Hole transport in p-type GaAs quantum dots and point contacts
B. Grbic, R. Leturcq, T. Ihn, K. Ensslin, D. Reuter, A. D. Wieck
aa r X i v : . [ c ond - m a t . m e s - h a ll ] N ov Hole transport in p-type GaAs quantum dots and point contacts
B. Grbi´c ∗ , R. Leturcq ∗ , T. Ihn ∗ , K. Ensslin ∗ , D. Reuter + , and A. D. Wieck + ∗ Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland + Angewandte Festk¨orperphysik, Ruhr-Universit¨at Bochum, 44780 Bochum, Germany
Strong spin-orbit interaction characteristic for p-type GaAs systems, makes such systems promis-ing for the realization of spintronic devices. Here we report on transport measurements in nanostruc-tures fabricated on p-type, C-doped GaAs heterostructures by scanning probe oxidation lithography.We observe conductance quantization in a quantum point contact, as well as pronounced Coulombresonances in two quantum dots with different geometries. Charging energies for both dots, ex-tracted from Coulomb diamond measurements are in agreement with the lithographic dimensionsof the dots. The absence of excited states in Coulomb diamond measurements indicates that thedots are in the multi-level transport regime.
The interest in low dimensional hole-doped GaAs sys-tems arises primarily from the fact that spin-orbit [1]as well as carrier-carrier Coulomb interaction effects aremore pronounced in such systems compared to the moreestablished electron doped systems, due to the fact thatholes have approximately 6 times larger effective massthan electrons [2]. However, the investigation of elec-tronic transport in low-dimensional p-type GaAs systemswas mainly limited to two-dimensional bulk samples, dueto difficulties to fabricate stable p-type nanodevices withconventional split-gate technique. The main problems weencountered in measurements on split-gate devices testedon several different p-type heterostructures are stronghysteresis effects in gate sweeps, as well as significantgate instabilities and charge fluctuations.In order to overcome these problems with metal-lic gates, we employ a different lithography technique,namely, Atomic Force Microscope (AFM) oxidationlithography [3, 4] to define nanostructures on two-dimensional hole gases (2DHG). We demonstrate thatfor a 2DHG 45 nm below the sample surface the AFMwritten oxide lines with a height of 15-18 nm completelydeplete the 2DHG beneath at low temperatures [5]. Den-sity and mobility of the unpatented sample at 4.2 K are:p = 4 × cm − , µ =120’000 cm /Vs.We fabricated a quantum point contact (QPC) witha lithographic width of 165 nm and tested its electron-ical functionality by measuring its conductance at lowtemperatures (Fig. 1). At the temperature of 500 mKquantized conductance plateaus are observed correspond-ing to transmission of one and two modes through theQPC. In addition, a plateau-like structure is observedat ∼ . × e /h . As the temperature is reduced to ∼
70 mK, this plateau-like feature evolves into a dip-like structure below the first plateau (Fig. 1). In differ-ential conductance vs. bias measurements we observea pronounced zero-bias peak for a QPC conductance ∼ . × e /h , which weakens as the conductance in-creases to 2 e /h , and completely disappears above thefirst plateau. This behavior might indicate that the struc-ture below the first plateau is related to Kondo-like effect[6]. Besides, at T= 70 mK another plateau-like structureat ∼ . × e /h appears. All features observed in this -0.4 -0.2 0 0.2 0.401234 plunger gate (V) c ondu c t an c e ( / h ) T=500mKT=70mK (cid:80) m FIG. 1: Two-terminal QPC conductance measurement atT=500 mK (black curve) and T=70 mK (gray curve). Thetrace corresponding to T=70 mK is shifted upwards by oneconductance unit for clarity. A bias of 10 µ V is applied sym-metrically across the QPC. Inset: AFM micrograph of theQPC sample were stable and reproducible in several differentcool-downs.Hole transport in p-type GaAs quantum dots is alsoexplored. Two quantum dots were fabricated with AFMlithography - one rectangular (Fig. 2(b)) with litho-graphic dimensions 430 ×
170 nm , and the other cir-cular (Fig. 2(d)) with lithographic radius ∼
320 nm.The transport measurements in both dots have been per-formed in a dilution refrigerator at a base temperature of ∼
70 mK. We have measured the two-terminal conduc-tance of the dots by applying either a small dc or ac biasvoltage V bias between source and drain, and measuringthe current through the dot with a resolution better than50 fA.The QPC gates are tuned to configurations where thedots are symmetrically coupled to the leads. PronouncedCoulomb resonances are observed in both dots (Fig. 2(a)shows Coulomb peaks from the rectangular dot). It is im-portant to note that the dots close when the value of theplunger-gate voltage increases − this is a clear indicationthat we measure hole transport. Coulomb resonances FIG. 2: (a) Differential conductance of the rectangular dot (b)in the configuration V qpc = -213 mV, V qpc = -236 mV as afunction of plunger gate voltage. (b) AFM micrograph of therectangular quantum dot with designations of the gates. (c)Coulomb diamonds in differential conductance for the rect-angular dot in the configuration V qpc = -225 mV, V qpc =-235 mV, represented in a logarithmic gray scale plot (whiteregions represent low conductance). (d) AFM micrograph ofthe circular quantum dot. (e) Coulomb diamonds in differ-ential conductance for the circular dot in the configuration:V pg = -32 mV, V = 72 mV, V = 120 mV, V = 310 mV,V = 200 mV represented in a logarithmic gray scale plot. are fitted both with an expression for a thermally broad-ened Coulomb blockade peak in the multi-level transportregime and a coupling broadened Lorentzian peak. In allcases the thermally broadened resonance fits better tothe data than a coupling broadened resonance, indicat-ing that the dots are in the weak coupling regime. Theelectronic temperature extracted from the fitting is ∼ E C,rect ≈ . α rect ≈ .
26. In caseof the circular dot we obtain E C,circle ≈ . α circle ≈ .
14. Assuming a disk-like shape of the dotsallows us to estimate electronic radius of the dots fromthe values of their charging energies. The obtained valuefor the rectangular dot is r rect ≈
115 nm, and for thecircular r circle ≈
340 nm, which is consistent with thelithographic dimensions of the dots and indicates thatthe dots are really formed in the regions encircled by theoxide lines.Due to the large effective mass of holes, the single-particle level spacing in case of hole quantum dots issignificantly smaller compared to electron quantum dotswith similar size. The estimated mean single-particlelevel spacing in the rectangular dot is △ rect ≤ µ eV,and in the circular dot is △ circle ≤ µ eV. Thereforewe were not able to resolve excited states in Coulombdiamond measurements in neither of the two dots. Thisfact, together with the observed temperature dependenceof Coulomb peak heights [5] indicates that both dots arein the multi-level transport regime. In order to be ableto investigate the single-particle level spectrum in holequantum dots, one has to significantly reduce the lateraldimensions of the dot as well as the hole temperature.In conclusion, we fabricated tunable nanodevices onp-type GaAs heterostructures by AFM oxidation lithog-raphy. By using this fabrication technique we were ableto overcome the problems with large hysteresis effectspresent in gate sweeps in conventional split-gate definednanostructures on p-type GaAs, and the stability of thestructures improved as well. Electronic functionality ofthese structures was demonstrated by observing conduc-tance quantization in a QPC, and Coulomb blockade intwo quantum dots with different geometries. Further re-duction in size of the p-type quantum dots is necessaryin order to explore the influence of spin-orbit and carrier-carrier interactions on single-particle level spectra.Financial support from the Swiss National ScienceFoundation is gratefully acknowledged. [1] R. Winkler, Springer Tracts in Modern Physics, Volume , Springer-Verlag (2003)[2] B. Grbi´c et al., Appl. Phys. Lett. , 2277 (2004)[3] R. Held et al., Appl. Phys. Lett. , 262 (1998). [4] L. P. Rokhinson et al., Superl. and Microstr. , 99 (2002).[5] B. Grbi´c et al., Appl. Phys. Lett. , 232108 (2005)[6] S. Cronenwett et al., Phys. Rev. Lett.88