arXiv subjects

F. Marsiglio

Publications and source records attributed to F. Marsiglio.

At least 37 records · Page 2Linked to original sources

arXiv2021

Intrinsic hysteresis in the presumed superconducting transition of hydrides under high pressure

Superconducting transitions in the absence of magnetic field should be non-hysteretic. Here we address the fact that the drops in electrical resistance that have been interpreted as evidence of superconductivity in several hydrides under high pressure (so-called "superhydrides") show hysteresis. We argue that the experimental evidence shows that the observed hysteresis cannot be attributed to experimental artifacts but is intrinsic to the samples. Assuming that the drops in resistance signal a thermodynamic phase transition, we argue that the presence of intrinsic thermal hysteresis indicates that these are first order transitions, whereas for standard superconductors the transition in the absence of applied magnetic field is always second order. We conclude that this is another feature that qualitatively distinguishes superhydrides from standard superconductors, in addition to the ones that have been pointed out earlier [1,2], $assuming$ these materials are superconductors. Alternatively and more likely, whether or not the drops in resistance signal a thermodynamic phase transition, our analysis indicates that superhydrides are not superconductors.

cond-mat.supr-con↗

arXiv2020

Absence of high temperature superconductivity in hydrides under pressure

The long-sought goal of room-temperature superconductivity has reportedly recently been realized in a carbonaceous sulfur hydride compound under high pressure, as reported by Snider et al. [1]. The evidence presented in that paper is stronger than in other similar recent reports of high temperature superconductivity in hydrides under high pressure [2-7], and has been received with universal acclaim [8-10]. Here we point out that features of the experimental data shown in Ref. [1] indicate that the phenomenon observed in that material is not superconductivity. This observation calls into question earlier similar claims of high temperature conventional superconductivity in hydrides under high pressure based on similar or weaker evidence [2-7].

cond-mat.supr-con↗

arXiv2020

Thermodynamics of Eliashberg theory in the weak-coupling limit

The weak-coupling limits of the gap and critical temperature computed within Eliashberg theory surprisingly deviate from the BCS theory predictions by a factor of $1/\sqrt{e}$. Interestingly, however, the ratio of these two quantities agrees for both theories. Motivated by this result, here we investigate the weak-coupling thermodynamics of Eliashberg theory, with a central focus on the free energy, specific heat, and the critical magnetic field. In particular, we numerically calculate the difference between the superconducting and normal-state specific heats, and we find that this quantity differs from its BCS counterpart by a factor of $1/\sqrt{e}$, for all temperatures below $T_{c}$. We find that the dimensionless ratio of the specific-heat discontinuity to the normal-state specific heat reduces to the BCS prediction given by $ΔC_{V}(T_{c})/C_{V,n}(T_c)\approx1.43$. This gives further evidence to the expectation that all dimensionless ratios tend to their "universal values" in the weak-coupling limit.

cond-mat.supr-con↗

arXiv2020

A quantum moat barrier, realized with a finite square well

The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions. Remarkably, we illustrate that similar solutions can be achieved using an attractive "barrier" potential (a "quantum moat") instead of a repulsive one (a "quantum wall"). The reason this works is intimately connected to the concepts of "orthogonalized plane waves" and the pseudopotential method, both originally used to understand electronic band structures in solids. While the main goal of this work is to use a simple model to demonstrate the barrier-like attribute of a quantum moat, we also show how the pseudopotential method is used to greatly improve the efficiency of constructing wave functions for this system using matrix diagonalization.

cond-mat.quant-gas↗

arXiv2019

Numerical and Analytical Study of the Bound States of the $-α/x^2$ Potential

The quantum mechanical bound states of the $-α/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the origin. The resulting solutions are completely well-defined and ``normal.'' We present results here as a case study in undergraduate research --- two independent methodologies are used: one analytical (with very unfamiliar non-elementary functions) and one numerical (with very straightforward methodology). These play complementary roles in arriving at solutions and achieving insights in this problem.

quant-ph↗

arXiv2019

Eliashberg theory in the weak-coupling limit: results on the real frequency axis

We formulate and solve the Eliashberg equations on the imaginary frequency axis at temperatures below $T_c$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a given coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary axis equations are also solved to obtain numerically exact analytic continuations from the imaginary frequency axis to the real frequency axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature $T_c$. We show that the normalized gap function on both the real and imaginary frequency axes, for an electron-phonon Einstein spectrum ($δ$-function) of a given strength, is a universal function of frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this non-trivial frequency dependence in the gap function. This modification, in the gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to their BCS values.

cond-mat.supr-con↗

arXiv2019

Eliashberg Theory: a short review

Eliashberg theory is a theory of superconductivity that describes the role of phonons in providing the attractive interaction between two electrons. Phonon dynamics are taken into account, thus giving rise to retardation effects that impact the electrons, in the form of a frequency-dependent electron self-energy. In the superconducting state, this means that the order parameter, generally considered to be a static quantity in the Bardeen-Cooper-Schrieffer (BCS) theory, also becomes frequency-dependent. Here we review the finite temperature formulation of Eliashberg theory, both on the imaginary and real frequency axis, and briefly display some examples of the consequences of a dynamical, as opposed to static, interaction. Along the way we point out where further work is required, concerning the validity of some of the assumptions used.

cond-mat.supr-con↗

arXiv2019

Hole superconductivity in infinite-layer nickelates

We propose that the superconductivity recently observed in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ with critical temperature in the range $9$ K to $15$ K results from the same charge carriers and the same mechanism that we have proposed give rise to superconductivity in both hole-doped and electron-doped cuprates: pairing of hole carriers in oxygen $pπ$ orbitals, driven by a correlated hopping term in the effective Hamiltonian that lowers the kinetic energy, as described by the theory of hole superconductivity. We predict a large increase in $T_c$ with compressive epitaxial strain.

cond-mat.supr-con↗

arXiv2019

Understanding electron-doped cuprate superconductors as hole superconductors

Since their experimental discovery in 1989, the electron-doped cuprate superconductors have presented both a major challenge and a major opportunity. The major challenge has been to determine whether these materials are fundamentally different from or essentially similar to their hole-doped counterparts; a major opportunity because answering this question would strongly constrain the possible explanations for what is the essential physics that leads to high temperature superconductivity in the cuprates, which is still not agreed upon. Here we argue that experimental results over the past 30 years on electron-doped cuprate materials have provided conclusive answers to these fundamental questions, by establishing that both in hole- and electron-doped cuprates, superconductivity originates in pairing of hole carriers in the same band. We discuss a model to describe this physics that is different from the generally accepted ones, and calculate physical observables that agree with experiment, in particular tunneling characteristics. We argue that our model is simpler, more natural and more compelling than other models. Unlike other models, ours was originally proposed before rather than after many key experiments were performed.

cond-mat.supr-con↗

arXiv2018

Eliashberg Theory in the Weak Coupling Limit

Eliashberg theory provides a theoretical framework for understanding the phenomenon of superconductivity when pairing between two electrons is mediated by phonons, and retardation effects are fully accounted for. BCS theory is often viewed as the weak coupling limit of Eliashberg theory, in spite of a handful of papers that have pointed out that this is not so. Here we present very accurate numerical solutions in the weak coupling limit to complement the existing analytical results, and demonstrate more convincingly the validity of this limit by extending the analytical results to first order in the coupling constant.

cond-mat.supr-con↗

arXiv2017

Double well potentials with a quantum moat barrier or a quantum wall barrier give rise to similar entangled wave functions

The solution to a problem in quantum mechanics is generally a linear superposition of states. The solutions for double well potentials epitomize this property, and go even further than this: they can often be described by an effective model whose low energy features can be described by two states --- one in which the particle is on one side of the barrier, and a second where the particle is on the other side. Then the ground state remains a linear superposition of these two macroscopic-like states. In this paper we illustrate that this property is achieved similarly with an attractive potential that separates two regions of space, as opposed to the traditionally repulsive one. In explaining how this comes about we revisit the concept of "orthogonalized plane waves," first discussed in 1940 to understand electronic band structure in solids, along with the accompanying concept of a pseudopotential. We show how these ideas manifest themselves in a simple double well potential, whose "barrier" consists of a moat instead of the conventional wall.

cond-mat.quant-gas↗

arXiv2017

The possible role of van Hove singularities in the high $T_c$ of superconducting H$_3$S

We observe that H$_3$S has a bcc structure and, with nearest neighbour hopping only, a strong singularity occurs at zero energy. This singularity is accompanied with a highly nested Fermi surface, which is {\it not} conducive to a stable superconducting instability. Introduction of next-nearest-neighbour hopping removes the singularity, but a `robust' peak remains in the electron density of states. Solution of the BCS equations shows an enhanced superconducting $T_c$ due to this peak. Furthermore, nesting is no longer present, so other instabilities will not compete effectively with superconductivity. We find high critical temperatures are possible, even with very modest coupling strengths. We also examine a limit of the $T=0$ equations (in an Appendix) where an analytical solution is possible over the entire range of coupling strengths, and therefore the BCS-BEC crossover is fully covered.

cond-mat.supr-con↗

arXiv2017

The tight-binding formulation of the Kronig-Penney model

We provide a derivation of the tight-binding model that emerges from a full consideration of a particle bound in a periodic one-dimensional array of square well potentials, separated by barriers of height $V_0$ and width $b$. We derive the dispersion for such a model, and show that an effective next-nearest-neighbor hopping parameter is required for an accurate description. An electron-hole asymmetry is prevalent except in the extreme tight-binding limit, and emerges through a "next-nearest neighbor" hopping term in the dispersion. We argue that this does not necessarily imply next-nearest-neighbor tunneling; this is done by deriving the transition amplitudes for a two-state effective model that describes a double-well potential, which is a simplified precursor to the problem of a periodic array of potential wells.

cond-mat.other↗

arXiv2016

The Coulomb potential in quantum mechanics revisited

The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are considered. We highlight this fact by solving a model for the Coulomb potential with a cutoff (representing the finite extent of the nucleus); in the limit that the cutoff is reduced to zero we recover the standard result, albeit in a non-standard way. This example is used to emphasize that a more consistent approach to solving the Coulomb problem in quantum mechanics requires an examination of the non-standard solution. The end result is, of course, the same.

physics.gen-ph↗

arXiv2016

A systematic study of the superconducting critical temperature in two and three dimensional tight-binding models: a possible scenario for superconducting H$_3$S ?

Ever since BCS theory was first formulated it was recognized that a large electronic density of states at the Fermi level was beneficial to enhancing $T_c$. The A15 compounds and the high temperature cuprate materials both have had an enormous amount of effort devoted to studying the possibility that such peaks play an important role in the high critical temperatures existing in these compounds. Here we provide a systematic study of the effect of these peaks on the superconducting transition temperature for a variety of tight-binding models of simple structures, both in two and three dimensions. In three dimensions large enhancements in $T_c$ can occur, due to van Hove singularities that result in divergences in the density of states. Furthermore, even in more realistic structures, where the van Hove singularity disappears, large enhancements in $T_c$ continue due to the presence of `robust' peaks in the densities of states. Such a peak, recently identified in the bcc structure of H$_3$S, is likely the result of such a van Hove singularity. In certain regimes, anomalies in the isotope coefficient are also expected.

cond-mat.supr-con↗

arXiv2016

The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model

Allowing a single electron to hop to next-nearest neighbours (NNN) in addition to the closest atomic sites in the Holstein model, a modified Trugman method is applied to exactly calculate the effect on the polaronic effective mass in one, two, and three dimensions, building on the previous study of the one-dimensional NNN Holstein model. We also present perturbative calculations and a heuristic scaling factor for the coupling strength and ion frequency to nearly map the NNN Holstein model back onto the original Holstein model. When account is taken of the modified electronic bandwidth near the electron energy, we find that including NNN hopping effectively increases the polaron effective mass.

cond-mat.str-el↗

arXiv2016

Calculation of 2D electronic band structure using matrix mechanics

We extend previous work applying elementary matrix mechanics to one-dimensional periodic arrays (to generate energy bands) to two-dimensional arrays. We generate band structures for the square lattice "2D Kronig-Penney model" (square wells), muffin-tin potential (cylindrical wells), and Gaussian wells. We then apply the method to periodic arrays of more than one atomic site in a unit cell, in particular, the case of materials with hexagonal lattices like graphene. These straightforward extensions of undergraduate-level calculations allow students to readily determine band structures of current research interest.

cond-mat.mes-hall↗

arXiv2015

Asymmetric wave functions from tiny perturbations

The quantum mechanical behavior of a particle in a double well defies our intuition based on classical reasoning. Not surprisingly, an asymmetry in the double well will restore results more consistent with the classical picture. What is surprising, however, is how a very small asymmetry can lead to essentially classical behavior. In this paper we use the simplest version of a double well potential to demonstrate these statements. We also show how this system accurately maps onto a two-state system, which we refer to as a `toy model'.

quant-ph↗