same as that shown in Fig. 4C for Vg = −1.2 V. It was found that the peak structure (i.e. a sharp conductance enhancement) appeared after the pinched-off state of the 2DEG appeared. Therefore, the observed conductance enhancement cannot be explained by the coherent Andreev reflection which is increased by the elastic scattering in the disordered 2DEG [14]. The measured peak height (in units of e2 / h) and the measured width of the peak VC are plotted against Vg in Fig. 7B. VC is the definition of the critical voltage for the conductance enhancement. It is found that the peak height (in units of e2 / h) ranges from 1 to 2 and that VC is about 0.25 mV. To obtain the critical magnetic field for the sharp conductance enhancement, we measured the zero-bias conductance G 0 for a fixed value of Vg and plotted it against the applied magnetic field B. The measured G 0 is shown in Fig. 7C as a function of B. From this figure it is found that G 0 was reduced from 8.5 to 6.2 in units of 2e2 / h at B of about 80 Gauss and was almost constant of 6.2. This value of 6.2 coincides with the value of G 0 for Vg = −1.25 V in Fig. 3B. However, G 0 with no gate voltage also showed a similar behavior in that G 0 decreased rapidly as B increased to about 80 Gauss and for larger values of B was almost constant. Therefore, 80 Gauss is considered to be the value above which the influence of superconductivity (i.e. Andreev reflection or the proximity effect) on the junction conductance can be neglected. G 0 in a narrow regime of B is plotted in Fig. 7D, which shows that G 0 decreases rapidly as B increases to about 7 Gauss. This value corresponds to the critical field BC . It is noted that because of flux-focusing by the diamagnetic Nb electrode, the magnetic field in the 2DEG is enhanced over the applied field by a factor of up to F = (2W/L)2/3 [15]. The geometry of the junction used in the present study yielded F = 11.7 and this value of F gives a BC ≈ 82 Gauss. Note that the value of 82 Gauss for BC is a roughly evaluated value because F strongly depends on the sample geometry. One explanation for the sharp conductance enhancement is the ballistic motion of electrons and holes. As shown in Fig. 8A, the motion occurs in the narrow region generated between the gate potential and the superconducting electrode. In this model the potential barrier plays the same role as the scatterer in a disordered metal. The elastic scattering at the potential wall results in an increase in Andreev reflection. According to a model based on the scattering theory [16], E C = eVC = ~/τdwell , where τdwell is the dwell time of an electron in the region between the Nb electrode and the potential barrier. The dwell time τdwell is given by X/vF 0, where X is the length of the electron motion. X is given by 3x(θ), where x(θ ) is the distance between point a and b in Fig. 8A. As shown in the figure, θ is the injection angle. In this case, BC corresponds to the magnetic field which satisfies the relation BC = 80 /S(θ ), where S(θ ) is the section of the triangle bcd and 80 is the flux quantum e/ h. The expected values of x(θ) and S(θ) are given by  Z π/2 Z π/2 hxi = x(θ)P(θ)dθ P(θ)dθ, 0

0

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A

1001

Differential conductance, dI/dV (2e2/h)

9 T = 0.05 K Vg = –1.25 V

8.8 8.6 8.4 8.2 8 7.8 7.6 –1

–0.5

0

0.5

1

Bias voltage, V (mV) 2.5

0.3 0.25

2 0.2 0.15

1.5

0.1

Peak height (e2/h)

Width of the peak, Vc (mV)

B

1 0.05 0.5 0 –1.4 –1.35 –1.3 –1.25 –1.2 –1.15 –1.1 –1.05 Gate voltage, Vg (mV)

Fig. 7. A, Differential conductance as a function of bias voltage at Vg = −1.25 V. B, Width and height of the conductance peak versus gate voltage. C, Zero-bias conductance G 0 as a function of applied magnetic field B at Vg = −1.25. Zero point of B was shifted because of the trapped fluxes in the superconductor. D, G 0 − B characteristics in a regime of B narrower than that in part C.

hSi =

Z

π/2 0

w 2 tan(θ)P(θ )dθ

Z

π/2

P(θ)dθ,

(1)

0

where w is the width of the region shown in Fig. 8A. P(θ) is the angular injection distribution. If we use the broad distribution P(θ) = cos θ , we obtain hX i = 3hxi = 1.5 wπ and hSi = w 2 . These expected values of X and S result in E C = 0.690 meV and BC = 1000 Gauss. Even though 0 = 0.7 is used, the calculated E C and BC values do not coincide with the values obtained experimentally. Moreover, it is shown that the actual distribution function of the injection angle is much sharper than cos θ because of the collimated effect [17]. The model shows that as the distribution becomes sharper, both E C and BC become larger and the discrepancies between the calculated and experimental values increases. Therefore, it is concluded that the model discussed here cannot explain the observed conductance enhancement.

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C

8.5

Zero-bias conductance, G0 (2e2/h)

T = 0.05 K

8 7.5 7 6.5 6 5.5 0

200

400

600

800

1000

Magnetic field, B (Gauss) D

8.5

G0 (2e2/h)

8 7.5 7 6.5 6 –20 –15 –10

–5

0

5

10

15

20

Magnetic field, B (Gauss) Fig. 7. continued

Another explanation for the conductance enhancement is based on a small number of modes in the channel. The normal current due to the coherent motion of the electrons and holes results in the increased conductance. Each mode in the channel has such a current with a different phase. When the semiconductor channel between the two superconductors is wide, the number of modes N is large (N  1) and mode-mixing occurs. The mode-mixing results in averaging the phase of such currents. Consequently, the sum of the currents which contribute to the conductance enhancement becomes small. However, if the number of modes is small (N ≥ 1), the mode mixing can be neglected and the conductance enhancement due to such a coherent motion of the electron and the hole becomes remarkable. It is noted that the enhanced conductance is sensitive to a magnetic field because the phase-coherent motion of the electron and the hole is sensitive to a magnetic field and this sensitivity is of the same order as that of a supercurrent. As discussed before, the width of the conductance peak is given by VC = E C /e = ~vF 0/eX . It is clear that the length X of the motion in Fig. 8B is L = 2 µm. Then VC = 0.23 mV is obtained when

Superlattices and Microstructures, Vol. 25, No. 5/6, 1999

A

1003

w Nb a Gate

B Gate

θ b

Nb

h

e

Nb

c d Fig. 8. Mechanism of the conductance enhancement. A, An electron emitted from point a is Andreev-reflected and comes back as a hole to point a. In some probability the electron is normally reflected at point b and finally Andreev-reflected at point d. The Andreevreflected hole also goes back to point a. Consequently, the interference occurs at point a. B, Phase-coherent motion of the electron and hole in a narrow channel with a small number of modes.

0 = 0.7. This calculated value of VC coincides well with the experimental value, 0.25 mV. As is well known, a magnetic field breaks the time-reversal symmetry. This effect appears as the decrease in the overlap between the electron wavefunction and the hole wavefunction in the same mode. In this model the critical magnetic field is given very roughly by BC = 80 /S and S is L W × L. Because L is 2 µm and L W is between 0.1 and 0.2 µm, BC is between 103 and 206 Gauss, a range that almost includes the value obtained experimentally. The second model seems to explain the experimentally obtained conductance peak very well even though the model for the evaluations of both BC and VC is simple. Further theoretical developments as well as more experimental data are required.

5. Conclusions We have fabricated a superconductor/semiconductor/superconductor junction with a long-split gate. This structure could provide both a long and wide channel and a long and narrow channel with a small number of modes. Even when the channel was long, narrow, and quasiballistic, the junction showed a focusing of Andreev-reflected holes and also showed multiple Andreev reflection. Surprisingly a superconducting critical current was observed in spite of a long distance of L = 2 µm when the channel was wide. The critical current decreased quickly, however, as gate voltage increased, and when the channel was narrow, the critical current disappeared even though several modes for normal current survived in the channel. A sharp conductance enhancement was also observed when the channel was narrow. This can be attributed to a coherent motion of the electron and hole in a narrow channel when the mode mixing is negligible. Acknowledgements—We thank Dr H. Nakano, Dr J. Nitta, and Dr T. Enoki for their valuable discussions on electron transport in the heterostructure. This work was financially supported by NEDO International Collaboration Fund.

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