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Title: Marginal metallic state at a fractional filling of ’8/5’ and ’4/3’ of Landau levels in the GaAs/AlGaAs 2D electron system
Abstract A metallic state with a vanishing activation gap, at a filling factor $$\nu = 8/5$$ ν = 8 / 5 in the untilted specimen with $$n= 2 \times 10^{11} cm^{-2}$$ n = 2 × 10 11 c m - 2 , and at $$\nu = 4/3$$ ν = 4 / 3 at $$n=1.2 \times 10^{11} cm^{-2}$$ n = 1.2 × 10 11 c m - 2 under a $$\theta = 66^{0}$$ θ = 66 0 tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at $$\nu =8/5$$ ν = 8 / 5 , and at $$\nu =4/3$$ ν = 4 / 3 under tilt as mentioned above, over the interval $$1 \le \nu \le 2$$ 1 ≤ ν ≤ 2 , that also includes the $$\nu = 3/2$$ ν = 3 / 2 more » state, which appears perceptibly gapped in the first instance. « less
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Scientific Reports
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  1. Abstract

    Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$gμBB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$νfor the$$R_{xx}$$Rxxminimum, e.g., from$$\nu = 11/7$$ν=11/7to$$\nu = 8/5$$ν=8/5, and a corresponding change in the$$R_{xy}$$Rxy, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$Rxy/RK=(11/7)-1to$$R_{xy}/R_{K} = (8/5)^{-1}$$Rxy/RK=(8/5)-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$ν=4/3and$$\nu = 7/5$$ν=7/5resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$Rxyat the$$R_{xx}$$Rxxminima- the latter occurring for$$\nu = 4/3, 7/5$$ν=4/3,7/5and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$νand$$R_{xy}$$Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated withmore »different Hall resistances.

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  2. Abstract
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  3. We investigate the molecular gas content of z  ∼ 6 quasar host galaxies using the Institut de Radioastronomie Millimétrique Northern Extended Millimeter Array. We targeted the 3 mm dust continuum, and the line emission from CO(6–5), CO(7–6), and [C  I ] 2−1 in ten infrared–luminous quasars that have been previously studied in their 1 mm dust continuum and [C  II ] line emission. We detected CO(7–6) at various degrees of significance in all the targeted sources, thus doubling the number of such detections in z  ∼ 6 quasars. The 3 mm to 1 mm flux density ratios are consistent with a modified black body spectrum with a dust temperature T dust  ∼ 47 K and an optical depth τ ν  = 0.2 at the [C  II ] frequency. Our study provides us with four independent ways to estimate the molecular gas mass, M H2 , in the targeted quasars. This allows us to set constraints on various parameters used in the derivation of molecular gas mass estimates, such as the mass per luminosity ratios α CO and α [CII] , the gas-to-dust mass ratio δ g/d , and the carbon abundance [C]/H 2 . Leveraging either on the dust, CO, [C  I ], ormore »[C  II ] emission yields mass estimates of the entire sample in the range M H2  ∼ 10 10 –10 11 M ⊙ . We compared the observed luminosities of dust, [C  II ], [C  I ], and CO(7–6) with predictions from photo-dissociation and X-ray dominated regions. We find that the former provide better model fits to our data, assuming that the bulk of the emission arises from dense ( n H  > 10 4 cm −3 ) clouds with a column density N H  ∼ 10 23 cm −2 , exposed to a radiation field with an intensity of G 0  ∼ 10 3 (in Habing units). Our analysis reiterates the presence of massive reservoirs of molecular gas fueling star formation and nuclear accretion in z  ∼ 6 quasar host galaxies. It also highlights the power of combined 3 mm and 1 mm observations for quantitative studies of the dense gas content in massive galaxies at cosmic dawn.« less
  4. Resonant tunneling diodes (RTDs) have come full-circle in the past 10 years after their demonstration in the early 1990s as the fastest room-temperature semiconductor oscillator, displaying experimental results up to 712 GHz and fmax values exceeding 1.0 THz [1]. Now the RTD is once again the preeminent electronic oscillator above 1.0 THz and is being implemented as a coherent source [2] and a self-oscillating mixer [3], amongst other applications. This paper concerns RTD electroluminescence – an effect that has been studied very little in the past 30+ years of RTD development, and not at room temperature. We present experiments and modeling of an n-type In0.53Ga0.47As/AlAs double-barrier RTD operating as a cross-gap light emitter at ~300K. The MBE-growth stack is shown in Fig. 1(a). A 15-μm-diam-mesa device was defined by standard planar processing including a top annular ohmic contact with a 5-μm-diam pinhole in the center to couple out enough of the internal emission for accurate free-space power measurements [4]. The emission spectra have the behavior displayed in Fig. 1(b), parameterized by bias voltage (VB). The long wavelength emission edge is at  = 1684 nm - close to the In0.53Ga0.47As bandgap energy of Ug ≈ 0.75 eV at 300 K.more »The spectral peaks for VB = 2.8 and 3.0 V both occur around  = 1550 nm (h = 0.75 eV), so blue-shifted relative to the peak of the “ideal”, bulk InGaAs emission spectrum shown in Fig. 1(b) [5]. These results are consistent with the model displayed in Fig. 1(c), whereby the broad emission peak is attributed to the radiative recombination between electrons accumulated on the emitter side, and holes generated on the emitter side by interband tunneling with current density Jinter. The blue-shifted main peak is attributed to the quantum-size effect on the emitter side, which creates a radiative recombination rate RN,2 comparable to the band-edge cross-gap rate RN,1. Further support for this model is provided by the shorter wavelength and weaker emission peak shown in Fig. 1(b) around = 1148 nm. Our quantum mechanical calculations attribute this to radiative recombination RR,3 in the RTD quantum well between the electron ground-state level E1,e, and the hole level E1,h. To further test the model and estimate quantum efficiencies, we conducted optical power measurements using a large-area Ge photodiode located ≈3 mm away from the RTD pinhole, and having spectral response between 800 and 1800 nm with a peak responsivity of ≈0.85 A/W at  =1550 nm. Simultaneous I-V and L-V plots were obtained and are plotted in Fig. 2(a) with positive bias on the top contact (emitter on the bottom). The I-V curve displays a pronounced NDR region having a current peak-to-valley current ratio of 10.7 (typical for In0.53Ga0.47As RTDs). The external quantum efficiency (EQE) was calculated from EQE = e∙IP/(∙IE∙h) where IP is the photodiode dc current and IE the RTD current. The plot of EQE is shown in Fig. 2(b) where we see a very rapid rise with VB, but a maximum value (at VB= 3.0 V) of only ≈2×10-5. To extract the internal quantum efficiency (IQE), we use the expression EQE= c ∙i ∙r ≡ c∙IQE where ci, and r are the optical-coupling, electrical-injection, and radiative recombination efficiencies, respectively [6]. Our separate optical calculations yield c≈3.4×10-4 (limited primarily by the small pinhole) from which we obtain the curve of IQE plotted in Fig. 2(b) (right-hand scale). The maximum value of IQE (again at VB = 3.0 V) is 6.0%. From the implicit definition of IQE in terms of i and r given above, and the fact that the recombination efficiency in In0.53Ga0.47As is likely limited by Auger scattering, this result for IQE suggests that i might be significantly high. To estimate i, we have used the experimental total current of Fig. 2(a), the Kane two-band model of interband tunneling [7] computed in conjunction with a solution to Poisson’s equation across the entire structure, and a rate-equation model of Auger recombination on the emitter side [6] assuming a free-electron density of 2×1018 cm3. We focus on the high-bias regime above VB = 2.5 V of Fig. 2(a) where most of the interband tunneling should occur in the depletion region on the collector side [Jinter,2 in Fig. 1(c)]. And because of the high-quality of the InGaAs/AlAs heterostructure (very few traps or deep levels), most of the holes should reach the emitter side by some combination of drift, diffusion, and tunneling through the valence-band double barriers (Type-I offset) between InGaAs and AlAs. The computed interband current density Jinter is shown in Fig. 3(a) along with the total current density Jtot. At the maximum Jinter (at VB=3.0 V) of 7.4×102 A/cm2, we get i = Jinter/Jtot = 0.18, which is surprisingly high considering there is no p-type doping in the device. When combined with the Auger-limited r of 0.41 and c ≈ 3.4×10-4, we find a model value of IQE = 7.4% in good agreement with experiment. This leads to the model values for EQE plotted in Fig. 2(b) - also in good agreement with experiment. Finally, we address the high Jinter and consider a possible universal nature of the light-emission mechanism. Fig. 3(b) shows the tunneling probability T according to the Kane two-band model in the three materials, In0.53Ga0.47As, GaAs, and GaN, following our observation of a similar electroluminescence mechanism in GaN/AlN RTDs (due to strong polarization field of wurtzite structures) [8]. The expression is Tinter = (2/9)∙exp[(-2 ∙Ug 2 ∙me)/(2h∙P∙E)], where Ug is the bandgap energy, P is the valence-to-conduction-band momentum matrix element, and E is the electric field. Values for the highest calculated internal E fields for the InGaAs and GaN are also shown, indicating that Tinter in those structures approaches values of ~10-5. As shown, a GaAs RTD would require an internal field of ~6×105 V/cm, which is rarely realized in standard GaAs RTDs, perhaps explaining why there have been few if any reports of room-temperature electroluminescence in the GaAs devices. [1] E.R. Brown,et al., Appl. Phys. Lett., vol. 58, 2291, 1991. [5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981). [2] M. Feiginov et al., Appl. Phys. Lett., 99, 233506, 2011. [6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995). [3] Y. Nishida et al., Nature Sci. Reports, 9, 18125, 2019. [7] E.O. Kane, J. of Appl. Phy 32, 83 (1961). [4] P. Fakhimi, et al., 2019 DRC Conference Digest. [8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018). [5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981). [6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995). [7] E.O. Kane, J. of Appl. Phy 32, 83 (1961). [8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018).« less
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