Possible absence of quasiparticles in a nanowire of a foreign metal

2023-12-14 15:33:37

Foreign metals are materials in which the resistivity depends linearly on temperature (ρ ∼ T); unlike “good” metals in which it depends parabolicly (ρ ∼ T²). Superconducting iron cuprates and punctures are foreign metals above their critical temperature (T > Tc). Is the electric current in foreign metals mediated by quasiparticles? An article in Science concludes that this is not the case, thanks to the study of shot noise (shot noise) on a nanowire of a foreign metal (YbRh₂Si₂). Specifically, a Fano factor F < 0.12 is observed for temperatures between 3 and 10 K. This value must be compared with F = 1/3 ≈ 0.33, which is observed for a gold nanowire of the same length; This value coincides with the theoretical prediction for the conductivity mediated by free electron-like quasiparticles in a nanowire with length L Lee (whose length is less than the typical length of electron-electron collisions; by the way, for L > Lee it is predicted that F = √3 / 4 ≈ 0.43, a value that has been observed with millimeter-sized gold nanowires). If the conductivity in foreign metals is not mediated by quasiparticles, what phenomenon is responsible? It is not known; There are many speculations, among them, that they are Planckian materials described by a holographic theory inspired by AdS/CFT duality.

The article is led by Douglas Natelson (Rice University, Houston, Texas), author of the famous blog Nanoscale Views. As a good experimental physicist, he does not favor any theoretical explanation for his observations. Electronic noise in a material has three components: thermal noise (Johnson–Nyquist noise), shot noise (shot noise) and 1/f noise (flicker noise). 1/f noise is pink noise (its spectrum is not flat), unlike thermal and shot noise, which are white noise (its spectrum is flat). The noise term (Johnson–Nyquist) dominates in a nanowire with a length L > Lph (greater than the typical length of electron-phonon interactions). For L < Lph is expected to dominate the shot noise SI = 〈(I − 〈I〉)²〉, the dispersion about the mean for electric current (its units are A²/Hz, amperes squared per hertz); was estimated by Schottky as SI = 2 e 〈I〉 and the Fano factor is defined as F = SI /(2 e 〈I〉), such that Schottky’s law corresponds to F = 1. In the new article, F < 0.1 has been obtained, a strong suppression of shot noise; could be interpreted as due to phonons if L > Lph, but it is interpreted as the absence of quasiparticles in the foreign metal nanowire, since it has been designed so that L < Lyes.

A suppression of shot noise has been observed, which is ruled out as being associated with the interaction between electrons and phonons. It is interpreted as a result of the absence of quasiparticles, something supported by a theoretical article in Physical Review Research which estimates the Fano factor F = 1/6 (compatible with the observations of Natelson et al.) for a foreign metal without quasiparticles. However, there could be other explanations for this suppression of shot noise, such as the appearance of bosonic states that interact with the quasiparticles in a similar way to phonons, as proposed in another theoretical article on arXiv. We will have to wait for a consensus to be reached in the community on how to interpret this new and very interesting result published in Science. Perhaps in the coming years the secret of rare metals will be revealed and, we can also dream, perhaps it will help to reveal the secret of high-temperature superconductivity. The new article is Liyang Chen, Dale T. Lowder, …, Douglas Natelson, “Shot noise in a strange metal,” Science 382: 907-911 (23 Nov 2023), doi: https://doi.org/10.1126/science.abq6100, arXiv:2206.00673 [cond-mat.str-el] (01 Jun 2022). The new theoretical article in favor of the absence of quasiparticles is Alexander Nikolaenko, Subir Sachdev, Aavishkar A. Patel, “Theory of shot noise in strange metals,” Phys. Rev. Research 5: 043143 (13 Nov 2023), doi: https://doi.org/10.1103/PhysRevResearch.5.043143y en contra es Suppression of Tsz Chun Wu, Matthew S. Foster, «Shot Noise in a Dirty Marginal Fermi Liquid,» arXiv:2312.03071 [cond-mat.str-el] (05 Dec 2023), two: https://doi.org/10.48550/arXiv.2312.03071.

Más información divulgativa en Charlie Wood, «Meet Strange Metals: Where Electricity May Flow Without Electrons. For 50 years, physicists have understood current as a flow of charged particles. But a new experiment has found that in at least one strange material, this understanding falls apart,» Quanta Magazine, 27 Nov 2023. And, of course, on Douglas Natelson’s blog, “Noise in a strange metal—pushing techniques into new systems,” nanoscale views, 27 Nov 2023.

A quasiparticle (electronic) is a wave of electrons, similar to the Mexican wave in a football stadium. The electrical conductivity of a material is due to the propagation of “electron” type and “hole” type quasiparticles. The electrical resistivity ρ is the ratio between the electric field E and the current density J (ρ = E/J). A metal is a material whose resistivity decreases as the temperature decreases (dρ/dT > 0); In a semiconductor the opposite occurs (dρ/dT < 0). At low temperature, a "good" metal behaves like an "electron" gas (called a Fermi liquid) and its resistivity is dominated by electron-electron scattering (or collisions); Since the number of excited electronic states depends on the temperature, the resistivity will depend on the square of the temperature ρ ∼ T². A good conductor whose resistivity ρ(T) has another dependence is called a “bad” metal. Specifically, a foreign metal is called a metal that has a resistivity that depends linearly on temperature, ρ ∼ T. The figure shows that the resistivity of a nanowire of a heavy fermion metal (YbRh2Si2, ytterbium-diruthenium-disilicon ) 60 nm thick, 660 nm long and 240 nm wide. Between 3 and 10 K temperature it is observed that the resistance is linear, as expected for a foreign metal.

Many materials whose resistivity shows a phase transition associated with a critical quantum dot (CQP) at a certain critical temperature Tc behave like foreign metals for T > Tc; especially when for T < Tc se observa un comportamiento antiferromagnético próximo. Por ejemplo, los superconductores de alta temperatura (cupratos y pnicturos de hierro), el grafeno bicapa rotado con ángulo mágico, los metales con fermiones pesados, etc., se comportan como metales extraños para T > Tc. The origin of the conductivity of foreign metals is not known, nor even if it is mediated by electronic quasiparticles (“electrons” and “holes”). How can you know if it is associated with quasiparticles or other types of electronic states? One option is to look for signals predicted by theories without quasiparticles; Unfortunately, for now these are signs that are impossible to observe. The other option is to look for the absence of phenomena associated with the existence of quasiparticles. The new article studies the so-called shot noise, due to quasiparticles.

Random fluctuations in current or voltage in a conductive material are called electronic noise. For example, for the current intensity I, the noise is characterized by its dispersion 〈(I − 〈I〉)²〉, around the average value of the current 〈I〉, where the average refers to the temporal evolution; It is usually characterized by its spectrum, the noise as a function of the frequency of the current, with units A²/Hz (ampere squared per hertz). This figure from the article shows the noise for the voltage 〈(V − 〈V〉)²〉, with units of V²/Hz (volt squared per hertz), as a function of current; The average noise level is flat, constant for all frequencies, which is called white noise. At low temperature, in a metal, electronic noise is usually separated into three types: thermal noise (Johnson–Nyquist noise), shot noise (shot noise) and 1/f noise (flicker noise). 1/f noise is pink noise (its spectrum is not flat), unlike thermal and shot noise which are white noise (its spectrum is flat).

The Johnson–Nyquist noise is associated with the thermal fluctuations of the “electrons” in a state of equilibrium in the Fermi liquid; These equilibrium fluctuations depend on the energy dissipated, that is, on the resistance in a conductor. Thus this thermal noise for voltage is SV = 4 kBT R measured in V²/Hz, and for current it is SI = 4 kB T/R measured in A²/Hz, where kB is the Boltzmann constant. Shot noise is associated with the out-of-equilibrium behavior of quasiparticles (both “electrons” and “holes”), that is, it is associated with charge transport due to the discrete nature of the carriers. Schottky used a Poisson distribution for the “electrons” (assumed to be independent of each other) which allowed him to derive a mathematical expression for the shot noise: SI = 〈(I − 〈I〉)²〉 = 2 e 〈I〉 measured in A²/Hz.

The Schottky formula for the shot noise of a real metal includes a correction factor, SI = 2 F e 〈I〉, called the Fano factor (F). This factor is usually interpreted as the “effective load” of the carriers; For example, in a superconductor where the carriers are Cooper pairs (paired electrons) we have F = 2. The calculation of the Fano factor in a nanowire of length L depends on its relationship to the typical electron-electron scattering length Lee and that of electron-phonon dispersion Lph (phonons are the vibrations of the crystal lattice). In the case of L Lyes Lph, the “electrons” behave like a gas of free particles, calculating F = 1/3 ≈ 0.33. When Lyes L < Lph, the “electrons” collide with each other before interacting with the phonons, so F = √3 / 4 ≈ 0.43.

The new article has estimated the Fano factor in a nanowire of a heavy fermion metal (YbRh2Si2, ytterbium-diruthenium-disilicon). The most complicated part of the experiment has been synthesizing the 60 nm thick, 660 nm long, and 240 nm wide nanowire (I will not discuss the details of the synthesis, perhaps the most relevant for those who want to reproduce this research). According to the authors, this nanowire is in the regime L < Lph and also behaves like a foreign metal with ρ(T) = ρ0 + A Tα, with α ≈ 1 for a temperature between 3 and 10 K (kelvin). This temperature range is small, so the linearity of the resistivity could be an artifact, since between 3 and 100 K a curvature of the resistivity similar to that of a “good” metal is observed; This issue will have to be elucidated by independent investigations.

As shown in the figure that opens this piece, a Fano factor F < 0.12 has been obtained, which is interpreted as meaning that conduction in this material is not mediated by quasiparticles. The value obtained is compatible with the recent theoretical prediction (F = 1/6) based on computer simulations of a SYK (Sachdev–Ye–Kitaev) model. However, the suppression of shot noise could originate from disorder in a Fermi liquid in which free quasiparticles interact with bound quasiparticles in bosonic states. I like this last model less when interpreting the results of Natelson et al., but we will have to wait for the community's opinion. Without a doubt, we are living in exciting times in the field of rare metals.