научная статья по теме SHOT NOISE OF THE EDGE TRANSPORT IN THE INVERTED BAND HGTE QUANTUM WELLS Физика

Текст научной статьи на тему «SHOT NOISE OF THE EDGE TRANSPORT IN THE INVERTED BAND HGTE QUANTUM WELLS»

Pis'ma v ZhETF, vol. 101, iss. 10, pp. 787-792

© 2015 May 25

Shot noise of the edge transport in the inverted band HgTe

quantum wells

In memory of V.F.Gantmakher

E. S. Tikhonov+*, D. V. Shovkun+*, V. S. Khrapai+*1\ Z. D. Kvonxo, N. N. Mikhailovv, S. A. Dvoretsky7

+ Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Russia * Moscow Institute of Physics and Technology 141700 Dolgoprudny, Russia x Rzhanov Institute of Semiconductor Physics SB of the RAS, 630090 Novosibirsk, Russia °Novosibirsk State University, 630090 Novosibirsk, Russia vInstitute of Semiconductor Physics, 630090 Novosibirsk, Russia Submitted 10 April 2015

We investigate the current noise in HgTe-based quantum wells with an inverted band structure in the regime of disordered edge transport. Consistent with previous experiments, the edge resistance strongly exceeds h/e2 and weakly depends on the temperature. The shot noise is well below the Poissonian value and characterized by the Fano factor with gate voltage and sample to sample variations in the range 0.1 < F < 0.3. Given the fact that our devices are shorter than the most pessimistic estimate of the ballistic dephasing length, these observations exclude the possibility of one-dimensional helical edge transport. Instead, we suggest that a disordered multi-mode conduction is responsible for the edge transport in our experiment.

DOI: 10.7868/S0370274X15100112

The topological insulator (TI) concept [1] allows to predict whether a general band insulator contains gap-less electronic surface states based solely on the symmetry considerations. If present, such states possess a linear dispersion relation along with a topological protection from elastic backscattering [2]. Though such Weyl-type states in semiconductor inverted band interfaces have been known since about three decades [3], their topological origin was hidden until recently. Surface states of a two-dimensional (2D) TI are represented by one-dimensional (ID) helical edge states, protected from elastic backscattering and propagating along the boundary between the 2D TI and the normal insulator or vacuum.

The 2D TI phase has been proposed in HgTe [4] and InAs/GaSb [5] quantum wells with the inverted band structure. Experimental evidence of the edge transport near the charge neutrality point (CNP) in such structures comes from a nearly quantized resistance in short samples [6, 7], strongly nonlocal transport [8-10], current density visualization [11], and Josephson interference experiments [12]. More recently, the edge states contribution was identified in conductance of the lat-

e-mail: dick@issp.ac.ru

eral p—n junctions in HgTe [13]. In samples longer than a few micrometers the regime of disordered edge transport is realized. Here the resistance scales with the device length [6, 10, 14] whereas its temperature (T) dependence is very weak [9, 10]. These observations is hard to reconcile with the theoretical models that consider inelastic scattering to account for the dephasing and broken topological protection, see e.g. Refs. [15, 16].

At a given T the dephasing time is fundamentally bounded from below by the uncertainty principle r^ > > h/(kBT), where h and are the Planck constant and the Boltzman constant, regardless the actual de-phasing mechanism [17]. At T = 0.5K, with the helical edge state velocity of v « 5 • 105m/s [18], this corresponds to the ballistic dephasing length of vt$ > 7 ¡im in HgTe quantum wells. Along with the weak T dependence, this suggests that in a few micrometer long HgTe devices the transport may already be coherent. This conjecture can be directly tested via the measurement of the current fluctuations (shot noise), that is related [19] to the quantum-mechanical transmission probability T = Rq/R via the Fano factor F = 1 — T, where R and Rq = h/e2 are, respectively the sample resistance and the resistance quantum.

IlHCbMa b >K3TO tom 101 bbin. 9-10 2015

787

9*

Fig. 1. Sample layout and linear response transport data. (a,-c) - Sketches of the two-terminal transport and noise measurement layouts in samples I, II, and III, respectively. The metallic gates are shown in grey and the gated mesa edges are shown by the thick lines. The mesa arms reaching to the ohmic contacts appear white and the black dots mark the bonded contacts. For the shot noise measurements all the available contacts are grounded except for the contact N. That contact is connected to the load resistor (rectangle), the cryogenic rf-amplifier (triangle) and the current source. The edges that mainly contribute to the noise signal are marked by even thicker lines. In sample I the edge current flows from the contact N via the two gated mesa edges mostly in the contacts 2 and 3, which absorb about 90 % of the total current. In sample II about 80 % of the edge current flows through the lower right edge to the ground. The rest of the current takes the higher resistance path along the three edge segments to the contact G. In all the noise measurements, the contact contribution was measured independently at Vg = 0 V and subtracted from the data presented below, (d) - Two-terminal linear response resistance for all samples as a function of the gate voltage at T ~ 0.52 K. Symbols mark the positions Rot — Vg near the CNP, where the noise data of Fig. 4 (see below) was measured in sample I (open), sample II (closed) and sample III (cross). Some symbols miss the corresponding lines because of the slight temporal drift of the sample state. Inset: T-dependence of the four-point resistance Rn-g,4-s in sample I at Vg = —3.2 V in the CNP region

In this Letter, we investigate the current noise in the regime of disordered edge transport (R Rq) near the CNP in the inverted band HgTe quantum wells. At low T the devices are well in the regime L < vtwhere L is the length of the edge state. The shot noise Fano factor exhibits gate voltage and sample to sample variations in the range 0.1 < F < 0.3. At the same time, the T dependence of the resistance is weakly insulating. These observations preclude the possibility of ID helical edge states and suggest a multi-mode diffusive conduction as the origin of the edge transport in our devices. Our data clearly demonstrates that a presumption of the single-channel helical edge transport in the inverted band structures calls for an independent verification.

Our samples are based on 8nm wide (013) CdHgTe/HgTe/CdHgTe quantum wells grown by molecular beam epitaxy, with mesas shaped by wet etching and covered with a Si02/SigN4 insulating layer, see Ref. [20] for the details. Metallic Au/Ti top gates enable us to tune the 2D system across the CNP by means of a field effect. Ohmic contacts are achieved by a few second In soldering in air, providing a typical resistance of the ungated mesa arms in the range of 10-30 kil at low T. The experiment was performed in a liquid 3He insert with a bath T of 0.52 Iv. The dc transport measurements were performed in a two-terminal or multi-terminal configurations with the help of a low-noise 100 MQ input resistance preamplifier. The shot noise voltage fluctuation is measured within

nucbMa B >K3T® TOM 101 Bun. 9-10 2015

h-G (nA)

Fig. 2. Evidence of the edge transport in the nonlinear response regime, (a) - Normal bulk transport for the p-type conduction (V9 = —4.3 V) and n-type conduction (V9 = —2 V) outside the CNP region. In each case, the data measured with the contacts 2, N, 3 and 4 are practically indistinguishable. Inset: layout of a three-terminal measurement in sample I with the source contact 1 and the ground contact G. (b,c) - Edge transport regime for Vg = —2.9 V and Vg = —3.3 V in the CNP region. The data measured with different contacts are marked respectively. Along with the data for the contacts 2, N, 3 and 4 here we also plot the contribution of the series resistance of the contact G and its mesa arm, marked by G. The vertical scale is the same for all panels

a 3 x 25 dB room-T amplification stage and a power detector. The noise measurement setup was calibrated via the Johnson-Nyquist thermometry. Below we present the results obtained on three samples which demonstrate similar behavior reproducible in respect to thermal recycling. The sample I had a mobility of about 150000 cm2/Vs at an electron density of 3 • 10ncm~2 measured at a zero gate voltage. The sample II was not characterized and is expected to have a similar quality. The lower quality sample III had a mobility of about 60000 cm2/Vs at an electron density of about 2 x 1011 cm-2 measured in the ungated region.

In Figs, la-c we sketch the experimental layouts used for two-terminal transport and noise measurements, respectively, in samples I, II, and III. All the dimensions correspond to those in real samples, see the scale bar. The top gated areas are shaded in grey and the edges of the gated part of the mesa are shown by thick solid lines. The bonded and floating ohmic contacts are marked, respectively, by the dotted and open rectangles. In all cases, the contact G was connected to the circuit ground and the contact N was used for both dc transport and rf noise measurements. This was achieved by means of the load resistor capacitively coupled to the ground, and a 10 nF capacitor coupled to the input of the cryogenic rf-amplifier (depicted by a triangle). All other bonded

0.16-

0.14-

0.12-

0.10

-0.5 0 0.5 V (mV)

Fig. 3. Shot noise and differential conductance in the edge transport regime in sample I. (a) - Shot noise spectral density as a function of current at Vg = —3.2 V (symbols) and the slope of the dashed guide line corresponds to the Fano factor of F = 0.2. (b) - Differential conductance as a function of the bias voltage across the device (scale on the left hand side) along with the corresponding Johnson-Nyquist like contribution Si = 4ksTg (scale on the right hand side). The contributions to g and V owing to the finite contact resistance in series with the device are subtracte

Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.

Показать целиком