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Romain Danneau(Redirected from O.V. Lounasmaa Laboratory:Holes) » Holes

Holes

1D Holes in GaAs

2004-06 Research Associate (Australian Research Council) in the QED group [22] at the School of Physics [23], University of New South Wales, Sydney, NSW, Australia (School of Physics, UNSW).

Subject: Electronic transport properties of low-dimensional hole systems

My research project was based on the study of low dimensional systems with strong spin-orbits coupling such as holes in GaAs. I measured conductance quantization in 1D hole system associated with the conductance anomaly at 0.7 × 2e²/h. I studied the Zeeman effect on this 1D system, as well as the "0.7 structure" and the zero bias anomaly (see list of publications).

I have been awarded by an Australian Research Council Discovery Project Award Fellowship. This project based on the electrical control of spin in GaAs nanostructures involved close collaborations with Ulrich Zülicke theoretical physicist from Massey University, NZ, Mickael Pepper’s group from the Cavendish Laboratory at University of Cambridge and Yoshiro Hirayama’s group of NTT Basic Research Laboratory, Japan for high mobility two-dimensional hole wafers.

• Quantization and 0.7 structure in 1D holes
  

  

I have studied the ballistic transport properties of a ballistic one-dimensional channel created in a high mobility bilayer 2D hole system formed in a back-gated GaAs-AlGaAs heterostructure. Clean and robust conductance quantization [1] in units of 2e²/h at dilution fridge temperatures without the hysteresis and irregular oscillations that have hampered previous studies of 1D hole systems [2,3]. In addition to the expected plateaus at multiples of 2e²/h, a clear step at 0.7 × 2e²/h was observed. Quantized steps were resolved in both the upper and lower quantum wires, with the strongest quantization obtained in the upper wire. The high stability of these devices and the clear conductance quantization has allowed to measure the energy spacing of the 1D subbands, which is significantly smaller than for comparable electron systems [4], due to the large effective hole mass. I have also been involved in measurements on induced hole quantum wires in which the quantized conductance and the 0.7 structure have been observed (see list of publications and measurements below).

[1] For review see C.W.J. Beenakker and H. van Houten, Solid State Physics, Volume 44, 1 (1991)

[2] A.J. Daveshnar et al., Phys. Rev. B. 55, R13409 (1997)

[3] L.P. Rokhinson et al., Superlattices Microstruct. 32, 99 (2002)

[4] I.M. Castleton et al., Physica B 249-251, 157 (1998)

Summary of these experiments

Schematic of the devices used in these experiments. They were fabricated from wafers consisting of a modulationdoped bilayer structure formed by two 20 nm GaAs quantum wells separated by a 30 nm layer of Al0.3Ga0.7As on a conducting (311)A n+−GaAs substrate, which serves as the back gate. The 1D constriction is aligned along the [233] direction. The hole densities and mobilities of the top and the bottom layer are, respectively, 1.2 × 1015 m-2 and 92 m2 V-1 s-1, and 1.0 × 1015 m-2 and 87 m2 V-1 s-1. Ti/Au gates, defined using optical and electron-beam lithography, are patterned on the surface, 280 nm above the top layer. The n+−GaAs back gate is 3 microns below the bottom layer. The back and middle gates to control the density and the confinement potential. From R. Danneau et al., Appl. Phys. Lett. 88, 012107 (2006)[1], also on cond-mat/0507592 [2].

Measurements were done in a dilution fridge with a base temperature of T = 20 mK. G vs VSG , showing the quantized conductance of the top wire. The arrow highlights the anomalous plateau at 0.7 × 2e2/h in a 1D hole system. Data have been corrected for a series resistance of 2.5 kOhm, and were taken with VBG=2.5 V and VMG=−0.7 V. The inset shows the raw data, which exhibits the four-stage definition/ depletion of the quantum wire. From R. Danneau et al., Appl. Phys. Lett. 88, 012107 (2006)[3], also on cond-mat/0507592 [4].

Color map of the transconductance dG/dVSD as a function of VSG and the applied dc source-drain bias VSD obtained at T = 20 mK, VBG=2.5 V and VMG=−0.5 V. The data have been corrected for the voltage drop across the series resistance. The plateaus show up as the light regions, with the steps between them appearing dark. The dashed lines serve as a guide to the eye, highlighting the standard plateaus and the additional odd-integer plateaus used to determine the subband spacings.From R. Danneau et al., Appl. Phys. Lett. 88, 012107 (2006)[5], also on cond-mat/0507592 [6].

(a) Schematic diagram of the heterostructure: in this system, holes are created by applying a negative voltage on the top gate; (b) Conductance (in \mu S) of the quantum wire as a function of the side gate voltage; (c) Conductance corrected for a series resistance due to the contacts and the measurement circuit (3 consecutive traces): the 0.7 structure is clearly visible. From O. Klochan et al., Appl. Phys. Lett. 89, 092105 (2006) [7], also on cond-mat/0607509 [8].

• Zeeman effect in 1D holes

Properties of holes in GaAs are closely link to the peculiar and complicated valence band of this zinc-blende structure material. In addition, holes are subject to strong spin-orbit coupling [1]. In this work, I used similar hole quantum wires as described above. I observed and studied an extreme anisotropy of the Zeeman splitting with respect to the magnetic field orientation. Using source-drain biasing spectroscopy [2], one can quantitatively measure the spin splitting and quantified the effective Landé g-factor g*. On the contrary to 1D electron systems, in 1D holes g* is clearly anisotropic and larger than the 2D values [3,4]. This anisotropic behavior of the Zeeman splitting in 1D hole systems can be explained by the reorientation of the total angular momentum J while the system goes from 2D to 1D. These results show that confining holes to a 1D system fundamentally alters their properties. This is a direct consequence of the spin-orbit coupling in this system.

[1] R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, 2003)

[2] L. I. Glazman and A.V. Khaetskii, Europhys. Lett. 9, 263 (1989)

[3] S. J. Papadakis, E. P. De Poortere, M. Shayegan, and R. Winkler, Phys. Rev. Lett. 84, 5592 (2000).

[4] R. Winkler, S. J. Papadakis, E. P. De Poortere, and M. Shayegan, Phys. Rev. Lett. 85, 4574 (2000).

Summary of these experiments

Evidence of the strong anisotropy of the Zeeman effect in hole quantum wires. (a) Differential conductance G, corrected for a series resistance, of the quantum wire for different in-plane magnetic fields parallel to the wire from 0 to 8.8 T in steps of 0.2 T (from left to right). T = 20 mK, back and middle gates are at 2.5 and -0.5 V, respectively. The second thicker curve (middle arrow) corresponds to when subbands are completely spin resolved; the third thicker curve (rightmost arrow) corresponds to when the 1D subbands cross. (b) Corresponding transconductance gray scale as a function of VSG; black regions correspond to low transconductance; white regions correspond to high transconductance (subband edges). (c) G of the same quantum wire for different in-plane magnetic fields perpendicular to the wire under similar experimental conditions. (d) Corresponding transconductance gray scale as a function of VSG and the magnetic fields perpendicular to the wire. From R. Danneau et al., Phys. Rev. Lett. 97, 026403 (2006)[9], also on cond-mat/0607355[10].

Source-drain bias spectroscopy 2D map of the nonlinear transconductance gray scale at T = 20 mK, back and middle gates are at 2.5 and 0.5 V, respectively, and B = 0 T as a function of VSG. The black parts correspond to low transconductance (plateaus). Quantized plateaus in units of 2e2/h at zero VSD and extra plateaus for half-odd multiple values of 2e2/h at nonzero VSD are labeled. Crossings of 1D subband edges are the white parts. From R. Danneau et al., Phys. Rev. Lett. 97, 026403 (2006)[11], also on cond-mat/0607355[12].

(a) Splitting of the 1D subband edges as function of B applied parallel to the wire for the five first subbands; (b) g* as a function of the subband index N extracted from the Zeeman splitting measurement and the VSD spectroscopy: Solid and open circles are the g* in the direction parallel to the wire calculated in two different ways. The upper line of the striped part represents an upper bound of g* for B perpendicular to the wire. The arrows define the absolute values of g* calculated for a 20 nm quantum well of HH grown on (311)A surface: the upper and lower arrows mark g* for B pointing along [233] and [011], respectively. From R. Danneau et al., Phys. Rev. Lett. 97, 026403 (2006)[13], also on cond-mat/0607355[14].

Sketch of the effect of a magnetic field perpendicular (a) and parallel (b) to the quantization axis for total angular momentum J, on a 2D hole and 1D hole system created by two side gates. From R. Danneau et al., AIP Conference Proceedings 893, 699 (2007), cond-mat/0607357[15].

• 0.7 structure and Zero Bias Anomaly in 1D holes

In the non-interacting point of view, the conductance of a 1D system in the ballistic regime is quantized in units of 2e²/h [1]. However, a small feature under the first conductance plateau was first pointed out in the early ninety's [2] and studied in detail five years later [3]. In these first experiments, it was shown that this resonance-like feature, known as the 0.7 structure, was not due to a defect in the vicinity of the constriction and could be related to spin. Since then, this non-expected conductance anomaly has been extensively studied in 1D electron system but its origin is still very much debated [4]. Another conduction anomaly at low conductance, but this time in the non-linear regime (i.e. at non-zero bias voltage), was studied later and related to the 0.7 structure due to its position below the first plateau. From the detail study of this zero bias anomaly (ZBA), it was then argue that the 0.7 structure could be related to a Kondo-like correlated phenomenon [5]. Even though this explanation of the phenomenon was getting very popular, the Kondo effect as to the origin of the 0.7 structure has been recently experimentally ruled out [6].

In these experiments, I have studied the behavior of the 0.7 structure and the ZBA as a function of T and different magnetic field orientation. These results show a strong anisotropic behavior of both, 0.7 structure and ZBA with respect to the magnetic field orientation. This demonstrates that the 0.7 structure and the ZBA are linked and related to spin. This result is also in agreement with recent calculations which shown that heavy hole-light hole band-mixing happens when the width of the wire is reduced to half of the size of the quantum well (for a 20 nm quantum well) [7].

[1] C.W.J. Beenakker and H. van Houten, Solid State Physics, Volume 44, 1 (1991).

[2] N. K. Patel, J. T. Nicholls, L. Martin-Moreno, M. Pepper, J. E. F. Frost, D. A. Ritchie, and G. A. C. Jones , Phys. Rev. B 44, 13549 (1991).

[3] K. J. Thomas, J. T. Nicholls, M.Y. Simmons, M. Pepper, D. R. Mace, and D. A. Ritchie, Phys. Rev. Lett. 77, 135 (1996).

[4] G. Fitzgerald, Phys. Today 55, No. 5, 21 (2002).

[5] S. M. Cronenwett , H. J. Lynch, D. Goldhaber-Gordon, L. P. Kouwenhoven, C. M. Marcus, K. Hirose, N. S. Wingreen, and V. Urmansky, Phys. Rev. Lett. 88, 226805 (2002).

[6] F. Sfigakis, C. J. B. Ford, M. Pepper, M. Kataoka, D. A. Ritchie, and M.Y. Simmons, Phys. Rev. Lett. 100, 026807 (2008).

[7] U. Zülicke, Phys. Stat. Sol. (c) 3, 4354 (2006).

Summary of these experiments

Temperature dependence of the 0.7 structure and the ZBA in a hole quantum wire: G versus side gate voltage VSG, for T = 20, 200, 320, 550 and 650 mK; (b) G versus source-drain bias VSD for different VSG at T = 20 mK; (c) G versus VSD for different VSG at T = 320 mK; Each curve is separated by 0.004 V and data are taken for back and middle gates fixed at 2.5 V and -0.225 V respectively. From R. Danneau et al., Phys. Rev. Lett. 100, 016403 (2008) [16], also on cond-mat/0702210 [17].

(a) G, corrected for a series resistance, of the quantum wire versus side-gate voltage VSG for different in-plane magnetic fields parallel to the wire from 0 T, i.e. when 1D subbands are degenerate with steps in units of 2e2/h, to 3.6 T, i.e. when 1D subbands are completely spin resolved with steps in units of e2/h, in steps of 0.2 T (from left to right), T = 20 mK, back and middle gates are at 2.5 V and -0.225 V, respectively; (b): grayscale of the transconductance dG/dVSG as a function of in-plane magnetic fields parallel to the wire up to 8.8 T and G. White regions correspond to low transconductance (conductance plateaus); (c) and (d): G versus source-drain bias VSD for different VSG of the same quantum wire at (c) 0 T and (d) a 3.6 T magnetic field applied parallel to the wire. Adapted from R. Danneau et al., Phys. Rev. Lett. 100, 016403 (2008) [18], also on cond-mat/0702210 [19].

Effect of an in-plane magnetic field perpendicular to the wire the 0.7 structure and the ZBA: (a): dG/dVSG versus in-plane magnetic fields perpendicular to the wire and G, back and middle gates fixed at 2.5 V and -0.225 V respectively, and T = 20 mK. As it was shown just above, no Zeeman splitting is observed for this magnetic field orientation. However the 0.7 structure evolves slowly to a position around 0.5 × 2e2/h at B = 10 T; (b), (c) and (d): G versus VSD, for different VSG, for B = 0, 3.6 and 10 T, in similar experimental conditions ((c) and Fig. 1 (b) are the same data): the ZBA is clearly observed at B = 0 and 3.6 T. At B = 10 T the ZBA disappears. Adapted from R. Danneau et al., Phys. Rev. Lett. 100, 016403 (2008) [20], also on cond-mat/0702210 [21].

Related publications:

• R. Danneau, O. Klochan, W.R. Clarke, L.H. Ho, A.P. Micolich, M.Y. Simmons, A.R. Hamilton, M. Pepper and D.A. Ritchie

0.7 structure and zero bias anomaly in one-dimensional hole systems

Physica E 40, 1501 (2008) [24]

• A. R. Hamilton, R. Danneau, O. Klochan, W.R. Clarke, A.P. Micolich, L.H. Ho, M.Y. Simmons, D.A. Ritchie, M. Pepper, K. Muraki and Y. Hirayama

The 0.7 anomaly in one-dimensional hole quantum wires

J. Phys. Condens. Matter. 20, 164205 (2008) [25]

• A. R. Hamilton, O. Klochan, R. Danneau, W.R. Clarke, L.H. Ho, A.P. Micolich, M.Y. Simmons, M. Pepper, D.A. Ritchie, K. Muraki and Y. Hirayama

Quantum transport in one-dimensional GaAs hole systems

Int. J. Nanotechnology 5, 318 (2008) [26]

• R. Danneau, O. Klochan, W.R. Clarke, L.H. Ho, A.P. Micolich, M.Y. Simmons, A.R. Hamilton, M. Pepper and D.A. Ritchie

0.7 structure and zero bias anomaly in ballistic hole quantum wires

Phys. Rev. Lett. 100, 016403 (2008) [27]. Also on cond-mat/0702210 [28]

• R. Danneau, O. Klochan, W. R. Clarke, L. H. Ho, A. P. Micolich, M. Y. Simmons, A. R. Hamilton, M. Pepper, D. A. Ritchie and U. Zülicke

Anisotropic Zeeman splitting in ballistic one-dimensional hole systems

AIP Conference Proceedings 893, 699 (2007), also on cond-mat/0607357 [29]

• O. Klochan, W. R. Clarke, R. Danneau, A. P. Micolich, L. H. Ho, A. R. Hamilton, K. Muraki and Y. Hirayama

Conductance quantization in induced one-dimensional hole systems

AIP Conference Proceedings 893, 681 (2007) AIP Conference Proceedings 893, 681 (2007) [30]

• O. Klochan, W. R. Clarke, R. Danneau, A. P. Micolich, L.H. Ho, A. R. Hamilton, K. Muraki and Y. Hirayama

Ballistic transport in induced one-dimensional hole systems

Appl. Phys. Lett. 89, 092105 (2006) [31], also on cond-mat/0607509 [32]

• R. Danneau, O. Klochan, W. R. Clarke, L.H. Ho, A. P. Micolich, M. Y. Simmons, A. R. Hamilton, M. Pepper, D. A. Ritchie and U. Zülicke

Zeeman splitting in ballistic hole quantum wires

Phys. Rev. Lett. 97, 026403 (2006) [33], also on cond-mat/0607355 [34]

• R. Danneau, W. R. Clarke, O. Klochan, L.H. Ho, A. P. Micolich, A. R. Hamilton, M. Y. Simmons, M. Pepper and D. A. Ritchie

Ballistic transport in one-dimensional bilayer hole systems

Physica E 34, 550 (2006) [35]

• R. Danneau, W. R. Clarke, O. Klochan, A. P. Micolich, A. R. Hamilton, M. Y. Simmons, M. Pepper and D. A. Ritchie

Conductance quantization and the 0.7 × 2e²/h conductance anomaly in one-dimensional hole systems

Appl. Phys. Lett. 88, 012107 (2006) [36], also on cond-mat/0507592 [37]

Other results on 2D holes:

• L.H. Ho, W.R. Clarke, A.P. Micolich, R. Danneau, O. Klochan, A.R. Hamilton, M.Y. Simmons, M. Pepper and D.A. Ritchie

The Effect of screening long range Coulomb interactions on the metallic behavior in two-dimensional hole systems

Phys. Rev. B 77, 201402(R) (2008) [38], also on arXiv:0804.4049 [39]

• L.H. Ho, W.R. Clarke, R. Danneau, O. Klochan, A.P. Micolich, A.R. Hamilton, M.Y. Simmons, M. Pepper and D.A. Ritchie

Screening long range Coulomb interactions in two-dimensional hole systems using a bilayer heterostructure

Physica E 40, 1700 (2008) [40]