Compressibility Measurements of Quasi-One-Dimensional Quantum Wires

L. W. Smith, A. R. Hamilton, K. J. Thomas, M. Pepper, I. Farrer, J. P. Griffiths, G. A. C. Jones, and D. A. Ritchie

Phys. Rev. Lett. 107, 126801 – Published 13 September 2011

Abstract

We report measurements of the compressibility of a one-dimensional quantum wire, defined in the upper well of a $GaAs / AlGaAs$ double quantum well heterostructure. A wire defined simultaneously in the lower well probes the ability of the upper wire to screen the electric field from a biased surface gate. The technique is sensitive enough to resolve spin splitting of the subbands in the presence of an in-plane magnetic field. We measure a compressibility signal due to the 0.7 structure and study its evolution with increasing temperature and magnetic field. We see no evidence of the formation of the quasibound state predicted by the Kondo model, instead our data are consistent with theories which predict that the 0.7 structure arises as a result of spontaneous spin polarization.

Received 27 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.126801

Authors & Affiliations

L. W. Smith^1,*, A. R. Hamilton², K. J. Thomas^3,†, M. Pepper⁴, I. Farrer¹, J. P. Griffiths¹, G. A. C. Jones¹, and D. A. Ritchie¹

¹Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 OHE, United Kingdom
²School of Physics, The University of New South Wales, Sydney 2052, Australia
³Department of Electronic and Electrical Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
⁴Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, United Kingdom

^*lws22@cam.ac.uk
^†kalarikad@skku.edu

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Vol. 107, Iss. 12 — 16 September 2011

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Images

Figure 1
(a) Conductance as a function of $V_{bar}$ . Labels ( $u$ ) and ( $l$ ) mark the depletion of the upper and lower electron layers, respectively. The arrow indicates $V_{bar} = - 0.7 V$ , typically applied to fully deplete the upper layer. (b) Device schematic, showing the bar gate, split gates, and midline gate. The source and drain Ohmic contacts are marked by $S$ and $D$ , respectively. (c) Simplified diagram of a cross section through the device, showing the electric fields generated by biasing the split gates ( $E_{sg}$ ), the midline gate ( $E_{0}$ ), and the field which penetrates the upper wire ( $E_{p}$ ). (d) Conductance measured through the lower wire alone ( $G_{2}$ ) as a function of $V_{sg}$ ( $V_{bar} = - 0.7 V$ ). The horizontal dashed line indicates a fixed $G_{2}$ . (e) Conductance through both wires ( $G_{12}$ ) as a function of $V_{sg}$ ( $V_{bar} = 0 V$ ). In both (d) and (e) $V_{mid}$ is stepped from 0.5 V on the left to $- 0.25 V$ on the right, in 25 mV intervals. Data are from a typical device, measured at 300 mK, and corrected for series resistance.Reuse & Permissions
Figure 2
(a) Compressibility signal $d V_{sg} / d V_{mid}$ against $V_{mid}$ [gray (red) trace, left axis], for $G_{2} \approx 1.5 (2 e^{2} / h)$ ( $B = 0 T$ ). The conductance of the upper wire ( $G_{1}$ ) is plotted in black (right axis). Minima in $d V_{sg} / d V_{mid}$ coincide with interplateau rising edges, as illustrated by the dashed lines. The equivalent data at $B = 15 T$ are shown in (b) for $G_{2} \approx 1.75 (2 e^{2} / h)$ . The lifting of the spin degeneracy results in the appearance of spin-split plateaus in $G_{1}$ , and we resolve additional minima in $d V_{sg} / d V_{mid}$ associated with the spin splitting of subbands (marked by the long-dashed lines). This measurement was performed at 25 mK.Reuse & Permissions
Figure 3
(a),(b) Magnetic-field dependence of $d V_{sg} / d V_{mid}$ and corresponding $G_{1}$ , respectively, for $B = 0$ , 5, 10, and 15 T. $B = 15 T$ data are shifted horizontally by 6.5 mV to align with other data. Measurements were performed at $T = 25 mK$ . In (b) data are vertically offset for clarity; the arrow marks the peak which develops as $B$ increases. (c),(d) Temperature dependence of $d V_{sg} / d V_{mid}$ and corresponding $G_{1}$ , respectively, at $T = 25 mK$ , 350 mK, 1.3 K, and 2.4 K. $T = 350 mK$ , 1.3 K, and 2.4 K data are shifted horizontally by 2.5, 5, and $- 3.5 mV$ , respectively, to align with 25 mK data [26]. In (c) $d V_{sg} / d V_{mid}$ are vertically offset for clarity; the peak which develops with increasing temperature is marked by the arrow. Temperature-dependent measurements were performed at $B = 0 T$ . $G_{2} = 0.23 (2 e^{2} / h)$ for both data sets [29].Reuse & Permissions
Figure 4
(a) Calculated conductance of the quantum point contact (QPC) from Lüscher et al. [22] (red traces, top axis), compared with $G_{1}$ at $B = 0 T$ and $T = 25 mK$ (black trace, bottom axis). Horizontal axes are scaled to align the conductance data. (b) Corresponding derivatives $D^{DFT}$ (from Ref. 22, red trace, right and top axes) and $d V_{sg} / d V_{mid}$ (experimental data, black trace, left and bottom axes). The two $y$ axes are equivalent [27], and are scaled such that the depth of the first minima, marked by $+$ , is of the same magnitude. The secondary dip in $D^{DFT}$ , marked by the vertical arrow, was predicted to be a signature of the formation of a quasibound state. The vertical dashed lines mark transitions between the plateaus as 1D subbands are populated.Reuse & Permissions

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