Impurity-induced states in conventional and unconventional superconductors

Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± id xy -wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

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“…[137]. Conventional s-wave superconductors are well-known to be robust against non-magnetic disorder.…”

Section: Impurity Effectsmentioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

171

176

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“…Thus impurity states in graphene distinguish strongly from their counterparts in usual semiconductors, where the DOS in the valence and conduction bands are very different and impurity levels lie generally far away from the middle of the gap. Impurity effects on the electronic structure of twodimensional systems with Dirac spectrum were investigated in detail in connection with the problem of hightemperature superconductivity in copper-oxide compounds, and STM visualization of the order parameter around impurities is one of the most straightforward evidences of the d-wave pairing in these systems [14]. For the case of a strong enough impurity potential, the formation of quasilocalized electron states in the pseudogap around the Dirac point is expected [14], whereas a weak potential will not lead to the formation of quasilocalized states at all.…”

mentioning

confidence: 99%

Molecular Doping of Graphene

et al. 2007

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Graphene, a one-atom thick zero gap semiconductor [1,2], has been attracting an increasing interest due to its remarkable physical properties ranging from an electron spectrum resembling relativistic dynamics [3,4,5,6,7,8,9,10,11,12] to ballistic transport under ambient conditions [1,2,3,4]. The latter makes graphene a promising material for future electronics and the recently demonstrated possibility of chemical doping without significant change in mobility has improved graphene's prospects further [13]. However, to find optimal dopants and, more generally, to progress towards graphene-based electronics requires understanding the physical mechanism behind the chemical doping, which has been lacking so far. Here, we present the first joint experimental and theoretical investigation of adsorbates on graphene. We elucidate a general relation between the doping strength and whether or not adsorbates have a magnetic moment: The paramagnetic single NO 2 molecule is found to be a strong acceptor, whereas its diamagnetic dimer N 2 O 4 causes only weak doping. This effect is related to the peculiar density of states of graphene, which provides an ideal situation for model studies of doping effects in semiconductors. Furthermore, we explain recent results on its "chemical sensor" properties, in particular, the possibility to detect a single NO 2 molecule [13].Controlling the type and the concentration of charge carriers is at the heart of modern electronics: It is the ability of combining gate voltages and impurities for locally changing the density of electrons or holes that allows for the variety of nowadays available semiconductor based devices. However, the conventional Si-based electronics is expected to encounter fundamental limitations at the spatial scale below 10 nm, according to the semiconductor industry roadmap, and this calls for novel materials that might substitute or complement Si. Being only one atomic layer thick, graphene exhibits ballistic transport on a submicron scale and can be doped heavily -either by gate voltages or molecular adsorbateswithout significant loss of mobility [1]. In addition, later experiments [13] demonstrated its potential for solid state gas sensors and even the possibility of single molecule detection.We show, that in graphene, aside from the donoracceptor distinction, there are in general two different classes of dopants -paramagnetic and nonmagnetic. In contrast to ordinary semiconductors, the latter type of impurities act generally as rather weak dopants, whereas the paramagnetic impurities cause strong doping: Due to the linearly vanishing, electron-hole symmetric density of states (DOS) near the Dirac point of graphene, localised impurity states without spin polarisation are pinned to the centre of the pseudogap. Thus impurity states in graphene distinguish strongly from their counterparts in usual semiconductors, where the DOS in the valence and conduction bands are very different and impurity levels lie generally far away from the middle of the gap. Impurity effects on t...

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“…Moreover, following the argument in Refs. [11,12] we expect sharp features in the response ∂ 2 I/∂V 2 ∝ ∂δN (r, ω)/∂ω at the inelastic resonances ω = ±ω 0 for low temperatures. These expected features of the response to the inelastic scattering are verified in Fig.…”

mentioning

confidence: 86%

“…Theoretically, it has been shown that vibrational modes in a arXiv:0811.1782v2 [cond-mat.mes-hall] 20 Apr 2010 molecular structure adsorbed on a metallic surface would be measurable by means of IETS in a narrow energy range around the vibrational mode [11,12]. Moreover, the inelastic scattering generates Friedel oscillations in the local surface density of states (DOS), thus enabling spatial imaging of the inelastic signatures.…”

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confidence: 99%

Detection and Cloaking of Molecular Objects in Coherent Nanostructures Using Inelastic Electron Tunneling Spectroscopy

2010

Self Cite

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We address quantum invisibility in the context of electronics in nanoscale quantum structures. We make use of the freedom of design that quantum corrals provide and show that quantum mechanical objects can be hidden inside the corral, with respect to inelastic electron scattering spectroscopy in combination with scanning tunneling microscopy, and we propose a design strategy. A simple illustration of the invisibility is given in terms of an elliptic quantum corral containing a molecule, with a local vibrational mode, at one of the foci. Our work has implications to quantum information technology and presents new tools for nonlocal quantum detection and distinguishing between different molecules.PACS numbers: IETS, quantum invisibility, quantum corral, STM, nanoscale engineering As we approach the quantum limit for a wide range of experiments and technologies, it is rather natural to ask whether it is possible to hide information from the measurements. A recent theoretical study suggested that a cloak of invisibility is in principle possible in optical applications, using the freedom of design offered by metamaterials in order to redirect electromagnetic fields [1]. It has since been shown that a copper cylinder may be hidden inside a metamaterial cloak constructed according to the theoretical prescription [2].Physical and chemical signal detection is based on the interactions between the probe and the sample. Those interactions are probed within a certain frequency range, which itself depends on the specific property we are probing, e.g spin or charge response. Thus, by eliminating or weakening the effect of the relevant interactions within the operational frequency range, the objects can be made invisible from the detector. In this sense, one has been able to show that metamaterials can be used as a cloaking device. One example is a copper cylinder, that was made invisible in the microwave frequency band range. Here, we discuss detection and invisibility within the THz band. The discussion is based on the ability to intentionally engineer the properties of quantum structures with tailored properties in the THz band range. This high frequency regime is accessible for nano structures and it opens the window for detection of species down to single molecules and atoms, based on their chemical (vibrational) signatures.In this Letter, we address invisibility in the context of electronics in nanoscale quantum structures, for which we use quantum corrals as a prototype coherent device. We take advantage of the freedom of design that quantum corrals provide and show that quantum mechanical objects located inside the corral can be made invisible with respect to certain measurement. We first need to ask how specific species of quantum matter can be detected. This can be accomplished through chemical identity of atoms and molecules for which molecular vibrations function as a fingerprint of species identity. In this case, the relevant frequency scale is THz rather than MHz. Remarkably, scanning tunneling microscopy (STM) c...

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Impurity-induced states in conventional and unconventional superconductors

Cited by 1,289 publications

References 347 publications

Chirald-wave superconductivity in doped graphene

Chirald-wave superconductivity in doped graphene

Molecular Doping of Graphene

Detection and Cloaking of Molecular Objects in Coherent Nanostructures Using Inelastic Electron Tunneling Spectroscopy

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