Search

Typically, Hall coefficient of materials near magnetic instabilities exhibits pronounced temperature dependence. To explore the reasons involved, we studied the temperature dependence of Hall coefficient in $Cr_{1-x}V_x$, $V_{2-y}O_3$ and some high-$T_c$ superconducting cuprates. We argue that it can be rationalized using the following unifying principle:\textit{ When a system is near a magnetic instability and temperature is reduced towards the instability, there is a progressive "loss" of carriers (progressive "tying down" of electrons) as they participate in long-lived and long-ranged magnetic correlations.} In other words, magnetic correlations grow in space and are longer-lived as temperature is reduced towards the magnetic instability. This is the mechanism behind reduced carrier density with reducing temperature and leads to an enhancement of the Hall coefficient. This unifying principle is implemented and quantitative analysis is done using the Gor'kov Teitel'baum Thermal Activation (GTTA) model. We also show that the Hall angle data can be understood using one relaxation time (in contrast to the "two-relaxation" times idea of Anderson) by taking into consideration of temperature dependence of carrier density. This unifying principle is shown to be working in above studied systems, but authors believe that it is of much more general validity., Comment: 15 pages, 17 figures, comments are welcomed

Predation by eagles on semi-domesticated reindeer (Rangifer tarandus) is an emerging human wildlife conflict in Fennoscandia. Both the Golden (Aquila chrysaetos) and the White-tailed eagle (Haliaeetus albicilla) are believed by herders to predate on reindeer, however, there is a considerable knowledge gap regarding extent of predation and scavenging by each species, and their distribution and behaviour within the reindeer herding areas. Lethal and non-lethal methods have been suggested to reduce this conflict with eagles. We developed this project to fill the existing knowledge gaps by investigating the patterns of eagle abundance before, during, and after reindeer calving in a herding district in northern Sweden, and testing the effect of two potential deterrents (air ventilators and rotating prisms) in diverting eagles away from reindeer calving areas. During the single study period, we made 12, 47, and 17 eagle observations before, during, and after calving respectively. Out of these observations, 34 were of Golden eagles, 33 of White-tailed eagles, and for 9 observations the species could not be confirmed. Eagle abundance increased during calving and decreased again after calving ended. No attacks by eagles on calves were observed. The odds of observing eagles were significantly higher in the control area compared to areas with deterrents. More sub-adults were observed during calving, and both species were present in the area. The extent of predation was difficult to infer using direct observations and deterrents seem to show promise in diverting eagles away from calving grounds. These studies should be replicated to get a general picture of the issue and testing the efficiency of deterrents in diverting eagles away from reindeer across reindeer herding districts., Comment: 17 pages, 4 Figures, 1 Table

While closing their famous paper entitled "Pseudogap: friend or foe of high-Tc?" Norman, Pines, and Kallin underlined that before we have a microscopic theory, we must have a consistent phenomenology. This was in 2005. As it turns out in 2006 a phenomenological theory of the pseudogap state was proposed by Gor'kov and Teitel'baum. This originated from their careful analysis of the Hall effect data, and it has been very successful model as numerous investigations over the years has shown. In this mini-review the essence of the idea of Gor'kov and Teitel'baum is presented. The pseudogap obtained by them from the Hall effect data agrees very well with that obtained from the ARPES data. This famous Gor'kov-Teitel'baum Thermal Activation model (in short GTTA model) not only presents a consistent phenomenology of the pseudogap state but also it rationalizes the Hall angle data and it presents a strong case against the famous "two-relaxation times" idea of Anderson and collaborators., Comment: 6 pages and 3 figures

As is well known, Paul Drude put forward the very first quantitative theory of electrical conduction in metals in 1900. He could successfully account for the Wiedemann-Franz law which states that the ratio of thermal to electrical conductivity divided by temperature is a constant called the Lorenz number. As it turns out, in Drude's derivation, there is a lucky cancellation of two errors. Drude's under-estimate (by an order of 100) of the value of square of the average electron velocity compensated his over-estimate of the electronic heat capacity (by the same order of 100). This compensation or cancellation of two errors lead to a value of the Lorenz number very close to its experimental value. This is well known. There is another error of a factor of two which Drude made when he calculated two different relaxation times for heat conductivity and electrical conductivity. In this article we highlight how and why this error occurred in Drude's derivation and how it was removed 5 years later (that is in 1905) by Hendrik Lorentz when he used the Boltzmann equation and a single relaxation time. This article is of pedagogical value and may be useful to undergraduate/graduate students learning solid state physics., Comment: 4 pages and 1 figure

This paper presents an innovative and cost-effective approach to understanding the Barkhausen effect through the design and implementation of an educational kit. The Barkhausen effect, characterized by Barkhausen noise (BN) during magnetization changes in soft magnetic materials, is explored for its application in probing hysteresis properties and magnetization dynamics. The study investigates scaling properties, categorizing ferromagnetic materials based on scaling exponents. The primary contribution is the introduction of a practical and accessible kit for hands-on Barkhausen Effect demonstrations, revolutionizing the educational experience. This kit enables students to not only comprehend the intricacies of BN but also calculate the scaling constant ($\tau$) for Soft Iron samples. The paper demonstrates the successful construction of the kit, its signal amplification capabilities, and data collection accuracy, showcasing its potential for widespread educational use.

Recently, Hall effect measurements are done on Lanthanum doped Strontium Iridate \(Sr_{2-x}La_{x}IrO_{4}\) which is 5d analogue of cuprates \cite{hsu2023carrier}. Hall effect measurements show that the effective carrier density \(n_{H}\) exhibits a crossover from \(n_{H} \sim x\) to \(n_{H} \sim 1+x\) near \(x\simeq 0.16\) . This is very similar to that found in cuprates around $p\simeq0.19$. It is proposed that a pseudogap (PG) state in \(Sr_{2-x}La_{x}IrO_{4}\) exists and is ending at \(x\simeq 0.16\) \cite{hsu2023carrier}. However, PG boundary (in doping-temperature phase diagram) remains unknown. In this work, we apply a very successfull the Gor'kov-Teitel'baum Thermal Activation (GTTA) model to \(Sr_{2-x}La_{x}IrO_{4}\) and obtain its PG phase boundary and draw an updated phase diagram. Our results agree with previously known signatures of PG phase in this system \cite{seo2017infrared,de2015collapse}. Using results from GTTA model we also obtain the evolution of "Fermi arcs" in this system as a function %of both doping and temperature for doping concentration $x\simeq0.08$ which are in qualitative agreement with the reported results., Comment: 6 pages and 7 figures

In cuprates, as doping $p$ is reduced from the overdoped side through the quantum critical point $p^*$, a transition in Hall number density of carriers is observed, in which this number of carriers reduces from $1+p$ holes per copper site to $p$ holes per copper site. The connection of this $1+p$ to $p$ transition with pseudogap and with superconductivity is discussed. A "panoramic" view or a "broad-brush" discussion is presented in which Anderson's "unhappy" electrons take on a central stage., Comment: 6 pages and 4 figures

The recent experimental verification of the charge-transfer superexchange mechanism as the microscopic pairing mechanism of high-$T_c$ cuprate superconductivity by Seamus Davis and collaborators\cite{sea} is a tour de force! The correct model for cuprates is the three band Emery model in which oxygen p-orbitals are explicitly taken into account. The doped holes go into these oxygen p-orbitals where they undergo charge-transfer superexchange with unpaired electrons in copper d orbitals. This charge transfer superexchange is the key which leads to bound pairs and superconductivity. In the experimental verification\cite{sea}, the system chosen is $Bi_2Sr_2CaCu_2O_{8+x}$. What is achieved is the direct functional dependence of the local electron pair density ($n_P(r)$) on local charge transfer energy ($\ep_{pd}(r)$) using state of the art single-electron and electron-pair (Josephson) scanning tunneling microscopy. The quantitative functional dependence of $n_P(r)$ on $\ep_{pd}(r)$ matches with that indicated and deduced by theory\cite{t1,t2,t3,t4,t5,t6,t7,t8,t9,t10}. The verdict of the experiment settles the debates on the microscopic mechanisms of the cuprate superconductivity in the clear favor of charge-transfer superexchange mechanism. We discuss this development in brief, and present a simple minded approach to the essence of cuprate superconductivity. We discuss what is settled now, and what is not settled yet. A "theoretical minimum" of the high-$T_c$ problem is also discussed., Comment: 7 pages, 3 figures, minor typos corrected

The way the topic of black-body radiation is presented in standard textbooks (i.e. from Rayleigh-Jeans to Max Planck) does not follow the actual historical timeline of the understanding of the black-body radiation problem. Authors believe that a presentation which follows an actual timeline of the ideas (although not a logical presentation of the field) would be of interest not only from the history of science perspective but also from a pedagogical perspective. Therefore, we attempt a concise history of this very interesting field of science., Comment: 27 pages, 10 figures

We report various phase transitions in half-Heusler TbPtBi compound using Density Functional Theory (DFT). Specifically, inclusion of spin-orbit coupling (SOC) leads to band inversion resulting in transition from the metallic to the topological semimetallic phase. However, in presence of SOC, there is a phase transition from the topological semimetal to the trivial semimetal when the material is subjected to compressive strain ($\lt -7\%$). Subsequently, under further increase of compressive strain ($\ge -7\%$), we find an opening of a direct band gap at the $\Gamma$ point, driving the system from the trivial semimetallic to the semiconducting state with changes in the sequence of bands. In the absence of SOC, only transition from the metallic to the semiconducting phase is noticed. Under tensile strain, the TbPtBi compound maintains its phase as in the unstrained condition but with an increase in the hole pocket at the Fermi level, both in the absence and presence of SOC. These tunable phase transitions (especially as a fraction of strain) make this compound very promising for application in various quantum devices such as highly sensitive strain gauges., Comment: 16 pages, 6 figures; Revised version

We answer in affirmative the absence of superconductivity in bulk prepared samples of doped infinite-layer Nickelates through a simple magnetostatic model. In an independent approach we also employ Density Functional Theory (DFT) calculations for the same investigation. Our investigations reveal that it is the formation of Nickel clusters and Nickel deficient regions in bulk prepared samples (as opposed to thin films) that leads to the absence of superconductivity in bulk prepared samples.

We have applied the powerful self-consistent renormalization theory of spin fluctuations for the system CaMn$_{2}$Al$_{10}$ discovered in 2015 and was conjectured to be an itinerant magnet. We have calculated the inverse static (paramagnetic) susceptibility and have compared it with the experimental data (Phys. Rev. B 92, 020413, 2015). The agreement is very good. We have calculated spin fluctuations at various temperatures and have also estimated the strength of the electronic correlation i.e., ($I=0.3136$ eV) in the Hubbard Hamiltonian. Based on our quantitative explanation of the inverse static (paramagnetic) susceptibility data within the framework of SCR theory, we can decisively conclude CaMn$_{2}$Al$_{10}$ exhibits the phenomena of itinerant magnetism. Further, our DFT and DFT+U calculations corroborate the strong Mn-Al hybridization which is the key behind the itinerant magnetism in this system. Our estimated correlations strength will provide a foundation for further studies of itinerant magnetism in this system.

Recent research\cite{fort} has shown that in the 20th century there is an exponential growth of the number of published scientific papers, but new ideas has only a linear growth with time. The 19th and the first half of the 20th century saw major scientific discoveries. But from the second half of the 20th century, the number of publications far exceeds the number of impactful discoveries. Does an exponentially growing number of publications indicate an element of pathological research? Pressure to publish a large number of papers has led to the phenomena of overproduction, unnecessary fragmentations, overselling, predatory journals (pay and publish), clever plagiarism, and deliberate obfuscation of scientific results so as to sell and oversell. This is harming the healthy scientific culture of passion driven research. It is an urgent problem which needs attention of the whole of the scientific community. Some ways to mitigate these grave problems are discussed., Comment: 9 pages; 5 figures; comments are welcomed

A colossal insulator-to-metal transition in high-spin pyrite phase of $MnS_{2}$ has been experimentally observed \cite{colomns2}. There are two possibilities behind this colossal insulator-to-metal transition: (1) migration of $Mn$ electrons to unoccupied $S^{2-}_{2}$ antibonding states under pressure which leads to conducting ligand states and hence metallic transition, and (2) possibility of band crossing transition. We have analyzed this experimental obervation theoretically using a toy statistical model and found that the transition is due to the migration of electrons from the transition metal ions to the ligand sites (i.e. the possibility (1)). The calculated resistivity compares well with the experimental data within the fitting parameters of the model., Comment: 5

A detailed review is given on the evolution of the theory of itinerant magnetism. The self-consistent renormalization (SCR) theory is quite successful in addressing the phenomenon of itinerant magnetism in weakly and nearly ferromagnetic and anti-ferromagnetic materials. It goes beyond the Stoner and random phase approximation (RPA) theories in taking the correlation effects into account. The Mathematical machinery of the SCR theory is rather complicated. The aim of these notes is to provide the required background. The problems with Stoner and RPA theory are discussed and the way in which the SCR theory rectifies those problems is also discussed.

A toy statistical model which mimics localized-to-itinerant electron transitions is introduced. We consider a system of two types of charge carriers: (1) localized ones, and (2) itinerant ones. There is chemical equilibrium between these two. The solution of the model shows that there is a crossover, at a specific value of a local interaction energy parameter $J$, at which carriers transfer from being itinerant to a localized/mixed valence state. The model has a very crude analogy to the observed $\gamma\rta\alpha$ transition in metal cerium., Comment: 6 pages, 8 figures

We present a review of the leading theoretical approaches in the field of cuprate high temperature superconductivity. We start out by defining the problem and ask the question: whether an overarching theory possible (which is capable of explaining not only the mechanism of unconventional superconductivity but also a coherent understanding of the strange metal phase and the pseudogap phase)? If it is possible, what should we expect from the overarching theory? We list various experimental facts, and point out what can we learn from them and where do current theories stand in addressing them? Next, we present a critique of the current leading approaches. We conclude that although progress in the field has been unprecedented, but we still lack a coherent understanding., Comment: 13 pages, and 9 figures; A new section on the cluster-DMFT based approaches is added. Some typos corrected. Comments/criticism is most welcomed!

It is a widely accepted view that COVID 19 is either transmitted via surface contamination or via close contact of an un-infected person with an infected person. Surface contamination usually happens when infected water droplets from exhalation/sneeze/cough of COVID sick person settle on nearby surfaces. To curb this, social distancing and good hand hygiene advise is advocated by World health Organization (WHO). We argue that COVID 19 coronovirus can also be airborne in a puff cloud loaded with infected droplets generated by COVID sick person. An elementary calculation shows that a $5~\mu m$ respiratory infected droplet can remain suspended for about 9.0 minutes and a $2~\mu m$ droplet can remain suspended for about an hour! And social distancing advise of 3 feet by WHO and 6 feet by CDC (Centers for Disease Control and Prevention) may not be sufficient in some circumstances as discussed in the text., Comment: 6 pages and 1 figure

We theoretically analyse D.C. resistivity($\rho$) in the Kondo-lattice model using the powerful memory function approach. The complete temperature evolution of $\rho$ is investigated using the W\"{o}lfle-G\"{o}tze expansion of the memory function. The resistivity in this model originates due to spin-flip magnetic scattering of conduction $s$-electron off the quasi-localized $d$ or $f$ electron spins. We find the famous resistivity upturn at lower temperature regime ($k_B T<<\mu_d$), where $\mu_d$ is the effective chemical potential of $d$-electrons. In the high temperature regime $(\mu_d<

We comment on the electronic structure of Nickelate system $Nd Ni O_2$ which shows superconductivity on doping. The doped system $Nd_{0.8}Sr_{0.2}NiO_2$ shows (most probably unconventional) superconductivity with transition temperatures ranging from $9~K$ to $15~K$\cite{dang}. The resistivity of the parent compound $Nd NiO_2$ shows a minimum at around 60K, and an up-turn at lower temperatures. In the current understanding it is thought to be originating from a Kondo like coupling between mobile d-states of the $Nd~5d$ bands and un-paired electrons in $Ni 3d_{x^2-y^2}-O2p$ hybrid orbitals of $Ni^{1+}$ and $O^{2-}$ions. In this note we offer alternative possibilities of the observed resistance minimum in $LaNiO_2$. We attempt to construct a "road-map" of various possibilities to comprehend the observed behaviour and suggest further experiments to prove or disprove a given explanation. We also compare and contrast Nickelates with Cuprates. Comparison points towards unconventional superconductivity in Nickelates., Comment: 8 pages, 3 figures

In a recent comment (arXiv:1906.05742) on the preprint (arXiv:1807.08572) entitled "Coexistence of Diamagnetism and Vanishingly Small Electrical Resistance at Ambient Temperature and Pressure in Nanostructures", it is pointed out that the reduction of the four-probe resistance ($R_{4P}$) to zero value is accompanied by a rise in the two probe resistance ($R_{2P}$) in the same temperature range. This curious correlation between $R_{4P}$ and $R_{2P}$ is said to be pointing towards a non-superconducting "conductance percolation" transition (rather than "percolating superconducting transition" as proposed in the revised version of arxiv:1807.08572). The explanation offered in preprint arXiv:1906.05742 is quite reasonable, but the author leaves open the question of giant diamagnetism. In this short comment I suggest a plausible cause of the giant diamagnetism found in nanostructures. It could be due to gapped electronic energy spectrum of nanoparticles which is due to quantum confinement effects, and that suppresses the electronic scattering mechanism leading to a very high value of Langevin diamagnetism., Comment: 5 pages, 1 figure

Related to the electronic structure of cuprate high-Tc superconductors there are two prevailing views: In one view, Pines and collaborators argue that cuprates consist of two electronic subsystems: one with localized spins and the other having itinerant character. Contrary to that, Phil Anderson has argued for one-component or one-band model for cuprates. Thus, a very natural question arrises: What is the actual electronic system in cuprates? Are these two-component or one-component systems? After a careful consideration of both the views, we argue in favor of one-component or Andersonian view. The key lies in the dual character of electrons in narrow d bands, and we put forward a semiclassical model using which we could quantitatively account for oxygen NMR shift data in $La_{2-x}Sr_xCuO_4$ within the single component view., Comment: 11 pages, 6 figures, comments will be appreciated

In this article an overview of the historical development of the key ideas in the field of magnetism is presented. The presentation is semi-technical in nature.Starting by noting down important contribution of Greeks, William Gilbert, Coulomb, Poisson, Oersted, Ampere, Faraday, Maxwell, and Pierre Curie, we review early 20th century investigations by Paul Langevin and Pierre Weiss. The Langevin theory of paramagnetism and the Weiss theory of ferromagnetism were partly successful and real understanding of magnetism came with the advent of quantum mechanics. Van Vleck was the pioneer in applying quantum mechanics to the problem of magnetism and we discuss his main contributions: (1) his detailed quantum statistical mechanical study of magnetism of real gases; (2) his pointing out the importance of the crystal fields or ligand fields in the magnetic behavior of iron group salts (the ligand field theory); and (3) his many contributions to the elucidation of exchange interactions in d electron metals. Next, the pioneering contributions (but lesser known) of Dorfman are discussed. Then, in chronological order, the key contributions of Pauli, Heisenberg, and Landau are presented. Finally, we discuss a modern topic of quantum spin liquids., Comment: 15 pages, 1 figure. arXiv admin note: text overlap with arXiv:1807.11291

Air travel has become one of the most common means of transportation. The most common question which is generally asked is: How does an airplane gain lift? And the most common answer is via the Bernoulli principle. It turns out that it is wrongly applied in common explanations, and there are certain misconceptions. In an alternative explanation the push of air from below the wing is argued to be the lift generating force via Newton's law. There are problems with this explanation too. In this paper we try to clear these misconceptions, and the correct explanation, using the Lancaster-Prandtl circulation theory, is discussed. We argue that even the Lancaster-Prandtl theory at the zero angle of attack needs further insights. To this end, we put forward a theory which is applicable at zero angle of attack. A new length scale perpendicular to the lower surface of the wing is introduced and it turns out that the ratio of this length scale to the cord length of a wing is roughly $0.4930\pm0.09498$ for typical NACA airfoils that we analyzed. This invariance points to something fundamental. The idea of our theory is simple. The "squeezing" effect of the flow above the wing due to camber leads to an effective Venturi tube formation and leads to higher velocity over the upper surface of the wing and thereby reducing pressure according the Bernoulli theorem and generating lift. Thus at zero angle of attack there is no need to invoke vortex and anti-vortex pair generation. In fact vortex and anti-vortex pair generation cannot be justified. We come up with the equation for the lift coefficient at zero angle of attack: \[C_l = \frac{1}{c}\int_0^c dx \left(\frac{h_c^2}{(h_c - f(x))^2}-1\right).\] Here $C_l$ is the lift coefficient, $h_c$ is our new length scale perpendicular to the lower surface of the wing and $f(x)$ is the functional profile of the upper surface of the wing., Comment: 9 pages, 5 figures

We calculate resistivity in the paramagnetic phase just above the curie temperature in a $2d$ ferromagnetic metal. The required dynamical susceptibility in the formalism of resistivity is calculated within the Random Phase Approximation(RPA). The mechanism of resistivity is magnetic scattering in which $s$-band electrons are scattered off the magnetic spin fluctuations of d-band electrons. We use the $s$-$d$ Hamiltonian formalism. We find that near the quantum critical point the resistivity in $2d$ scales as $T^{\frac{4}{3}}$, whereas in $3d$ it scales as $T^{\frac{5}{3}}$. In contrast to it, resistivity due to phonon scattering is given by $T^5$ in low temperature limit as is well known. Our RPA result agrees with the Self-Consistence Renormalisation(SCR) theory result., Comment: 11 pages

A key point from the experiment related to the "noise" pattern in figure 3(a) of arXive:1807.08572 is that it is a function of temperature. We put forward a possible explanation. We argue that it is the elasto-magnetic coupling in which the diamagnetic surface currents on the surface of nanoparticles couple to surface phonon modes. As the temperature is increased (say from 210 K to 220 K), successive phonon modes are excited, one by one. This is due to quantum confinement where phonon modes take discrete values of energy (in bulk, the modes are quasi-continuous). One by one excitation of phonon modes modulates the surface currents on nano-particles that led to a fluctuating magnetization thus "noise" in the lower part of the susceptibility data where the system is in the superconducting state., Comment: 2 pages, no figure

This article is devoted to the development of the central ideas in the field of magnetism. The presentation is semi-technical in nature and it roughly follows the chronological order. The key contributions of Van Vleck, Dorfman, Pauli, Heisenberg, and Landau are presented. Then the advent of the field of itinerant electron magnetism starting with the investigations of Bloch and Wigner, and more successful formulation by Slater and Stoner is presented. The physical basis of the Slater-Stoner theory is discussed and its problems are summarized. Then, an overview of the debate between itinerant electron view of Stoner and localized electron view of Heisenberg is presented. Connected with this debate are the issues of exchange interactions. The issues related to the origin of exchange interaction in Stoner model are discussed. We review the "middle-road" theory of van Vleck and Hurwitz--the very first theory which takes into account the electron correlation effects in the itinerant model. We close our presentation with the discussion of the very important issue of strong electron correlation in the itinerant picture., Comment: Paper provides an overview of an important chapter in magnetism: exchange and correlation in transition metals

Oscillatory effects in magnetic susceptibility of free electrons in a strong magnetic field is well known phenomenon and is well captured by Lifshitz-Kosevich formula. In this paper we point out similar oscillatory effects in Stoner susceptibility which makes the system to oscillate between paramagnetic phase and ferromagnetic phase alternatively as a function of external magnetic field strength. This effect can happen in a material which is tuned near to its magnetic instability. We suggest an experimental set-up to observe this effect. We also suggest that our result can be exploited to control a quantum critical system around its quantum critical point to study its thermodynamical or transport properties.

We apply the powerful method of memory function formalism to investigate non-equilibrium electron relaxation in graphene. Within the premises of Two Temperature Model (TTM), explicit expressions of the imaginary part of the Memory Function or generalized Drude scattering rate ($1/\tau$) are obtained. In the DC limit and in equilibrium case where electron temperature ($T_e$) is equal to phonon temperature (T), we reproduce the known results (i.e. $ 1/\tau \propto T^4$ when $T<<\Theta_{BG}$ and $1/\tau \propto T$ when $T>>\Theta_{BG}$, where $ \Theta_{BG}$ is the Bloch-Gr\"{u}neisen temperature). We report several new results for $1/ \tau$ where $T \neq T_e$ relevant in pump-probe spectroscopic experiments. In the finite frequency regime, we find that $1/\tau \propto \omega^2$ when $\omega<<\omega_{BG}$, and for $\omega>>\omega_{BG}$ it is $\omega$ independent and also electron temperature independent. These results can be verified in a typical pump-probe experimental setting for graphene., Comment: 5 figures and 2 Tables

We extend the well known phenomenon of magnetoresistance (extra resistivity of materials in transverse magnetic field) to a new and unexplored regime where in addition to a transverse magnetic field, a transverse AC field of resonant frequency is also applied. In a magnetic field, electron spin levels are Zeeman split. In a resonant AC field, we uncover a new channel of momentum relaxation in which electrons in upper Zeeman level can deexcite to lower Zeeman level by generating spin fluctuation excitation in the lattice (similar to what happens in Electron Spin Resonance (ESR) spectroscopy). An additional resistivity due to this novel mechanism is predicted in which momentum randomization of Zeeman split electrons happen via bosonic excitations (spin fluctuations). An order of magnitude of this additional resistivity is calculated. The whole work is based upon an extension of Einstein's derivation of equilibrium Planckian formula to near equilibrium systems., Comment: 5 pages; 3 figures; comments welcome

An introduction to the Zwanzig-Mori-G\"{o}tze-W\"{o}lfle memory function formalism (or generalized Drude formalism) is presented. This formalism is used extensively in analyzing the experimentally obtained optical conductivity of strongly correlated systems like cuprates and Iron based superconductors etc. For a broader perspective both the generalised Langevin equation approach and the projection operator approach for the memory function formalism are given. The G\"{o}tze-W\"{o}lfle perturbative expansion of memory function is presented and its application to the computation of the dynamical conductivity of metals is also reviewd. This review of the formalism contains all the mathematical details for pedagogical purposes., Comment: 17 pages; 2 figures and 2 tables

We report a comparative study of the scattering rates using different formalisms such as Allen\cite{allen_71}, Shulga et al.\cite{shulga_91}, Mitrovi\'c et al.\cite{mitrovic_85}, Sharapov et al\cite{sharapov_05} and memory function formalism\cite{mori_65}. We discuss the frequency and the temperature dependent scattering rates for the case of electron-phonon interactions in these formalisms. The analysis has been done for different forms of phonon density of states (PDOS) and electron density of states (EDOS). An advantage of our study is that it shed light on the physical assumptions used in these formalisms. From this detailed comparison, we observe that the memory function formalism is the most general one. All other formalisms are based on restrictive assumptions as discussed in this work., Comment: 13 pages, 7 figures

The Kelvin Water Dropper was discovered by Lord Kelvin in 1867 and it works on the principle of electrostatic induction. A working model of Kelvin Water Dropper is fabricated in the workshop facility of Physical Research Laboratory, Ahmedabad. We, for the first time, performed a quantitative measurement of the temporal development of charge using a new method that we call "Effective Capacitance method". With this, the Kelvin Water Dropper experiment can be introduced in undergraduate curriculum, where students can perform quantitative measurements with the apparatus using our "Effective Capacitance method". This should change the generally held view of Kelvin water dropper as being an entertaining toy to a mature educational device., Comment: 10 pages, 8 figures

For graphene (a Dirac material) it has been theoretically predicted and experimentally observed that DC resistivity is proportional to $ T^4$ when the temperature is much less than Bloch- Gr\"{u}neisen ($\Theta_{BG}$) temperature and T linear in opposite case ($T>>\Theta_{BG}$). Going beyond the DC case, we investigate the dynamical conductivity in graphene using the powerful method of memory function formalism. In the DC (zero frequency regime) limit, we obtained the above mention behavior which was previously obtained using the Bloch-Boltzmann kinetic equation. In the finite frequency regime, we obtained several new results: (1) the generalized Drude scattering rate, in the zero temperature limit, shows $\omega^4 $ behavior at low frequencies ($\omega << k_B \Theta_{BG}/ \hbar$) and saturates at higher frequencies. We also observed the Holstein Mechanism, however, with different power laws from that in the case of metals; (2) At higher frequencies, $\omega>>k_B \Theta_{BG}/ \hbar$, and higher temperatures $T>>\Theta_{BG}$, we observed that the generalized Drude scattering rate is linear in temperature. In addition, several other results are also obtained. With the experimental advancement of this field, these results should be experimentally tested., Comment: 8 pages, 4 figures, 1 table

We study the dynamical thermoelectric transport in metals subjected to the electron-impurity and the electron-phonon interactions using the memory function formalism. We introduce a generalized Drude form for the Seebeck coefficient in terms of thermoelectric memory function and calculate the later in various temperature and frequency limits. In the zero frequency and high temperature limit, we find that our results are consistent with the experimental findings and with the traditional Boltzmann equation approach. In the low temperature limit, we find that the Seebeck coefficient is quadratic in temperature. In the finite frequency regime, we report new results: In the electron-phonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime ($\omega \gg \omega_{D}$, where $\omega_{D}$ is the Debye frequency) and in the low frequency regime ($\omega \ll \omega_{D}$), whereas in the intermediate frequencies, it is a monotonically increasing function of frequency. In the case of the electron-impurity interaction, first it decays and then after passing through a minimum it increases with the increase in frequency and saturates at high frequencies., Comment: 11 pages, 6 figures

The Mori's projection method, known as memory function method is an important theoretical formalism to study various transport coefficients. In the present work, we calculate the dynamical thermal conductivity in the case of metals using the memory function formalism. We introduce thermal memory functions for the first time and discuss the behavior of thermal conductivity in both zero frequency limit and in the case of non-zero frequencies. We compare our results for the zero frequency case with the results obtained by the Bloch-Boltzmann kinetic approach and find that both approaches agree with each other. Motivated by some recent experimental advancements, we obtain several new results for the ac or the dynamical thermal conductivity., Comment: 13 pages, 4 figures and 2 tables

The memory function formalism is an important tool to evaluate the frequency dependent electronic conductivity. It is previously used within some approximations in the case of electrons interacting with various other degrees of freedom in metals with great success. However, one needs to go beyond those approximations as the interaction strengths become stronger. In this work, we propose a systematic expansion of the memory function involving its various moments. We calculate the higher order contribution to the generalized Drude scattering rate in case of electron-impurity interactions. Further we compare our results with the results from previously studied lowest order calculations. We find larger contributions from the higher moments in the low frequency regime and also in the case of larger interaction strength., Comment: 10 pages, 3 figures