Quantum Transport

Nazarov, Yuli V.; Blanter, Yaroslav M.

doi:10.1017/cbo9780511626906

Cited by 629 publications

(314 citation statements)

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“…Conversely, the gaps do not appear if a substantial fraction of the transmission eigenvalues is close to zero, as is the case for tunnel, diffusive [34], or dirty contacts [31]. We note that in our Letter, the so-called Ehrenfest time separating semiclassical from wave dynamics is small and plays no role, different from other studies [19,21].…”

Section: Prl 112 067001 (2014) P H Y S I C a L R E V I E W L E T T Econtrasting

confidence: 71%

“…Unlike the bridge geometry of [27], we assume that, for the geometry we consider, the spatial dependence of the Green's functions is not relevant. Therefore, we can make use of the discretized form of the method-the so-called quantum circuit theory [30,31]. The crucial equation that relates the retarded matrix Green's functionsĜ c in the normal metal and thosê G 1;2 in the two superconductors 1,2, takes the form of matrix current conservation…”

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confidence: 99%

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“Smile” Gap in the Density of States of a Cavity between Superconductors

et al. 2014

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The density of Andreev levels in a normal metal (N) in contact with two superconductors (S) is known to exhibit an induced minigap related to the inverse dwell time. We predict a small secondary gap just below the superconducting gap edge-a feature that has been overlooked so far in numerous microscopic studies of the density of states in S-N-S structures. In a generic structure with N being a chaotic cavity, the secondary gap is the widest at zero phase bias. It closes at some finite phase bias, forming the shape of a "smile". Asymmetric couplings give even richer gap structures near the phase difference π. All the features found should be amendable to experimental detection in high-resolution low-temperature tunneling spectroscopy. DOI: 10.1103/PhysRevLett.112.067001 PACS numbers: 74.45.+c, 74.78.Na The modification of the density of states (DOS) in a normal metal by a superconductor in its proximity was discovered almost 50 years ago [1]. Soon afterwards, it was predicted, theoretically, for diffusive structures that a socalled minigap of the order of the inverse dwell time in the normal metal (or the Thouless energy) appears in the spectrum [2]. The energy-dependent DOS reflects the energy scale of electron-hole decoherence, and is sensitive to the distance, the geometry, and the properties of the contact between the normal metal and the superconductor [3][4][5]. The details of the local density of states in proximity structures have been investigated experimentally many years later [6][7][8][9][10] and the theoretical predictions have been confirmed [11][12][13] Substantial interest has been paid to the density of states in a finite normal metal between two superconducting leads with different superconducting phases [14,15]. The difference between diffusive [5] and classical ballistic [16] dynamics has been investigated [17]. Many publications have addressed the dependence of the minigap on the competition between dwell and Ehrenfest time [18,19]. The most generic model in this context is that of a chaotic cavity, where a piece of normal metal is connected to the superconductors by means of ballistic point contacts that dominate the resistance of the structure in the normal state. The Thouless energy is given by E Th ¼ ðG Σ =G Q Þδ S , G Q ¼ e 2 =πℏ being the conductance quantum, G Σ ≫ G Q being the total conductance of the contacts, and δ S being the level spacing in the normal metal provided the contacts are closed. The DOS in chaotic cavities has been studied for years [19][20][21][22].The DOS depends on the ratio of E Th and the superconducting energy gap Δ, and on the superconducting phase difference. If the dwell time exceeds the Ehrenfest time, qualitative features of the DOS do not seem to depend much on the contact nature and are the same for ballistic, diffusive, and tunnel contacts. Mesoscopic fluctuations of the DOS [23,24] are small provided G ≫ G Q . It looks like everything is understood, perhaps except a small dip or peak in the DOS just at the gap edge for the diffusive case, which has ...

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Section: Prl 112 067001 (2014) P H Y S I C a L R E V I E W L E T T Econtrasting

confidence: 71%

mentioning

confidence: 99%

“Smile” Gap in the Density of States of a Cavity between Superconductors

et al. 2014

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“…At the same time, at G > G m , there is at least one electron channel in the contact disk with almost perfect transparency. This guarantees [22,23] that the charging energy of every single NC, E c = e 2 /ε r d, is reduced to a value much smaller than δ (ε r is effective dielectric constant of the NC film). Accordingly, the Mott-Hubbard localization is eliminated at the same time as the Anderson localization.…”

Section: Critical Doping Concentration At Mitmentioning

confidence: 99%

“…This conductance can be easily understood with the help of the Landauer formula [22]. The number of conducting channels in the contact area is ∼ (k F ρ) 2 and each of them additively contributes ∼ e 2 /π to G. It was proven that the MIT occurs if the average conductance between two neighboring NCs G in an array of NCs is equal to the minimal conductance G m [23,24]:…”

Section: Critical Doping Concentration At Mitmentioning

confidence: 99%

Metal–insulator transition in films of doped semiconductor nanocrystals

Chen¹,

Reich²,

Kramer³

et al. 2015

Nature Mater

109

134

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To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration nc for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted nc, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.Semiconductor nanocrystals (NCs) have shown great potential in optoelectronics applications such as solar cells [1], light emitting diodes [2], and field-effect transistors [3,4] by virtue of their size-tunable optical and electrical properties [5] and low-cost solution-based processing techniques [6,7]. These applications require conducting NC films and the introduction of extra carriers through doping can enhance the electrical conduction. Several strategies for NC doping have been developed. Remote doping, the use of suitable ligands as donors in the vicinity of NC surface, increased the conductivity of PbSe NC films by 12 orders of magnitude [8]. Electrochemical doping, which tunes the carrier concentration accurately and reversibly, resulted in conducting NC films [9,10]. Lately, stoichiometric control has emerged as a strategy to dope lead chalcogenide NCs [11]. Finally, electronic impurity doping of NCs, originally impeded by synthetic challenges [12], was recently achieved in InAs [13] and CdSe [14] NCs.While many experimental studies have been directed towards increasing the conductivity of NC films, there is still no clear consensus on the fundamental question: what is the condition for the metal-insulator transition (MIT) in NC films [15][16][17]? In a bulk semiconductor, the critical electron concentration n M for the MIT depends on the Bohr radius a B according to the well-known Mott criterion [18] n M a 3 B 0.02, where a B = ε 2 /m * e 2 is the effective Bohr radius (in Gaussian units), ε is the dielectric constant of the semiconductor, and m * is the effective electron mass. It is obvious that a dense film of undoped semiconductor NCs is an insulator, while a film of touching metallic NCs with the same geometry is a conductor. Therefore, the MIT has to occur in semiconductor NC films at some criti-FIG. 1. The origin of the metal-to-insulator transition in semiconductor nanocrystal films. The figure shows the cross section of two nanocrystals in contact through facets with radius ρ. The blue spherical cloud represents an electron wave packet which moves through the contact. Such a compact wave pac...

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“…In this case, the reservoirs provide an equilibration and dissipation mechanism for the dc transport. In particular, at low frequencies, the chiral current is given by the Landauer-Büttiker formula [17] …”

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confidence: 99%

Thin-Film Magnetization Dynamics on the Surface of a Topological Insulator

2012

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We theoretically study the magnetization dynamics of a thin ferromagnetic film exchange-coupled with a surface of a strong three-dimensional topological insulator. We focus on the role of electronic zero modes imprinted by domain walls (DW's) or other topological textures in the magnetic film. Thermodynamically reciprocal hydrodynamic equations of motion are derived for the DW responding to electronic spin torques, on the one hand, and fictitious electromotive forces in the electronic chiral mode fomented by the DW, on the other. An experimental realization illustrating this physics is proposed based on a ferromagnetic strip, which cuts the topological insulator surface into two gapless regions. In the presence of a ferromagnetic DW, a chiral mode transverse to the magnetic strip acts as a dissipative interconnect, which is itself a dynamic object that controls (and, inversely, responds to) the magnetization dynamics.PACS numbers: 72.15.Gd, Following theoretical predictions [1] and experimental realizations [2] of three-dimensional topological insulators (TI's), vigorous ongoing activities in this burgeoning field are aimed at introducing spontaneous symmetry breaking mechanisms into the system. This could be accomplished by bulk or surface doping to induce magnetism or superconductivity in the parent (essentially free-electron) TI, or by a heterostructure design wherein symmetry breaking is instilled at the TI surface by a quantum proximity effect. We are following the latter route, considering an insulating ferromagnetic layer (MI) capping the bulk TI, such that the TI surface states are exchange coupled to the collective magnetic moment of the MI. Previous theoretical investigations of a similar TI/MI heterostructure were concerned with currentinduced spin torques experienced by a monodomain MI [4], Gilbert damping by a doped TI [4], electric charging of magnetic textures [4], and the rectification of charge pumping by a monodomain precession [4], all in case of a well-defined spatially uniform sign of the time-reversal symmetry breaking gap in the TI. The essential physical ingredient underlying the key ideas in these papers is the axion electrodynamics [3] associated with the TI [8], with a quantized magnetoelectric coupling that is odd under time reversal. In this Letter, we are interested in salient features associated with dynamic magnetic textures that imprint a spatially inhomogeneous gap onto the TI surface states, both in regard to its magnitude and sign. The latter, in particular, engenders electronic chiral modes at the magnetic domain boundaries [1], whose hydrodynamics become intricately coupled with magnetic precession.According to the spin-charge helicity of the TI electronic states, the spin-transfer torques acting on the MI are locked with the self-consistent electronic charge currents in the TI. These currents, in turn, can respond to a combination of electromagnetic fields and fictitious forces induced by MI dynamics, having several distinct contributions: (i) two-dimensional (2D) surface c...

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Quantum Transport

Cited by 629 publications

References 0 publications

“Smile” Gap in the Density of States of a Cavity between Superconductors

“Smile” Gap in the Density of States of a Cavity between Superconductors

Metal–insulator transition in films of doped semiconductor nanocrystals

Thin-Film Magnetization Dynamics on the Surface of a Topological Insulator

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