Quantum Flutter: A Dance of an Impurity and a Hole in a Quantum Wire

[Clockwise from Top left]: Charles J. M. Mathy, Eugene Demler, Mikhail B. Zvonarev.

Authors: 
Charles J. M. Mathy^1,2, Mikhail B. Zvonarev^2,3,4, Eugene Demler²

Affiliation:
¹ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts, USA
³Université Paris-Sud, Laboratoire LPTMS, UMR8626, Orsay, France,
⁴CNRS, Orsay, France.

What happens when a particle moves through a medium at a velocity comparable to the speed of sound? The consequences lie at the heart of several striking phenomena in physics. In aerodynamics, for example, an object experiencing winds close to the speed of sound may experience a vibration that grows with time called flutter, which can ultimately have dramatic consequences such as the destruction of aeroplane wings or the iconic Tacoma Narrows bridge collapse. Other examples of physics induced by fast motion include acoustic shock waves and Cerenkov radiation. What we addressed in our work [1] was the effect of fast disturbances in strongly interacting quantum systems of many particles, in a case where the particles are effectively restricted to move in one dimension known as a quantum wire.

When the interactions between particles are weak, quantum systems can sometimes be described by a simple hydrodynamic equation. For example, the Gross-Pitaevskii Equation (GPE) describes the evolution of a weakly coupled gas of bosons at low temperatures when it forms a Bose-Einstein condensate. The GPE is analogous to equations found in hydrodynamics, which explains why one can see analogs of classical hydrodynamical effects such as shock waves and solitons in these systems [2,3]. But what if the interactions are too strong and such an approximation breaks down?

We have found a model that shows interesting physics induced by supersonic motion which goes beyond a hydrodynamical description [1]. The system is a one-dimensional gas of hardcore bosons known as a Tonks-Girardeau gas (TG) [4]. We start the system in its ground state and inject a supersonic impurity that interacts repulsively with the background particles. We obtained exact results on what happens next using an approach from mathematical physics called the Bethe Ansatz approach, coupled with large-scale computing resources [5]. Thus we track the impurity velocity as a function of time and find two main surprising features. Firstly, the impurity does not come to a complete stop, instead it only sheds part of its momentum and keeps on propagating at a reduced velocity forever (Fig 1a). Secondly, the impurity velocity oscillates a function of time, a phenomenon we call quantum flutter as it arises from nonlinear interactions of a fast particle with its environment (see Fig. 1b).

Figure 1: Impurity momentum evolution and quantum flutter:
a, Schematic picture of our setup. Top: We start with a one-dimensional gas of hardcore bosons of mass m known as a Tonks Girardeau (TG) gas (red arrows), in its ground state. We then inject an impurity also of mass m with finite momentum Q (green arrow). Middle: The impurity loses part of its momentum by creating a hole around itself (sphere) and emitting a sound wave in the background gas (blue arrow). However it retains a finite momentum Q_sat after this process and carries on propagating without dissipation. Bottom: legend of the different characters in the story.
b, Time evolution of the expected momentum of the impurity, <P̂_↓(t)>. The momentum decays to a finite value Q_sat, and shows oscillations around Q_sat at a frequency we call ω_osc. The background gas has density ρ_↑, and we define a Fermi momentum k_F = πρ_↑, a Fermi energy E_F = k_F²/(2m) where m is the mass of the particles, and a Fermi time t_F = 1/E_F. Inset: zoom into the plot of <P̂_↓(t)> showing the oscillations we call quantum flutter.
c, Time evolution of the density of the background gas in the impurity frame. More precisely, shown is the density-density correlation function G_↓↑(x,t) = <ρ_↓(0,t) ρ_↑(x,t)> in units of ρ_↑/L where L is the system size, and the position along the wire is written in units of the interparticle distance ρ_↑^-1 in the background gas. Here ρ_↑ is the density of the background gas, and ρ_↓ the density of the impurity. G_↓↑(x,t) is effectively the density of the background gas with respect to the impurity position. We see the formation of the correlation hole around x ρ_↑ = 0 (blue valley), and the emission of the sound wave (red ridge). Underneath a schematic illustration of the dynamics is given: the blue arrow represents the emitted sound wave, the sphere is the hole, and the green arrow the impurity (see a). Inside the correlation hole the impurity and hole are dancing, meaning that they are oscillating with respect to each other, the phenomenon we denote as quantum flutter.

Using the exact methods just mentioned we were able to look in detail at the dynamical processes underlying quantum flutter. The time evolution of the impurity in the gas of bosons can be broken down into several steps. First the impurity carves out a depletion of the gas around itself, called a correlation hole. It expels the background density into a sound wave that carries away a large part of the momentum of the impurity, but not of all it (fig 1c). In fact the impurity retains part of its momentum and no longer sheds momentum because of kinematic constraints: there are no sound waves it can emit in the background gas while conserving momentum and energy.

After formation of the correlation hole, the impurity momentum starts to oscillate. When the dynamics of a quantum system shows a feature that is periodic in time, typically the frequency of the feature corresponds to an energy difference between two states of the system. Examples include light emission of an atom, or spin precession in response to a magnetic field, which underlies Nuclear Magnetic Resonance. In our case, the two states are an exciton and a polaron. The exciton corresponds to the impurity binding to a hole, since if the impurity repels the background gas, it is attracted to a hole (i.e. a missing particle in the background). The polaron is an impurity dressed due to interactions with the background particles, which affects its properties such as its effective mass: it becomes heavier as it carries a cloud of displaced background particles around it [6]. Thus we arrive at the following picture, as shown schematically in Fig. 2: first the impurity causes the emission of a sound wave in the background gas and creation of a hole close to it. It can bind to this hole and form an exciton, or not bind to it and form a polaron instead. In fact the impurity does both in the sense that it forms a quantum superposition of a polaron and an exciton. This quantum superposition leads to oscillations in the impurity velocity, a phenomenon called quantum beating, which is analogous to Larmor precession of a spin in a magnetic field. The difference here is that the two states that are beating, the exciton and polaron, are strongly entangled many-particle states. That we observe long-lived quantum coherence effects in a system composed of infinitely many particles is surprising. Namely, typically such systems exhibit decoherence, such that if one puts a particle in a quantum superposition of two states, the superposition decays because of interactions with other particles.

Figure 2: Origin of quantum flutter:
a, The quantum flutter oscillations originate from the formation of a superposition of entangled states of the impurity with its environment. After the impurity is injected in the system is creates a hole around itself. It can then bind to this hole and form an exciton, or not bind to it and form a state that is dressed with its environment called a polaron. In fact the system forms a coherent superposition of these two possibilities, which then leads a quantum beating and oscillations in the impurity momentum with a frequency given by the energy difference between these two possibilities.
b, Comparison between the frequency ω_osc of oscillations in the impurity momentum, and the energy difference between the polaron E(Pol(0)) and the exciton E(Exc(0)) (the zero between brackets refers to the exciton and polaron having momentum zero). The x-axis denotes the interaction strength between the impurity and the background particles: the interaction between a background particle at position x_i and the impurity at position x_↓ is a contact interaction of the form g δ(x_i - x_↓), and one defines the dimensionless interaction parameter γ = m g/ρ_↑. ℏω_osc and E(Pol(0))-E(Exc(0)) are in quantitative agreement, which motivates the interpretation of quantum flutter as quantum beating between exciton and polaron.

To see quantum flutter in the laboratory directly, one can use methods from the field of ultracold atoms, in which neutral atoms are cooled and trapped using a combination of lasers and magnetic fields. The trapping potential can be chosen to restrict the atoms to move along 1D tubes, and effectively behave like a TG gas [7,8]. The interaction between the particles can be tuned using a Feshbach resonance. Impurity physics in one-dimensional TG gases has already been studied [9,10,11]. The only added ingredient needed for quantum flutter is to create impurities at finite velocities, which can be done using two-photon Raman processes. Quantum flutter can be observed by measuring the expected impurity velocity as a function of time. Thus cold atom experiments could confirm our predictions, and one could vary different parameters of the model so see how robust quantum flutter is. Our preliminary calculations suggest that quantum flutter survives within a certain window of varying all the parameters in the theory such as the interaction between background particles, the relative mass of the impurity and the background particles, and the form of the interactions.

In summary, we have found an example of a system of many particles where injecting a supersonic impurity leads to the spontaneous formation of a long-lived quantum superposition state which travels through the system at a finite velocity. The question of which systems allow transport of quantum coherent states is important for quantum computing applications [12], and has surfaced in recent studies of quantum effects in biology [13]. Thanks to the advent of exact methods and the development of precise experiments in the study of many-particle quantum dynamics, we expect to see progress being made on this question in the near future.

References
[1] Charles J. M. Mathy, Mikhail B. Zvonarev, Eugene Demler. "Quantum flutter of supersonic particles in one-dimensional quantum liquids". Nature Physics, 8, 881 (2012). Abstract.
[2] A.M. Kamchatnov and L.P. Pitaevskii. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 100, 160402 (2008). Abstract.
[3] I. Carusotto, S.X. Hu, L.A. Collins, and A. Smerzi. "Stabilization of solitons generated by a supersonic flow of a bose-einstein condensate past an obstacle". Physical Review Letters, 97, 260403 (2006). Abstract.
[4] M. Girardeau. "Relationship between systems of impenetrable bosons and fermions in one dimension". Journal of Mathematical Physics, 1, 516 (1960). Abstract.
[5] Jean-Sébastien Caux. "Correlation functions of integrable models: a description of the abacus algorithm". Journal of Mathematical Physics, 50, 095214 (2009). Abstract.
[6] A.S. Alexandrov, S. Devreeze, and T. Jozef. "Advances in Polaron Physics". Springer Series in Solid-State Sciences, Vol. 159 (2010).
[7]  Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "A quantum newton's cradle". Nature, 440, 900 (2006). Abstract.
[8] Toshiya Kinoshita, Trevor Wenger and David S. Weiss. "Observation of a one-dimensional tonks-girardeau gas". Science, 305, 1125 (2004). Abstract.
[9] Stefan Palzer, Christoph Zipkes, Carlo Sias, Michael Köhl. "Quantum transport through a tonks-girardeau gas". Physical Review Letters, 103, 150601 (2009). Abstract.
[10] P. Wicke, S. Whitlock, and N.J. van Druten. "Controlling spin motion and interactions in a one-dimensional bose gas". ArXiv:1010.4545 [cond-mat.quant-gas] (2010).
[11] J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi. "Quantum dynamics of impurities in a one-dimensional bose gas". Physical Review A, 85, 023623 (2012). Abstract.
[12] D.V. Averin, B. Ruggiero, and P. Silvestrini. "Macroscopic Quantum Coherence and Quantum Computing". Plenum Publishers, New York (2000).
[13] Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomá Manal, Yuan-Chung Cheng, Robert E. Blankenship, Graham R. Fleming. "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems". Nature, 446, 782 (2007). Abstract.

Surmounting The Great Silica Integration Problem

The Team [From Left to Right]: 
Masood Naqshbandi, John Canning, Brant Gibson, Melissa Nash, Maxwell Crossley

Authors: John Canning¹, Brant Gibson²

Affiliation:
¹interdisciplinary Photonics Laboratory (iPL), School of Chemistry, The University of Sydney, Australia,
²School of Physics, The University of Melbourne, Australia

The global interconnectedness we all share today, primarily via the optical internet, comes from one material: silica. It makes up the global web that carries communication to most corners containing bipeds. Only silica, with a sprinkling of germanium and a few trace dopants, has offered both an extraordinary toughness, chemical inertness and a super-extraordinary transparency that enables this to happen, aided by silicate-based amplifiers lightly doped with erbium to kick these signals along. So it’s no wonder a Nobel Prize was awarded to acknowledge this impact, literally the backbone of the Glass Age [1]. And its existence continues to fire the imagination and yearning for something even greater – an intelligent web that can emulate a living organism with sensors along its paths providing data on the environment and a distributed intelligence analysing, sifting and even making decisions based on this data [2].

These sensors promise to span remote intelligent energy monitoring, machinery control, remote telemedicine and teaching and more. But in order to do this it has become clear that the very properties that enabled the global village – robustness, stability and reliability – are the same that limits the transformation of the optical web from a passive transport medium to an active, dynamic intelligent network. For this, silica must have added functionality at least in places along the grid. For the time being, all solutions explore externalisation onto alternative material platforms, the majority of which are simply incompatible making integration with the web one of the most prolific research areas across all disciplines.

This begs the question: why cannot silica be functionalised? The answer comes down to simple thermodynamics involved with the traditional chemical bond – silica processing involves extraordinarily high temperatures: 1900 °C plus before it can be melted and drawn into fibre. Very little material can survive these conditions – some of the rare earths are fortunately, enabling critical amplification to exist; but organic or carbon systems, which increasingly underpin sensors and new technologies such as diamond based photonics [3], are not.

At the interdisciplinary Photonics Laboratories at The University of Sydney, Australia, we believe we have come up with a solution: using nanoparticles held together by intermolecular forces [4]. Unlike chemical bonds, intermolecular forces are universal with most cases being attractive at the same temperature, namely 25 °C. To exploit and demonstrate the potential of this approach, we take a novel fabrication avenue that nearly everyone has some experience with, albeit often without realising it – evaporative self-assembly.

Figure 1: A batch of self-assembled wires approximately 10 μm by 5 cm long fabricated from 20 nm silica nanoparticles on a glass substrate. An aspect ratio > 50 000 is easily demonstrated.

Watching a coffee drop evaporate [5] can be like sticking needles into one’s eyes but if you watch carefully enough you’ll see a relatively wonderful example of physics in action – convective flow directing particles to the outer rim so that the brown spot becomes clear in the middle. When intermolecular forces are thrown in by replacing the coffee with silica nanoparticles, packing constraints take place and the steadily shrinking drop experiences very high radial stresses – cracks form, and after a couple of bifurcations, uniform cracking is obtained to produce silica wires (Figure 1). In further work, by controlling the evaporation conditions using laser processing, a very high degree of directionality is possible improving uniformity of wires and more [6]. Intermolecular forces are often seen as weak and at the molecular level this is often the case – but unlike the chemical bond they are additive so the more of it there is the stronger a material.

Since these forces are universal and operate at room temperature – this means we can mix in almost anything and have done so using organic dyes to dope the wires during their fabrication. Importantly, in collaboration with the School of Physics at the University of Melbourne, mixed nano-particle self-assembly has allowed a wire to be fabricated containing nanodiamonds. Some of these nanodiamonds themselves have nitrogen vacancy defect sites which emit single photons (Figure 2). With little blinking observed and good thermal stability, diamond is one of the most ideally suited material systems for single photon generation. We have now been able to integrate this into silica itself, clearly demonstrating the potential of our approach for enabling the tools for quantum techniques into the global web.

Figure 2. (a) A scanning confocal map of the photoluminescence from nitrogen-vacancy (NV) defect centres within the nanodiamond-embedded silica microwire sample (image is taken from the top surface of the microwire; scale bar corresponds to 10 μm). (b) Single photon emission detected from the particle shown in the zoomed region of (a) where the scale bar corresponds to 2 μm. The inset shows the photostable emission from the single emitter.

The silica nanoparticle platform, held together by intermolecular forces, allows total integration of new materials into existing silica communications and sensor networks. This hybrid material has the potential to open up a vast field for compositional control of other organic, inorganic and biological molecules and species within silica waveguides (or any other nanoparticle platform) for applications in opto-electronics (for example, graphite), photovoltaics (for example, customised porphyrins and metals), plasmonics and metamaterials (for example, metals) and novel optical circuitry (for example, magnetic materials).

References:
[1] 2009 Nobel Prize in Physics, Charles Kao. Link to Nobel Prize 2009.
[2] J. Canning, “Optical sensing: the last frontier for enabling intelligence in our wired up world and beyond”, Photonic Sensors, SpringerOpen, 2 (3), 193-202, (2012). Abstract.
[3] Mark P. Hiscocks, Kumaravelu Ganesan, Brant C. Gibson, Shane T. Huntington, François Ladouceur, and Steven Prawer, “Diamond waveguides fabricated by reactive ion etching”, Optics Express, 16, 19512-19519 (2008). Abstract.
[4] Masood Naqshbandi, John Canning, Brant C. Gibson, Melissa M. Nash & Maxwell J. Crossley, “Room temperature self-assembly of mixed nanoparticles into photonic structures”, Nature Communications, 3, 1188 (2012). Abstract.
[5] Robert D. Deegan, Olgica Bakajin, Todd F. Dupont, Greb Huber, Sidney R. Nagel and Thomas A. Witten, “Capillary flow as the cause of ring stain from dried liquid drops”, Nature 389, 827–829 (1997). Abstract.
[6] J. Canning, H. Weil, M. Naqshbandi, K. Cook, and M. Lancry, “Laser tailoring surface interactions, contact angles, drop topologies and the self-assembly of optical microwires”, To appear in Opt. Mat. Express (2013).

Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.