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GaSb heterostructures under a tilted magnetic field
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Physica E 20 (2004) 232 – 235 www.elsevier.com/locate/physe
Quantum Hall e ect in back-gated InAs/GaSb heterostructures under a tilted magnetic *eld K. Suzukia;∗ , S. Miyashitab , K. Takashinaa , Y. Hirayamaa; c a NTT
Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b NTT Advance Technology Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan c CREST-JST, Kawaguchi-shi, Saitama 331-0012, Japan
Abstract We investigate the quantum Hall e ect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic *eld perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) *lling factors of the net-carriers, where the net-carrier density is the di erence between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-net discontinuous. Under tilted magnetic *elds, these Rxx maxima disappear in the high magnetic *eld region. The results show that the in-plane magnetic *eld component enhances the electron–hole hybridization and the formation of minigaps at LL crossings. ? 2003 Elsevier B.V. All rights reserved. PACS: 73.20.−r; 73.40.−c; 73.43.−f Keywords: Electron–hole hybridization; Quantum Hall e ect; Back-gate
1. Introduction In InAs/GaSb heterostructures, the conduction band in the InAs and the valence band in the GaSb overlap. When the Fermi-level lies in the overlap region, electrons in the InAs and holes in the GaSb coexist in close proximity. This system is of great interest with respect to the electron–hole band hybridization [1] which leads to the formation of a minigap. New physics phenomena such as Bose–Einstein condensation of excitons are expected [2]. The most remarkable feature known up to now is the unique ∗
Corresponding author. E-mail address: [email protected] (K. Suzuki).
quantum Hall e ect [3]. When the Landau-level (LL) *lling-factors of electrons and holes (e , h ) become integers simultaneously, the longitudinal resistance (Rxx ) becomes zero and the Hall resistance (Rxy ) is quantized by the di erence between the *lling-factors Rxy = h=e2 |e − h |. It has been believed that the phenomenon arises due to Landau quantization of both electrons and holes simultaneously. However, recent experiments on gated-structures strongly indicate that the condition necessary to observe the QHE is that the *lling-factor of the net-carries net = |e − h | has to be an integer, rather than both e and h , although the detailed mechanism of the QHE has not been discussed [4,5]. In this paper we report magneto-resistance measurements in InAs/GaSb
1386-9477/$ - see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2003.08.071
K. Suzuki et al. / Physica E 20 (2004) 232 – 235
233
40
In contact
GaSb Al0.7Ga0.3Sb
MBE grown Fig. 1. Sample structure.
heterostructures grown on a conductive InAs substrate acting as a back-gate under perpendicular and tilted magnetic *elds. The e ect of an in-plane magnetic *eld component on the hybridization are examined. 2. Experimental procedure The sample structure is shown in Fig. 1. An InAs substrate (nominally undoped but conductive) is used as a back-gate. A 30 nm-InAs/18 nm-GaSb heterostructure which is sandwiched between Al0:7 Ga0:3 Sb barriers is grown on a GaSb/AlSb superlattice and an AlSb bu er layer on the substrate, by molecular beam epitaxy [5–7]. A thin GaSb layer is then grown on the surface as a capping layer. Indium contacts for both electron and hole layers are deposited. A Hall-bar structure was made by mesa-etching. The magnetoresistance was measured in a cryostat at 1:6 K applying a magnetic *eld of up to 15 T while sweeping the back-gate voltage VG . 3. Results and discussion Fig. 2 shows the gate leakage current as a function of the gate-voltage (VG ). The gate-voltage can be applied from −0:8 to 2:7 V without any e ect on magnetoresistance measurements which use DC currents of the order of A. The magnetoresistance with *eld perpendicular to the surface was measured
Leak Current (nA)
InAs GaSb Al0.7Ga0.3Sb AlSb/GaSb SL AlSb n-InAs Substrate (Nominally undoped)
20
0 -0.8 V
2.7 V
-20
-40
-1
0
1
2
3
VG (V) Fig. 2. Gate-leakage current as a function of the applied gate-voltage.
at di erent values of VG . Fig. 3 shows a contour plot of Rxx as functions of VG and the magnetic *eld (B). The dark regions correspond to regions of higher resistance and the bright regions show regions of lower resistance. Strong Shubnikov–de Haas oscillations as a function of B were observed. The oscillations are dominated by the electrons at low *eld because the mobility of the electrons is much higher than that of the holes. It was found that the electron density n = 10:75 × 1015 m−2 obtained from the oscillations stayed constant with increasing VG up to VG = 1:75 V. On the other hand, the hole density (p) obtained from the quantized Rxy and the classical *tting is p = (2:22–1:26VG ) × 1015 m−2 [8]. The electron mobility e = 8:0 m2 V−1 s−1 and hole mobility h = 0:5 m2 V−1 s−1 are also extracted from the *tting. After the depletion of the holes, VG ¿ 1:75 V, the system changes from the hybridized system to a two-dimensional electron gas system (2DEG) and Rxx maxima starts to be strongly a ected by VG since there are no more holes to screen the gate potential. The carrier densities in the InAs/GaSb system are determined by the gate, intrinsic charge transfer, effects due to the surface pinning [9], interface defects and impurities. If the electrons and holes were completely separated and independent, the hole and electron densities are well-de*ned quantities. In the opposite limit where the states in the InAs and GaSb are strongly hybridized, the individual densities are less
234
K. Suzuki et al. / Physica E 20 (2004) 232 – 235
νh=1
νe =3
R xx
14 νh=2
12 4
High
νh =3
10 B (T)
5
8 6 4
6 7
νnet =1
Low 2
34
56
2 0
-6
-4
-2 VG (V)
0
2
Depletion of holes
Fig. 3. Contour plot of Rxx as functions of gate-voltage (VG ) and magnetic *eld (B).
meaningful. However the net carrier density nnet = n−p must always be a well-de*ned quantity. Here, we describe our data in terms of e =nh=eB, h =ph=eB and net = nnet h=eB, where we have used values obtained from the data as already described. Since the SdH oscillation maxima arising from electronic extended states describe horizontal lines on the plot while electrons and holes coexist (VG ¡ 1:75 V), we take the electron density to be independent of VG in this region. We will interpret this behavior (Fig. 3) to be neither in the strongly hybridized limit nor the independent limit, so that the behavior does not depend on net alone [4] nor on separate e and h alone. The horizontal dashed lines represent integer-e and the dotted lines are integer-h . If the QHE in the hybridized system was caused by the independent QHE’s of the electrons and holes, the pattern of the Rxx minima should show Rxx minima along lines of integer-e and integer-h . However, the patterns of Rxx minima in the high magnetic *eld region in Fig. 3 correspond to the QHE appearing along lines of integer-net (one-point-dashed lines) and integer-e , and the quantization of Rxy is consistent with the integer-net . Put di erently, the QHE occurs along integer-net with extra Rxx maxima corresponding to the extended states of the original electron LLs, making the QHE regions along integer-net discontinuous. We can account for the behavior of the QHE in the hybridized system qualitatively as follows [10].
νnet =2 νnet =1
3
2
E
EF 1
E4
Minigap (Band gap) H1 H2
E3
E1 B
E
EF EF EF
H3 Valence band
E2
(a)
Conduction band
H4 B
(b)
Fig. 4. (a) A schematic diagram of the Landau-level (LL) hybridization. Hybridized LLs above the band gap (regions of net integer *lling of zero) are *lled by net-carriers. (b) A schematic diagram illustrating the relationship between LL broadening and the minigap at anti-crossing points. When the minigap is small, the Fermi-level reaches the extended states of the upper empty LL.
The Fermi-level lies just above the minigap in the hybridized band structure without magnetic *eld. Under a perpendicular magnetic *eld, Landau levels derived from the original conduction and valence bands are hybridized (Fig. 4(a)). Anti-crossings appear at the crossing points [1,11]. The region in (E; B) with the net quantized *lling factor of zero is e ectively a band gap [12]. The net carriers are *lled into the hybridized LLs above this band gap in a similar manner as in
K. Suzuki et al. / Physica E 20 (2004) 232 – 235 νe =3
14 12
4
10
R xx
B
High
65.6˚
B ⊥ (T)
5 8 6
6 7
4
νnet =1
235
continuous. The hybridization gaps have become large compared with the broadening of LLs so that the extended states of the original electron LLs are no longer strongly visible. It can be deduced that the in-plane magnetic *eld component enhances the hybridization and the minigap at the original LL crossing points, although the details remain unclear.
Low
2 3 4 5 6
4. Conclusions
2 0 -10
-8
-6
-4
-2 V G (V)
0
2
4
Fig. 5. Contour plot of Rxx for the sample (di erent peace from the same wafer) under a tilted magnetic *eld as shown in the inset.
conventional 2DEG systems. Therefore, QHE dominated by integer-net is expected. If the anti-crossing energy-gap is smaller than the LL broadening, around the crossing points, the extended state of the upper empty LL reaches the Fermi-level and the carriers are transferred from the occupied LL to the upper empty LL (Fig. 4(b)). As a result, a Rxx maximum is expected. If we considered the 2DEG without hybridization, the magnetic *eld where the extended states of the original electron LLs pass over the Fermi-level should be the same as that where Rxx maxima are observed in the hybridized system. In addition, the electron mobility is much higher than that of the holes. As a result, the Rxx maxima were observed horizontally in Fig. 3. Fig. 5 shows the result of Rxx measurements under a magnetic *eld at an angle of 65:6◦ to the surface. The longitudinal axis B⊥ represents the component of magnetic *eld perpendicular to the surface. The hole densities are slightly di erent from Fig. 3. (The sample is a di erent piece from the same wafer.) In the low magnetic *eld region the pattern of the QHE is almost the same as Fig. 3. The Rxx maxima corresponding to the extended state of the original electron LLs are dominant. In high magnetic *eld above 7 T, however, the horizontal Rxx maxima weaken dramatically and the QHE regions along integer-net become
The QHE in the hybridized electron–hole system was investigated using InAs/GaSb heterostructures with back-gates. The QHE occurred according to net-carriers *lling the hybridized LLs and appeared along integer-net . When the hybridization is small compared with the LL broadening, Rxx maxima coming from the overlap of the extended states at the crossing point of the original electron and hole LLs, make the QHE region along integer-net discontinuous. Under tilted magnetic *elds, Rxx maxima disappear in the high magnetic *eld region. It shows that the component of the magnetic *eld parallel to the surface enhances the hybridization. References [1] M. Altarelli, Phys. Rev. B 28 (1983) 842. [2] S. de-Leon, B. Laikhtman, Phys. Rev. B 61 (2000) 2874. [3] E.E. Mendez, L. Esaki, L.L. Chang, Phys. Rev. Lett. 55 (1985) 2216. [4] M.J. Yang, C.H. Yang, B.R. Bennett, Phys. Rev. B 60 (1999) R13958. [5] K. Suzuki, S. Miyashita, Y. Hirayama, Inst. Phys. Conf. Ser. 171, published on CD-ROM. [6] J.H. Roslund, K. Saito, K. Suzuki, H. Yamaguchi, Y. Hirayama, Jpn. J. Appl. Phys. Part 1 39 (2000) 2448. [7] K. Suzuki, S. Miyashita, Y. Hirayama, Phys. Rev. B 67 (2003) 195319. [8] R.A. Smith, Semiconductors, Cambridge University Press, Cambridge, 1978, pp. 114. [9] M. Altarelli, J.C. Maan, L.L. Chang, L. Esaki, Phys. Rev. B 35 (1987) 9867. [10] K. Suzuki, K. Takashina, S. Miyashita, Y. Hirayama, unpublished. [11] A. Fasolino, M. Altarelli, Surf. Sci. 142 (1984) 322. [12] R.J. Nicholas, K. Takashina, M. Lakrimi, B. Kardynal, S. Khym, N. Mason, D.M. Symons, D.K. Maude, J.C. Portal, Phys. Rev. Lett. 85 (2000) 2364.
Physica E 20 (2004) 232 – 235 www.elsevier.com/locate/physe
Quantum Hall e ect in back-gated InAs/GaSb heterostructures under a tilted magnetic *eld K. Suzukia;∗ , S. Miyashitab , K. Takashinaa , Y. Hirayamaa; c a NTT
Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b NTT Advance Technology Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan c CREST-JST, Kawaguchi-shi, Saitama 331-0012, Japan
Abstract We investigate the quantum Hall e ect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic *eld perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) *lling factors of the net-carriers, where the net-carrier density is the di erence between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-net discontinuous. Under tilted magnetic *elds, these Rxx maxima disappear in the high magnetic *eld region. The results show that the in-plane magnetic *eld component enhances the electron–hole hybridization and the formation of minigaps at LL crossings. ? 2003 Elsevier B.V. All rights reserved. PACS: 73.20.−r; 73.40.−c; 73.43.−f Keywords: Electron–hole hybridization; Quantum Hall e ect; Back-gate
1. Introduction In InAs/GaSb heterostructures, the conduction band in the InAs and the valence band in the GaSb overlap. When the Fermi-level lies in the overlap region, electrons in the InAs and holes in the GaSb coexist in close proximity. This system is of great interest with respect to the electron–hole band hybridization [1] which leads to the formation of a minigap. New physics phenomena such as Bose–Einstein condensation of excitons are expected [2]. The most remarkable feature known up to now is the unique ∗
Corresponding author. E-mail address: [email protected] (K. Suzuki).
quantum Hall e ect [3]. When the Landau-level (LL) *lling-factors of electrons and holes (e , h ) become integers simultaneously, the longitudinal resistance (Rxx ) becomes zero and the Hall resistance (Rxy ) is quantized by the di erence between the *lling-factors Rxy = h=e2 |e − h |. It has been believed that the phenomenon arises due to Landau quantization of both electrons and holes simultaneously. However, recent experiments on gated-structures strongly indicate that the condition necessary to observe the QHE is that the *lling-factor of the net-carries net = |e − h | has to be an integer, rather than both e and h , although the detailed mechanism of the QHE has not been discussed [4,5]. In this paper we report magneto-resistance measurements in InAs/GaSb
1386-9477/$ - see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2003.08.071
K. Suzuki et al. / Physica E 20 (2004) 232 – 235
233
40
In contact
GaSb Al0.7Ga0.3Sb
MBE grown Fig. 1. Sample structure.
heterostructures grown on a conductive InAs substrate acting as a back-gate under perpendicular and tilted magnetic *elds. The e ect of an in-plane magnetic *eld component on the hybridization are examined. 2. Experimental procedure The sample structure is shown in Fig. 1. An InAs substrate (nominally undoped but conductive) is used as a back-gate. A 30 nm-InAs/18 nm-GaSb heterostructure which is sandwiched between Al0:7 Ga0:3 Sb barriers is grown on a GaSb/AlSb superlattice and an AlSb bu er layer on the substrate, by molecular beam epitaxy [5–7]. A thin GaSb layer is then grown on the surface as a capping layer. Indium contacts for both electron and hole layers are deposited. A Hall-bar structure was made by mesa-etching. The magnetoresistance was measured in a cryostat at 1:6 K applying a magnetic *eld of up to 15 T while sweeping the back-gate voltage VG . 3. Results and discussion Fig. 2 shows the gate leakage current as a function of the gate-voltage (VG ). The gate-voltage can be applied from −0:8 to 2:7 V without any e ect on magnetoresistance measurements which use DC currents of the order of A. The magnetoresistance with *eld perpendicular to the surface was measured
Leak Current (nA)
InAs GaSb Al0.7Ga0.3Sb AlSb/GaSb SL AlSb n-InAs Substrate (Nominally undoped)
20
0 -0.8 V
2.7 V
-20
-40
-1
0
1
2
3
VG (V) Fig. 2. Gate-leakage current as a function of the applied gate-voltage.
at di erent values of VG . Fig. 3 shows a contour plot of Rxx as functions of VG and the magnetic *eld (B). The dark regions correspond to regions of higher resistance and the bright regions show regions of lower resistance. Strong Shubnikov–de Haas oscillations as a function of B were observed. The oscillations are dominated by the electrons at low *eld because the mobility of the electrons is much higher than that of the holes. It was found that the electron density n = 10:75 × 1015 m−2 obtained from the oscillations stayed constant with increasing VG up to VG = 1:75 V. On the other hand, the hole density (p) obtained from the quantized Rxy and the classical *tting is p = (2:22–1:26VG ) × 1015 m−2 [8]. The electron mobility e = 8:0 m2 V−1 s−1 and hole mobility h = 0:5 m2 V−1 s−1 are also extracted from the *tting. After the depletion of the holes, VG ¿ 1:75 V, the system changes from the hybridized system to a two-dimensional electron gas system (2DEG) and Rxx maxima starts to be strongly a ected by VG since there are no more holes to screen the gate potential. The carrier densities in the InAs/GaSb system are determined by the gate, intrinsic charge transfer, effects due to the surface pinning [9], interface defects and impurities. If the electrons and holes were completely separated and independent, the hole and electron densities are well-de*ned quantities. In the opposite limit where the states in the InAs and GaSb are strongly hybridized, the individual densities are less
234
K. Suzuki et al. / Physica E 20 (2004) 232 – 235
νh=1
νe =3
R xx
14 νh=2
12 4
High
νh =3
10 B (T)
5
8 6 4
6 7
νnet =1
Low 2
34
56
2 0
-6
-4
-2 VG (V)
0
2
Depletion of holes
Fig. 3. Contour plot of Rxx as functions of gate-voltage (VG ) and magnetic *eld (B).
meaningful. However the net carrier density nnet = n−p must always be a well-de*ned quantity. Here, we describe our data in terms of e =nh=eB, h =ph=eB and net = nnet h=eB, where we have used values obtained from the data as already described. Since the SdH oscillation maxima arising from electronic extended states describe horizontal lines on the plot while electrons and holes coexist (VG ¡ 1:75 V), we take the electron density to be independent of VG in this region. We will interpret this behavior (Fig. 3) to be neither in the strongly hybridized limit nor the independent limit, so that the behavior does not depend on net alone [4] nor on separate e and h alone. The horizontal dashed lines represent integer-e and the dotted lines are integer-h . If the QHE in the hybridized system was caused by the independent QHE’s of the electrons and holes, the pattern of the Rxx minima should show Rxx minima along lines of integer-e and integer-h . However, the patterns of Rxx minima in the high magnetic *eld region in Fig. 3 correspond to the QHE appearing along lines of integer-net (one-point-dashed lines) and integer-e , and the quantization of Rxy is consistent with the integer-net . Put di erently, the QHE occurs along integer-net with extra Rxx maxima corresponding to the extended states of the original electron LLs, making the QHE regions along integer-net discontinuous. We can account for the behavior of the QHE in the hybridized system qualitatively as follows [10].
νnet =2 νnet =1
3
2
E
EF 1
E4
Minigap (Band gap) H1 H2
E3
E1 B
E
EF EF EF
H3 Valence band
E2
(a)
Conduction band
H4 B
(b)
Fig. 4. (a) A schematic diagram of the Landau-level (LL) hybridization. Hybridized LLs above the band gap (regions of net integer *lling of zero) are *lled by net-carriers. (b) A schematic diagram illustrating the relationship between LL broadening and the minigap at anti-crossing points. When the minigap is small, the Fermi-level reaches the extended states of the upper empty LL.
The Fermi-level lies just above the minigap in the hybridized band structure without magnetic *eld. Under a perpendicular magnetic *eld, Landau levels derived from the original conduction and valence bands are hybridized (Fig. 4(a)). Anti-crossings appear at the crossing points [1,11]. The region in (E; B) with the net quantized *lling factor of zero is e ectively a band gap [12]. The net carriers are *lled into the hybridized LLs above this band gap in a similar manner as in
K. Suzuki et al. / Physica E 20 (2004) 232 – 235 νe =3
14 12
4
10
R xx
B
High
65.6˚
B ⊥ (T)
5 8 6
6 7
4
νnet =1
235
continuous. The hybridization gaps have become large compared with the broadening of LLs so that the extended states of the original electron LLs are no longer strongly visible. It can be deduced that the in-plane magnetic *eld component enhances the hybridization and the minigap at the original LL crossing points, although the details remain unclear.
Low
2 3 4 5 6
4. Conclusions
2 0 -10
-8
-6
-4
-2 V G (V)
0
2
4
Fig. 5. Contour plot of Rxx for the sample (di erent peace from the same wafer) under a tilted magnetic *eld as shown in the inset.
conventional 2DEG systems. Therefore, QHE dominated by integer-net is expected. If the anti-crossing energy-gap is smaller than the LL broadening, around the crossing points, the extended state of the upper empty LL reaches the Fermi-level and the carriers are transferred from the occupied LL to the upper empty LL (Fig. 4(b)). As a result, a Rxx maximum is expected. If we considered the 2DEG without hybridization, the magnetic *eld where the extended states of the original electron LLs pass over the Fermi-level should be the same as that where Rxx maxima are observed in the hybridized system. In addition, the electron mobility is much higher than that of the holes. As a result, the Rxx maxima were observed horizontally in Fig. 3. Fig. 5 shows the result of Rxx measurements under a magnetic *eld at an angle of 65:6◦ to the surface. The longitudinal axis B⊥ represents the component of magnetic *eld perpendicular to the surface. The hole densities are slightly di erent from Fig. 3. (The sample is a di erent piece from the same wafer.) In the low magnetic *eld region the pattern of the QHE is almost the same as Fig. 3. The Rxx maxima corresponding to the extended state of the original electron LLs are dominant. In high magnetic *eld above 7 T, however, the horizontal Rxx maxima weaken dramatically and the QHE regions along integer-net become
The QHE in the hybridized electron–hole system was investigated using InAs/GaSb heterostructures with back-gates. The QHE occurred according to net-carriers *lling the hybridized LLs and appeared along integer-net . When the hybridization is small compared with the LL broadening, Rxx maxima coming from the overlap of the extended states at the crossing point of the original electron and hole LLs, make the QHE region along integer-net discontinuous. Under tilted magnetic *elds, Rxx maxima disappear in the high magnetic *eld region. It shows that the component of the magnetic *eld parallel to the surface enhances the hybridization. References [1] M. Altarelli, Phys. Rev. B 28 (1983) 842. [2] S. de-Leon, B. Laikhtman, Phys. Rev. B 61 (2000) 2874. [3] E.E. Mendez, L. Esaki, L.L. Chang, Phys. Rev. Lett. 55 (1985) 2216. [4] M.J. Yang, C.H. Yang, B.R. Bennett, Phys. Rev. B 60 (1999) R13958. [5] K. Suzuki, S. Miyashita, Y. Hirayama, Inst. Phys. Conf. Ser. 171, published on CD-ROM. [6] J.H. Roslund, K. Saito, K. Suzuki, H. Yamaguchi, Y. Hirayama, Jpn. J. Appl. Phys. Part 1 39 (2000) 2448. [7] K. Suzuki, S. Miyashita, Y. Hirayama, Phys. Rev. B 67 (2003) 195319. [8] R.A. Smith, Semiconductors, Cambridge University Press, Cambridge, 1978, pp. 114. [9] M. Altarelli, J.C. Maan, L.L. Chang, L. Esaki, Phys. Rev. B 35 (1987) 9867. [10] K. Suzuki, K. Takashina, S. Miyashita, Y. Hirayama, unpublished. [11] A. Fasolino, M. Altarelli, Surf. Sci. 142 (1984) 322. [12] R.J. Nicholas, K. Takashina, M. Lakrimi, B. Kardynal, S. Khym, N. Mason, D.M. Symons, D.K. Maude, J.C. Portal, Phys. Rev. Lett. 85 (2000) 2364.