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View the table of contents for this issue, or go to the journal homepage for more 2009 J. Phys.: Conf. Ser. 150 022052
The formation of bound states and the conductance
modulation on 0.7 anomaly in a quantum wire
1KM Liu, 2JH Hsiao, 2TM Hong, 3V Umansky and 1SY Hsu
1 Department of Electrophysics, National Chiao Tung University, Hsinchu, 30010, Taiwan 2 Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan
3 Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot 76100, Israel
E-mail: arthurliu.ep91g@nctu.edu.tw
Abstract. The electron transport in a short quasi-1D quantum wire is studied. In addition to the conductance quantization, several resonances are observed. Two of the resonances appear as extra plateaus below 2e2/h. A gate voltage offset is used to tune the local potential of the
quantum wire. A robust resonance is seen and the resonances evolve continuously with respect to the offset. The conductance has opposite responses to temperature in successive regions of gate voltage Vg. In the source-drain bias spectroscopy, two more conductance peaks are observed
in addition to the Zero-Bias-Anomaly. The locations of the extra peaks evolve with respect to
Vg showing a pattern similar to that in a quantum dot. We suggest that a bound state forms
in the quantum wire. The prominent 0.7 anomaly in our quantum wire is recognized as the residue of conductance resonance.
1. Introduction
In a 1D quantum wire(QW), the conductance is the integer multiple of 2e2/h because of the quantized state in the direction transverse to the electron motion. It has been a while since an additional conductance plateau in a value of ∼ 0.7(2e2/h) below the first conductance plateau was observed. The first proposed mechanism to this phenomenon was spontaneous polarization.[1] Many works have been intrigued afterward. Reilly et al proposed that exchange interaction between the electrons in the wire and the contacts leads to lift of spin degeneracy of the subbands, and the strength is density dependent.[2] Cronenwett et al associated the temperature dependence of the conductance with Kondo-like effect.[3] F. Sfgakis et al recently found that the temperature dependence on conductance of a tunable bound state in a quantum wire matches with the Kondo model in a quantum dot(QD).[4] In that work 0.7 anomaly and Kondo resonance are claimed to be two separate effects. However, the origin of the anomaly is still under discussion and not yet determined. In this paper, the local potential of a QW is tuned by a gate voltage offset ∆Vg. A robust conductance resonance along with mild resonances are observed. Temperature dependence of the resonances and source-drain-bias(SDB) spectroscopy of the QW are studied. The conductance has different temperature responses in successive regions of gate voltage Vg. In addition to the Zero-Bias-Anomaly(ZBA), two more conductance
peaks are seen in the spectroscopy. The evolution of the peaks has similarity of the spectroscopy of a QD. We believe that a bound state exits in the QW. Moreover, conductance anomalies close to 0.7(2e2/h) at high temperatures are observed as the remanence of resonances. Our result casts a light on the revelation of long indetermination.
by ac lock-in technique with a small ac voltage of 15µV in a3He cryostat with base temperature of 0.3K. A serial resistance of ∼ 300Ω due to the residual scattering of the wire and 2DEG is subtracted in all data.
3. Results and Analysis
When both gates are applied to the same negative voltage, the potential confining the wire is transversely symmetric and the transport is the typically quantized behavior. As shown in Fig.1(a), there are five conductance plateaus in units of 2e2/h due to the transmission of 1D subbands. Besides the quantized conductance, several features are observed in the trace. Anomalous shoulders appears at 1.7, 2.6, and 3.5(2e2/h) corresponding to extra plateaus below the 2nd, 3rd, and 4th plateaus. Two more additional plateaus occur at 0.6 and 0.78(2e2/h). As known, 1D transport is sensitive to its environment such as temperature, external field, and confining potential. By differentially biasing both gates by ∆Vg, Vg1= Vg and Vg2= Vg+ ∆Vg,
the confining potential becomes asymmetric and conductance traces evolve differently. In Fig.1(a) we also plot other conductance traces with a finite ∆Vg. The QW is shifted and
effectively narrowed, therefore the number of plateau reduced with increasing |∆Vg|. A robust
conductance resonance appears near the pinch-off for finite ∆Vg. The location of this resonance along with the two extra plateaus move continuously with decreasing ∆Vg and depend on
microconstrictions. This conductance resonance has the resemblance of Coulomb Blockade(CB) resonance, however there is no sign of localized state by judging the physical geometry.
-0.4 -0.2 0 1 2 3 4 5 G ( 2 e 2 / h ) V g (volt) (a ) -3 -2 -1 0 1 2 3 0.0 0.5 1.0 (b ) G ( 2 e 2 / h ) V sd (mV)
Figure 1. (a)Conductance as a function of gate voltage Vg. From left to right: ∆Vg = 0 to
−0.5V in 0.1V steps at T=0.3K. Inset: The micrograph of the quantum wire with a scale bar of 0.4µm. (b)Differential conductance ∂I/∂Vsd as a function of source drain voltage Vsd and
Vg for ∆Vg = 0, from Vg = −0.380V (top most) to the pinch-off voltage at T=0.3K. Orange:
Vg = −0.382V . The locations of the satellite peaks are marked by the blue dotted lines.
Fig.1(b) is SDB spectroscopy. In addition to the ZBA close to 2e2/h, two satellite peaks are observed as well. While the ZBA is suppressed with decreasing Vg, the two peaks get closer
and unite near 0.78(2e2/h). The united peak tends to split away, get closer, merge again at
0.6(2e2/h), and split apart thereafter. The evolution of the peaks forms a pattern analogous to the diamond structure of QD excitation spectrum.[5] The energy level of a well defined quantum dot can be tuned by an external voltage. In the circumstance of small SDB, there is a maximum of density of state when the energy level of the dot is aligned with the fermi energy in the leads. Therefore a conductance peak appears corresponding to a maximized tunneling at zero bias. On the other hand, when the level of the dot is tuned away from the fermi level, a finite bias is required to align the chemical potential with QD energy level and hence, conductance peaks are present at finite Vsd. One thing worth being noticed is that the extra plateaus at 0.6 and 0.78(2e2/h) on the trace of ∆V
g = 0 in Fig.1(a) occur exactly where the peaks merge in the
spectroscopy. This implies that the extra plateaus are actually CB resonances.
At finite Vsd, unexpected conductance resonances appear distinctly. For Vsd ∼
±0.9, ±1.0, and ± 1.2mV , the resonances appear in the values of ∼ 0.9, 0.77, and 0.6(2e2/h), respectively. Similar phenomena is also observed by other authors.[2] According to the model for nonlinear transport through a QW, when Vsd is larger than one energy spacing of subband only
the electrons coming from one lead can contribute to transport. Thus, plateaus of half integer are observed. However, the conductance is expected to decrease monotonically with decreasing Vg at a finite bias.[6, 7, 8] Models considering more than a quantum wire is required to explain
the resonance here.
In order to further understand the abnormality, Fig.2 shows G versus Vg for various
temperatures T for ∆Vg = −0.3V . The valley conductance beside the resonance, Gvalley, does not change much from 0.3 to 1.48K, and gradually increases for T>1.86K. On the other hand, the resonance conductance Gres decreases slightly with increasing temperature. The width of the resonance does not broaden until 1.48K. A QD is in resonant tunneling regime as long as kBT < hΓ ¿ ∆E, Ec. Here ∆E, Ec, and Γ are level spacing, charging energy, and tunneling
rate of a quantum dot, respectively. Gvalley of the CB resonance does not increase much due to
lack of thermal broadening and the resonance width is mainly determined by Γ. On the other hand, Gres decreases with increasing temperature.[9, 10] Our QW has a short length of 0.2µm.
If a bound state ever exists in the QW, it would be quite small in size and ∆E and Ecare very
likely to exceed kBT . The typical conductance of CB resonance in a QD is in order of a few 0.01(2e2/h). In comparison G
res observed here is much larger implying a large Γ. The result
is consistent with the scenario of resonant tunneling. Comparing the traces of 0.3 and 1.86K, besides the conductance increase in the valley, there is a conductance decrease in the region of Vg = −0.230 to − 0.246V . Along the traces, opposite conductance responses with respect to
temperature in successive regions of Vg can be recognized. This is similar to the Kondo phase in a QD whereas enhanced conductance is found only in regions of voltage with odd number of electrons inside.[9, 11, 12] Armed with these evidences, we suggest that a bound state exits in our QW.
In addition, as shown in Fig.2, two conductance anomalies appear at T=5.05K. One of them has the value of ∼ 0.5(2e2/h) and is clearly the remenant of the CB resonance at low temperatures. The other has a value of ∼ 0.7(2e2/h) and is a remainder of a conductance shoulder which appears as soon as the enhanced conductance is suppressed for T>0.87K. The inset of Fig.2 shows the temperature response for ∆Vg = 0. Two anomalies appearing at
∼ 0.6(2e2/h) and ∼ 0.8(2e2/h) at higher temperatures originate from the extra plateaus at low temperature. From the SDB spectroscopy(not shown for ∆Vg = −0.3V ), the two anomalies
correspond to the unite of conductance peaks which has been mentioned in the previous paragraph. This result is a token that the conductance anomalies are the consequences of CB resonance while the Kondo resonance of the bound state induces enhance conductance. Journal of Physics: Conference Series 150 (2009) 022052 doi:10.1088/1742-6596/150/2/022052
-0.25 -0.20 -0.15 0 -0.4 -0.3 0 G V g G V g (volt)
Figure 2. Conductance versus Vg for various temperatures from 0.3 to 5.05K with ∆Vg =
−0.3V . Temperature ranges are distinguished by colors: 0.3(thick blue), 0.50-1.48(blue), 1.86(thick orange) and 3.00-5.05K(green), respectively. Inset: Conductance versus gate voltage with ∆Vg = 0V for 0.30(blue), 0.50, 0.68, 0.87, 1.10, 1.48, 1.86, 3.00, and 5.00K(green) from
left to right respectively 4. Conclusion
Coulomb blockade resonance is observed in a quantum wire coupled with a bound state. While the conductance at successive regions has different responses to temperature, the satellite peaks alongside the ZBA moves with Vg in the SDB spectroscopy. The pattern of evolution has
similarity of excitation spectrum of a quantum dot. The root of bound state formation is beyond the scope of this paper and requires further study. Due to different temperature responses of Coulomb Blockade and Kondo resonances, they appear as conductance anomalies at high temperatures, which we propose to explain the long undetermined mechanism of 0.7 anomaly. Acknowledgments
This work was supported by NSC grant in Taiwan under project No NSC96-2112-M-009-030-MY3 and MOE ATU program.
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