Physics of Zero- and One-Dimensional Nanoscopic Systems


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Only the very rich could afford to follow them all. The same goes for the models - certainly, the one thing they do have in common is thinness, that weird kind where it looks like your limbs are on backwards - but how different they all look, and yet how strangely they all look like a foodstuff. Photoshop has turned fashion photography into something you'd want to lick, rather than emulate.


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And the whole libidinal economy of half-naked women staring up at you, as if you were the owner of a peculiarly classical male gaze. It's not clear whether you are supposed to envy or admire them - but then, that's not clear in the real world e ither. Clearly 'not knowing which' model to look like, fashion to pick is a brilliant way of creating just the right kind of anxiety appropriate to a form of shopping frenzy that will buy as many and as varied kinds of shoes, etc.

For fashion to survive the one thing the magazines and adverts can never say, of course, is: 'work out 31 One-Dimensional Woman what suits you and stick to that! Fashion magazines are most definitely tied up with impossible demands, but they seem far more comprehensible as motors of economic expenditure than as ego-ideals. Ariel Levy in Female Chauvinist Pigs has gone some way in describing this cu l ture: A tawdry, tarty, cartoonlike version of female sexuality has become so ubiquitous, it no longer seems particular.

What we once regarded as a kind of sexual expression we now view as sexuality. Capitalism, which in a sense knows no morals or at least can change them easily , couldn't care less about the positive, happy, 'feminist' reclaiming of sex so long as it makes a buck out of skimpy nightwear and thongs. Levy's concept of 'female chauvinist pigs', 'women who make sex objects of other women and of.

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Physics of Zero- and One-Dimensional Nanoscopic Systems

There are many who regard the sexualized treatment of women by other women w i th an u nd erstandable kind of feminist-humanist horror: women can't possibly treat other women the way we said unenlightened men do! But they can, and they do. Sometimes this sexualization is done directly - take, for example, the vexed role of the performance of lesbianism to 32 2. Clearly there is nothing inherently nicer about women than men. Levy ultimately falls into the trap of opposing a nice, liberated version of sexuality - 'we need to allow ourselves the freedom to figure ,out what we internally , want from sex 29 - to a plastic, cartoon world of breast implants and pole-dancing.

There is nothing wrong with Levy's position, in fact, it is extremely sympathetic. But there is problem if there is no way back to this ' freedom' to explore some supposed 'real' sexuality. What if there is no longer a gap between an internal realm of desires, wants and fantasies and the external presentation of oneself as a sexual being? If the image is the reality? As depressing as this might be, it would make a more useful starting point than to assume there is a real humanist reserve of nice sexual desire lying beneath all the images.

If indeed there are moments of subjective resistance, they might not be particularly pleasant. What we are dealing with is an attempt to induce reality, to. Tattoos, on the other hand, for all their counter-cultural history ultimately indicate some sort of acceptance of the realm of conditioned meaning. Self-harm as the anti-tattoo. Each individualized real-time concentrated creation of reality is the true point of the pain, not the residual scratches however deep that remain. Christina Ricci speaks about her own experience of cutting her arms with nails and the tops of fizzy-drinks cans: 'it's a sort of experiment, to see if I can handle pain.

Currently, women are ' doing well' and make 'good workers'. The 'genius' typically possesses feminine characteristics - i magination, intui tion, emotion, madness - but is not of course an actual woman: the great artist is a feminine male, but not a feminine female or a masculine female.

Women can be mad, but not aesthetically inspired, or they can be sane, and provide comfort for the true creators, who are a little bit womanish, but not too much. B u t are women really more sensible? It's unlikely that women are inherently more stable than men, and historically at various points they definitely weren't supposed to be consider the 'hysterical' woman of the 19th century, the Soviet divorce and abortion laws of 1 that recognized that women were just as uncommitted to the bourgeois family set-up as men, Friedan's 'the problem with no name' of the 1 s and 60s.

Sometimes women are supposed to be demented harpies with wombs full of devils and other times they're supposed to fold up nicely like the ironing board in a suburban bungalow. It seems disingenuous, a kind o f cover story t o mask the fact that, among other things, they might actually enjoy playing with their kids or hanging out with their partner.

I t also subtly perpetuates the idea that it's men who really have obsessions, even if they mock themselves a bit about it. It's Hke a safety net - you can like 34 2. Men have ideas and arguments and fixations, women are balanced and well-rounded. Because women are so much more worldly, aren't they? They just know how things work.

But really, women no more know what's going on than men do, and they certainly don't have a insight into nice, stable normality as if anyone does. The current sorted young woman imago is rather conveniently the sort of worker best suited for the type of jobs on offer, but it doesn't mean that in a few years time women won't go back to being depicted as deranged Jezebels hell-bent on fucking society up with their roaming womb-induced crazy-thoughts. One of the problems with the kind of up-beat jolly feminism presented by Valenti et al. Take some of the following lines from Full Frontal Feminism: 'When you're a feminist, day-to-day life is better.

You make better decisions. You have better sex. Of course not. But let's be honest: No one wants to be associated with something that is seen as uncool and unattr active. Absolutely nothing. An obligation, even. Few things are more menacing. According to Valenti, masturbation 'even motivates you to buy fun vibrators that are , neon or shaped like rabbits. But a hip young feminist must have her indulgences.

Just as pink has become the color tha t somehow symbolizes both freedom and sexual availability, like a curious form of hygienic nakedness think of Hugh Hefner 's claim that 'the Playboy girl has no lace, no underwear, she is naked, well-washed with soap and water, and she is happy'36 , chocolate has come to indicate that its female devourer is a little bit, well, 'naughty'. Take, for example, the Iranian business woman, Anousheh Ansari, who paid to go into space: Ansari said to ABC News that she d idn't care what was on the menu on the International Space Station as long as there was one thing - chocolate.

A l l humanity'S technological and mathematical capacities stretched to breaking-point in the name of the abstract, pointless beauty of extra-terrestrial exploration, and yet a Flake in front of the telly might have done? Chocolate represents that acceptable everyday extravagance that all-too-neatly encapsulates just the right kind of perky passivity that feminized capitalism just loves to reward wi th a bubble bath and some crumbly cocoa solids.

I t sticks in the mouth a bit. In a total abnegation of her own subjective capacity as well as the entire history of human achievement, Fay Weldon, for example, claims that: What makes women happy? Ask them and they'll reply, i n 36 2. I think there's a very real sense in which woman are supposed to say 'chocolate' whenever someone asks them what they want.

It , irresistibly symbolizes any or all of the following: ontological girlishness, a naughty virginity that gets its kicks only from a widely-available mucky cloying substitute, a kind of pecuniary decadence. Never when in the company of the man you're after do you give him a haret time. You never. It is hard to decide which of the sexes Weldon is actually more insulting to here. Men she portrays as too stupid to see through bad porn acting while spending the rest of the time apparently thinking 'solely about pleasure and completion'.

Women, on the other hand, are stunted, physically limi ed creatures who gamer pathetic slips of happiness from chocolate and shoes and never come. But where do we get these ideas from? Cinema and television just might have something to do with it. Here a thought experiment comes in handy: The so-called 'Bechdel Test', first described in Alison Bechdel's comi c strip Dykes to Watch Out For, consists of the following rules, to be applied to films, but could easily be extended to literature: 1.

Does it have at least two women in itt 2. Who [at some point talk to each other, 3. About something besides a man. Stross is right - huge quantities of cultural output possibly even more than he suggests fail. Several questions emerge from the test: 1. Does reality itselfpass the test? How much of the time? Vera Chyti lova's Daisies is one of the few films that basically passes the test throughout, and i t's clear that it disturbs as much as i t charms.

This 1 Czech fil m features two young women who dedicate their lives to spoiling everything in increasingly surreal ways, wi th seemingly l ittle rhyme or reason. W ho are these irresponsible young women who find it more amusing to play with each other, and occasionally wi th men, but only so they can return to each other and be yet more 'spoiled' as in ruined, rather than pampered, of course? The formal inventiveness of the film would undermine its claims to 'realism', but this is all the beUer.

For all the male 'coming of age' stories in the world, it makes sense that their rare female equivalent would have to be as bizarre as possible. Contemporary mainstream cinema seems, on the whole, retrograde compared to i ts earlier incarnations, as if a possible space for such things has been closed off for good. B u t let's not get too nostalgic. There is something strange about the absence of women talking from cinema. Aren't women su pposed to always be talking? Of course, they're not meant to be talking about anything important, which is presumably why the camera only turns to them when men are mentioned.

It's not that women think just about men, it's that they think about everything, madly, all the time. How could cinema possible deal with that? Films that appear to be 'all about women', such as Sex and the City are paeans to a curious combination of ultra-mediation and a post-religious obsession with ' the one'. You go to 'the City' in search of 'labels and love'; the one mediating the other - the nicest thing your boyfriend can do for you is h ave a gia.

Drinks with ' the girls' are dominated by discussions about whether he is ' the one' or not. What does this obsession with ' the one' mean? The bourgeoisie may have drowned the most heavenly ecstasies of religious fervor, of chivalrous enthusiasm, of philistine sentimentalism, in the icy water of egotistical calculation, as Marx and Engels observed, but certain religious motifs are harder to shake than others. The 'one' as the transcendent culmination of an entire romantic destiny demonstrates a curious melange of the senti, mental 'we were always meant to be' together!

Marriage, for example, for many is still something other than a mere contract. But this strange mix of sentimentality and pragmatism - ideology, if ever there were a definition - reproduces itself seemingly spontaneously, in culture and conversation. Contemporary cinema is profoundly conservative in this regard; and the fact that it both reflects and d ictates modes of current behavior is depressingly effective, and effectively depressing.

Perhaps the only thing worse than wondering about what women are talking about is seeing them actually do i t, at least as far as Sex And The City goes. If cinema tends to show women talking to each other only about men or marriage, or babies perhaps the most important aspect of this is brevity.

An entire film given over to such things would be obscene according to the logic of mainstream cinema, which can barely tolerate a few minu tes of such footage, even in its 'unambiguously flattering' mode. I think this is indicated by the common observation that men feel alienated and frustrated by an hour or so of Sex and the City.

A winsome few moments of love-lorn anguish shared between two friends is ok, lengthy d iscussions of fel latio are not. Mainstream cinema mediates the relationship between men through the odd woman, who rarely gets to mediate anything at all through anyone or anything else. But in the 'real world' do women mediate their relationships through discussion of men? One could ask a similar question about make-up and fashion.

Prettifying for the boys or warning signs for the other ladies? Obviously the idea tha t straight women are constantly 'competing' for men is an awful one, bu t they are most definitely supposed to, according to the crazy logic of scarcity that consumerism depends u pon. He's the one! That handbag is the one! Of all the industries most symbol ic of the death of interiority and the central i ty of sex, pornography is the one that stands out most, 42 2.

The 'pornification' of contemporary life has often been noted, but too often the discussion takes place in moral terms. Both positions frame the issue in moral terms - pornography is either degrading therefore bad or it is enjoyable and thus morally good. But pornography is, we must first of all acknowledge, a massive industry with major economic and social import. It is also an industry w ith its own self-perpetuating culture, one that has I trouble remembering its own history, unless there is m oney ,to be , made from 'retro' footage.

It often seems disgusted with i tself, with its own past, as the pornographic mode of production seeks to close in on itself and deny its own parentage. The following section juxtaposes contemporary pornography with earlier cinematic examples to point out not only that pornography has changed quite radically, but further that its future need not be as grim as its present.

Tracing the origins of 45 One-Dimensional Woman certain contemporary forms of pornography back through a part of its earl y cinematic history, shows that we can analyze porn not only in terms of its immediate effects on i ts viewers as if these are easily discernible anyway but in terms of the ways i t organizes the senses d ifferently over time. B y looking at the origins of cinematic pornography we can learn much about the way we understand porn tropes today, and precisely, despite all the 'choice', what we're missing.

It seems clear that there is a break in cinematic pornography that happens in the post-World War II period. One place that we see this change - in this case a direct reflection of the rapid rise i n consumerism in the s and 60s - i s in the altered relation of sexuali ty to objects in porn films d uring the period; namely, the rise of the sex toy as prop. At the same time, as one can see in examples of the American 'stag' film of the 1 s, there is a switch from the viewer as voyeur on a private scene to the viewer as explicitly addressed by the participants in the film.

It is no surprise that this turn to the viewer coincides with the reduction in sexual participants on camera. However, one should be wary of presenting an overly cumulative story about the development and qualitative if not quantitative decline of pornography. It is not simply the case that we move from an open to a closed, albeit multi ple, model. Porn today deploys sex as something to be treated outside of other human and social relations, even as it depicts 'office sex', t teacher sex', cop sex', etc.

Revolu tion, where it was used as a way of attacking the monarchy and the established order. The ahistorical approach to pornography neglects to consider the social and economic conditions surrounding both the form and content of pornography as it 47 One-Dimensional Woman exists at any given time. There is no doubt that the porn uppermost in Dworkin's mind was the often extremely nasty, violent porn of the s, and that the exploitation of women in a porn industry was as brutal and any other in the increasingly neo-liberal and unjust society of American capitalism.

But this is precisel y the point. Violence, and the violence specific to certain kinds of pornography cannot be completely removed from a complete analysis of the society that produces i t. In that sense, then, the argument about pornography is ultimately a positive one, taking up Angela Carter's point that: Pornographers are the enemies of women only because of our contemporary ideology of pornography does not encompass the possibility of change, as if we were the slaves of history and not i ts makers, as if sexual relations were not necessarily an expression of social relations, as if sex itsel f were an external fact, one as immutable as the weather, creating human practice but never a part of i t.

The pneumatic Calvinism of rubberized piston porn-duty, the grim orgasm of unsmiling physical moil. But sex-as-work is the lesser partner in the invention of porn-capitalism. Where does it all end up, after all but in the money shot. Oppose to this the short, silent black-and-white films from around the s to the s. They are overwhelmingly French, because of advances in French cinematography and relatively lax censorship laws compared to Britain and Germany at the time.

The first thing you notice in these early films is the sheer level of silliness on show: sex isn't just a succession of grim orgasms and the parading of physical prowess, but something closer to slapstick and vaudeville. Men pretend to be statues of fauns for curious women to tickle; two seamstresses fall into a fit of giggles as their over-excited boss fal ls off the bed; a bawdy waitress serves a series of sexually-inspired meals to a man dressed as a musketeer before joining him for 'dessert'. Bu t the beauty of these early short films lies in the details, the laughter of its participants and the sheer variety of the bodies on parade: the unconventionally attractive mingle with the genuinely pretty; large posteriors squish overjoyed little men.

The fact that the rules of pornographic film-making haven't yet been formally established, as well as the rudimentary nature of the film equipment, means that often the filming cuts off before any sort of climax, which only adds to the amateurish, unstructured, anarchic charm of it all. As the narrator of Malone Dies recounts: And though both were com pletely impotent they finally succeeded, summoning to their aid all the resources of the skin, the mucus and the imagination, in striking from their dry and feeble clips a kind of somber gratification.

In fact, some of the footage in the Reilhac collection is so explicit that it received a 52 3. What shocks the contemporary audience more than any of the specific acts on display, however, is the fact that the participants genuinely seem to be enjoying themselves, and that they might even be quite keen on sleeping with each other. Furthermore, for all the shouting and screaming of contemporary porn, it's rare to see a woman smile, or laugh: vintage pornography abounds in sweet expressions and moments of shared affection. The polymorphous perversity of the actors reminds us that sex can be both witty, but also that it's not a competition - many of the short films from the early twentieth century involve the inability of men to achieve erection and the increasingly comical attempts of their remarkably understanding lovers to try to amend the situation.

The humanist promise of early cinema seems to have been betrayed by a combination of artificial and destructive antagonisms between men and women and unnecessary anxieties about 'performance' and desirability. One of the most interesting things about so-called 'vintage erotica', for all its indifference to the well-timed cut, its wasteful expenditure in the pursuit of female pleasure, and so on is the presence of the 'money shot' of course, this term too is now rather coy - we mean cum shot surely.

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It is initially surprising - the money shot seems like it should have been a recent invention, something suited to a more hyper-real, obsessively graphic age" but there it is, all over the s, as if the logic of the tension between make-believe and au thenticity has already been encoded for the big porn Other. The money shot has always been about different kinds of ' money', however. It's not clear whether the mainstream meaning of 'money shot' literally, the most expensive scene in the film got transplanted to porn or vice versa: the money shot these days is just as likely to be the action hero's virile escape from a terrorist-induced explosion as a guy trying his best to 'put 53 One-Dimensional Woman out'.

But the porn meaning is complex: is i t the point at which the guy completes his 'product' and thus makes the thing he gets paid for, in a base capitalist form? And we should bear in mind that porn is one of the only industries in which men usually get paid less than women.

Or is i t, instead, the point at which the audience 'get their money's worth? Of course not - just like any other woman, the porn actress cou ld be faking it. But there is no way of measuring her pleasure, of course, even though vintage porn does its best to assure us that female jouissance has its own place. Even money can sometimes get cheaper. One of the things about early 20th-century erotic photography, on the other hand, is its lack of taxonomy.

Contemporary pornography has more c. You could be into women who look like cats who specialize in shaving biscuits whilst bouncing up and down on trampolines, and there'd probably be a website 54 3. The excessive taxonomical drive of contemporary pornography is merely one element of its quest to bore us all to death and remind us that everything is merely a form of work, including, or even most especially, pleasure.

Women sit alone in houses filled with consumer goods, popping out only to purchase the biggest vibrator they can find. Occasionally they might flick through a book, or more likely, a magazine, but it never distracts them for long. Unlike the comedic role-play of twenties and thirties porn, or the frenetic war-apocalypse porn of the s, Fifties European porn looks like a cross between a Godard film in which women hang around looking a bit bored most of them surely are and a rape fantasy.

In a final, psychotic twist, one of the short s films, 'The Demon of Boredom', involves a listless housewife inviting over the sex-shop owner who has just sold her a vibrator. Once at her place, she spikes his aperitif and orally rapes him with the same dildo while he sits unconscious in her chair.

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The toy is both bizarrely emancipatory and shockingly aliena ting. Chances are that even the most adamant defender of the charms of adult material would struggle to find much evidence of compassion or affection in today's relentlessly lurid output. Contemporary pornography informs us of one thing above all else: sex is a type of work, just like any other. What matters most is quantity - the bigger the better. It is not for nothing that one of the most successful sex videos of all time, starring Annabel Chong, features sex acts performed with approximately 70 men during a ten hour period.

Contemporary pornography is realistic only in the sense that it 55 One-Dimensional Woman sel ls back to us the very worst of our aspirations: domination, competition, greed and brutality. I t makes more money than Hollywood and all major league sports put together. Almost any genre and type of sexual taste i s catered for, just s o long as you aren't looking for anything as recherche as sweetness or wit.

On one level, we might say, so what? Pornography serves a certain practical purpose, why expect anything more from i t? I f you want romance, g o and read M i l ls and Boon! But what if there was another history of porn, one that was fi l led less with pneumatic shaven bodies pummeling each other into submission than with sweetness, silliness and bodies that didn't always function and purr like a well-oiled machine?

The early origins of cinematic pornography tell a very different story about the representation of sex, one that suggests a way both out of the rubberized inhumanity of today's hardcore obsession, but also out of the claim that pornography is inherently exploitative. But pornography alone tells us nothing unless we accept Angela Carter's argument that there is an intimate link between sexual relations and social relations. Despite the claim that ' there is no such thing as too much fun', plastered all over the dirty Teflon of the reopened Millennium Dome, we must sadly come to terms with the fact that we live in a world in which enjoyment has been profoundly circumscribed.

Don't be misled: The imperative to 'Enjoy! We can have as many vibrators as we like, and drink as much booze as we can physically tolerate, but anything else outside the echo chamber of money-possessions-pleasure is strictly verboten. Communes, you say!

Alternative models of the family! Guinea, G. Montambaux, A. Castro Neto. B 79 , B 77 , Pierre Delplace, 22 octobre Delplace and G. B 82, B 82 , B 80 , Texier , P. B 80, Goerbig, J. Fuchs, G. Mallet, F. Schopfer , J. Ericsson, L. Saminadayar , C. Mailly , C. Texier and G. Takayanagi , J. Nitta and H. Nakano eds. Avishai and G. Montambaux, and F.

Ferrier, A. Rowe, S. Bouchiat, C. Fiebig , C. Aegerter , W. Akkermans, G. Montambaux and G. Maret ,. Akkermans and G. Cambridge University Press, April Cayssol and G. JMMM , 94 Mueller, C. Miniatura, E. Akkermans et G. Montambaux, J. A 38 , B 72 , Montambaux, "Quantum information and decoherence in nanosystems", D. Glattli, M. Sanquer and J. Rencontres de Moriond, The Gioi publishers, Montambaux, Phys.

Montambaux and A. Akkermans, "Nanotubes: Science and Applications ", Eds. Loiseau, P. Launois, P. Petit, S. Roche, J. Salvetat Springer Verlag-Frontiers in Physics, Montambaux , J. B 21, Montambaux, "Wave scattering in complex media: From theory to applications", B. Van Tiggelen et S. Skipetrov eds, vol.

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Bjelis, D. Zanchi and G. Montambaux J. The subsequent discovery of new carbon allotropes, showing stable structures either in 0D fullerenes , 1D carbon nanotubes and 2D graphene consolidated this scenario in an exciting research field [ 4 ]. The isolation of strictly one atom thick layers in the first years of the present century opened a wider window for both basic physics and device applications [ 5 ]. These new disruptive research efforts, initially impulsed by graphene, are nowadays detaching from carbon-based roadmaps, as also envisaged, at the beginning of the graphene boost, by Novoselov, Geim and co-workers [ 6 ].

A very recent 2D atomic crystal of black phosphorous [ 7 — 10 ], namely phosphorene, is a promising system in which 2D properties together with strictly 1D chain behavior are present in different energy windows. This allows the same device to be tuned from a 1D to a 2D system by simply tuning the Fermi energy.

In the present work we focus on the 1D energy window, created by an effective doubly degenerate band in the relevant energy scale associated to states strongly localized at the zigzag edges [ 11 — 12 ] of phosphorene nanoribbons, whose properties are explored using a new strictly one-dimensional resonant tunnelling device. The double-barrier resonant tunnelling device [ 1 , 13 — 14 ], conceived here as an atomically precise segmentation at one of the edges, shows unusual geometry, since the direction of the barriers is perpendicular to the well and contact regions [ 15 — 16 ].

Among our findings we show that for a thin barrier case constriction with narrow step from the upper zigzag edge , the resonant tunnelling permits a spectroscopy of the band structure of phosphorene nanoribbons in this energy window. Furthermore, progressive widening of the barriers enhancing the step width of the constriction , thus nearing the constriction to the other edge leads to edge-coupling effects featuring resonances with Fano line shapes [ 17 — 19 ]. For this latter coupled-edge system, the transmission probability characteristics turn out to present clear features of both i the actual finite confining segment coupled to an infinite not segmented edge and, ii the properties of an infinite narrow nanoribbon with strongly coupled edges.

These results are independent of the area of the device region. They solely depend on the length of the segmented region and distance between the edges, revealing an effective chain-like behavior of the edges of the nanoribbons. We present the model calculation framework, as well as the effects of edge coupling on the conductance of these infinite zigzag ribbons, which are essential to understand the resonant tunnelling spectra.

Next, the geometry of the actual investigated segmented device is presented, introducing the resonant tunnelling effects. Subsequently, the core of the results is devoted to explore the resonant tunnelling behavior of the segmented-edge device, showing how the defects on the edge may actually enrich the scenario instead of solely washing out the announced effects. This provides further evidence that the phenomenon is restricted to the atoms at the very edge.

Finally, the conclusion suggest a bridge between the present 1D systems embedded in a 2D crystal and ongoing research on isolated atomic chains. The essential atomistic aspects of the structures investigated are depicted in Fig. The tight-binding hopping parameters considered, as discussed below, are indicated in Fig. The quite complex electronic structure of phosphorene, already at energy ranges rather close to the Fermi energy, hinders a wider use of single-orbital tight-binding models in chasing the alluded electronic and transport properties of systems based on this new material.

Nevertheless, the use of such model is well validated, by means of comparisons with first-principle electronic structure calculations [ 20 — 21 ], for the very energy window of interest around the gap, namely a double central band. This central band for zigzag phosphorene nanoribbons has been predicted for phosphorene [ 11 — 12 ] and is absent in graphene.

We use here the same tight-binding parametrization for phosphorene proposed by Rudenko [ 20 ] considering a Hamiltonian , where c i is the creation annihilation electronic operator at site i and t ij is the hopping integral between sites i and j. Other electronic properties such as the local density of states LDOS are also calculated. The electronic and transport properties of a host zizgzag nanoribbon, in which a finite segment will be latter tailored in, are also summarized in Fig.

The inset in Fig. These central bands present cosine-like dispersions characteristic for 1D systems [ 11 ]. Hence, this width will be chosen for the host ribbon where the constriction will be introduced. The effect of edges coupling with the band structure can be followed in the main part of Fig. Indeed an incipient overlap of wave functions in this situation is illustrated in Fig.

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The consequences of the edge coupling on the transmission probabilities along the edges are qualitatively significant as can be seen in Fig. This condition, evidenced by the electronic band structure discussed in the previous section raises the question of a means to observe experimentally those effective one-dimensional chains embedded in the rather complex phosphorene crystalline structure.

In order to test our hypothesis we propose the segmented nanoribbon structure constriction illustrated in Fig. The segment of a thinner region of the nanoribbon of width m Z , the number of zigzag chains, is defined by a length L in units of atoms removed along one zigzag direction. Transmission plateaus above and below the edge states band are shown, for the sake of completeness, since these structures are of entirely different character than the resonances in the central band we will be focusing on. These transmission plateaus are due to the lateral confinement in a nanoribbon.

These effects are already well known for graphene and square lattice nanoribbons with constrictions [ 25 — 29 ]. The edge states, observed here in the energy range from 0. Red and green correspond to the cases in Fig. When m Z is further diminished, the barriers to the upper-edge contacts become too large, but now the coupling to the lower edge becomes relevant. It should be recalled here that only for extremely thin nanoribbons the strong coupling between the edges widens the central band. In our constriction the role of both channels discrete states and continuum at the upper and lower edges can be made explicit by picturing the local density of states LDOS in Fig.

In Fig. The confined state at the constriction in the upper edge clearly stands out. It should be noted that this LDOS is slightly asymmetric, since the structure with L equal to an even number of atoms is asymmetric see Fig. The LDOS along the upper edge outside the constriction region is less intense in the figure scale, due to the prominence of the confined state. Far from a resonance, actually between two resonances, is the situation pointed out by arrow 2 in Fig.

The LDOS in the confined part of the upper edge is strongly suppressed, enhancing the contribution along the entire lower edge and the upper-edge contact sections i. A quite different situation is depicted in Fig. LDOS at the energies pointed out by the arrows, labeled 1, 2, 3 and 4, in Fig. This indicates that the transmission shows a spectroscopy of the 1D states at the edge of the constriction.

Indeed, increasing the length of the constriction will increase at the same proportion the number of the resonances not shown here. The fact that the resonances are insensible to the constriction width hence the area for a fixed length is a further indication that we are dealing with a strictly 1D effect at the edges. Albeit there is the underlying 2D crystal, the behavior revealed here is the one of an effective atomic chain. Here we should note that the only signature of the underlying 2D crystal is given by the resonances widths.

Recalling Fig.

Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems Physics of Zero- and One-Dimensional Nanoscopic Systems
Physics of Zero- and One-Dimensional Nanoscopic Systems

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