1. Introduction 2. Quantum confined systems 3. Transmission in nanostructures 4. Quantum dots and single electron phenomena 5. Interference in diffusive transport 6. Temperature decay of fluctuations 7. Non-equilibrium transport and nanodevices.

Transport in Nanostructures

1 Introduction 2 Quantum confined systems 3 Transmission in nanostructures 4 Quantum dots and single electron phenomena 5 Interference in diffusive transport 6 Temperature decay of fluctuations 7 Non-equilibrium transport and nanodevices

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Transport in nanostructures

TOPICAL REVIEW: Semiconductor nanowires

Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions through which they communicate by Josephson tunneling to establish the macroscopic superconducting state [1]. Although crystals of the cuprate high-Tc superconductors are not granular in a structural sense, theory indicates that at low hole densities the holes can become concentrated at some locations resulting in hole-rich superconducting domains [2-5]. Granular superconductivity due to Josephson tunneling through 'undoped' regions between such domains would represent a new paradigm for the underdoped cuprates. Here we report studies of the spatial interrelationships between STM tunneling spectra in underdoped Bi2Sr2CaCu2O8+x. They reveal an apparent spatial segregation of the electronic structure into ~3nm diameter domains (with superconducting characteristics and local energy gap delta 50(2.5) meV. These observations suggest that underdoped Bi2Sr2CaCu2O8+x is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor.

Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+x

Two-dimensional electron and hole gas systems, enabled through band structure design and epitaxial growth on planar substrates, have served as key platforms for fundamental condensed matter research and high-performance devices. The analogous development of one-dimensional (1D) electron or hole gas systems through controlled growth on 1D nanostructure substrates, which could open up opportunities beyond existing carbon nanotube and nanowire systems, has not been realized. Here, we report the synthesis and transport studies of a 1D hole gas system based on a free-standing germanium/silicon (Ge/Si) core/shell nanowire heterostructure. Room temperature electrical transport measurements clearly show hole accumulation in undoped Ge/Si nanowire heterostructures, in contrast to control experiments on single-component nanowires. Low-temperature studies show well-controlled Coulomb blockade oscillations when the Si shell serves as a tunnel barrier to the hole gas in the Ge channel. Transparent contacts to the hole gas also have been reproducibly achieved by thermal annealing. In such devices, we observe conductance quantization at low temperatures, corresponding to ballistic transport through 1D subbands, where the measured subband energy spacings agree with calculations for a cylindrical confinement potential. In addition, we observe a “0.7 structure,” which has been attributed to spontaneous spin polarization, suggesting the universality of this phenomenon in interacting 1D systems. Lastly, the conductance exhibits little temperature dependence, consistent with our calculation of reduced backscattering in this 1D system, and suggests that transport is ballistic even at room temperature.

https://www.pnas.org/content/pnas/102/29/10046.full.pdf

One-dimensional hole gas in germanium/silicon nanowire heterostructures

In zero magnetic field, conductance measurements of clean one-dimensional (1D) constrictions defined in GaAs/AlGaAs heterostructures show up to 26 quantized ballistic plateaus, as well as a structure close to $0.7({2e}^{2}/h)$. In an in-plane magnetic field all the 1D subbands show linear Zeeman splitting, and in the wide channel limit the $g$ factor is $\ensuremath{\mid}g\ensuremath{\mid}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.4$, close to that of bulk GaAs. For the last subband, spin splitting originates from the structure at $0.7({2e}^{2}/h)$, indicating spin polarization at $B\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. The measured enhancement of the $g$ factor as the subbands are depopulated suggests that the ``0.7 structure'' is induced by electron-electron interactions.

/pdf/possible-spin-polarization-in-a-one-dimensional-electron-gas-5f2673s5tz.pdf

Possible Spin Polarization in a One-Dimensional Electron Gas.

We have investigated the transport properties of one-dimensional (1D) constrictions defined by split-gates in high quality ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures In addition to the usual quantized conductance plateaus, the equilibrium conductance shows a structure close to ${07(2e}^{2}/h)$, and in consolidating our previous work [K J Thomas et al, Phys Rev Lett 77, 135 (1996)] this 07 structure has been investigated in a wide range of samples as a function of temperature, carrier density, in-plane magnetic field ${B}_{\ensuremath{\Vert}},$ and source-drain voltage ${V}_{\mathrm{sd}}$ We show that the 07 structure is not due to transmission or resonance effects, nor does it arise from the asymmetry of the heterojunction in the growth direction All the 1D subbands show Zeeman splitting at high ${B}_{\ensuremath{\Vert}},$ and in the wide channel limit the $g$ factor is $|g|\ensuremath{\approx}04$, close to that of bulk GaAs As the channel is progressively narrowed we measure an exchange-enhanced $g$ factor The measurements establish that the 07 structure is related to spin, and that electron-electron interactions become important for the last few conducting 1D subbands

http://personal.rhul.ac.uk/ukap/042/PDFs/inter.pdf

Interaction effects in a one-dimensional constriction

We show that small structures can be defined in high mobility two‐dimensional electron gases formed at a depth of 2770 A below the surface in GaAs/Al0.33Ga0.67As heterostructures. The differential conductance of one‐dimensional constrictions defined by split gates in such deep electron gases showed more than 20 quantised plateaus. The absence of resonant structures on the plateaus demonstrates the absence of potential fluctuations in the constrictions. By applying a dc source‐drain bias we have measured the energy spacings of the first 18 subbands, and the effect of a small perpendicular magnetic field on the energy spacings has been investigated.

Ballistic transport in one‐dimensional constrictions formed in deep two‐dimensional electron gases

We have investigated experimentally an open semiconductor system in which electron confinement around an obstacle is obtained using a magnetic field. The magnetic field gives rise to Landau levels, and each associated edge state circulates around the obstacle, forming a set of quantized states. Tunable constrictions are fabricated by using a technique which enables us to control transport in and out of these states, producing Aharonov-Bohm oscillations as the magnetic field is swept. Surprisingly, a strong extra oscillation with the same h/e frequency develops, phase shifted by \ensuremath{\pi} so that the frequency appears to have doubled. We explain these results in terms of charging of isolated circulating edge states.

Charging and double-frequency Aharonov-Bohm effects in an open system.

We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a large magnetic field $B$. The field confines electrons around the antidot in closed orbits, the areas of which are quantized through the Aharonov-Bohm effect. Increasing $B$ reduces each state's area, pushing electrons closer to the center, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. Addition and excitation spectra in dc bias confirm the Coulomb blockade of tunneling.

https://arxiv.org/pdf/cond-mat/9907466.pdf

D. R. Mace

Papers

Possible Spin Polarization in a One-Dimensional Electron Gas.

Interaction effects in a one-dimensional constriction

Ballistic transport in one‐dimensional constrictions formed in deep two‐dimensional electron gases

Charging and double-frequency Aharonov-Bohm effects in an open system.

Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime