arXiv subjects

Navinder Singh Bathinda

Publications and source records attributed to Navinder Singh Bathinda.

At least 55 records · Page 3Linked to original sources

arXiv2018

Quantum oscillations of the Stoner susceptibility: theory

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.

cond-mat.str-el↗

arXiv2018

Non-equilibrium electron relaxation in Graphene

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 ($1/τ$) 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/τ\propto T^4$ when $T<<Θ_{BG}$ and $1/τ\propto T$ when $T>>Θ_{BG}$, where $ Θ_{BG}$ is the Bloch-Grüneisen temperature). We report several new results for $1/ τ$ where $T \neq T_e$ relevant in pump-probe spectroscopic experiments. In the finite frequency regime, we find that $1/τ\propto ω^2$ when $ω<<ω_{BG}$, and for $ω>>ω_{BG}$ it is $ω$ independent and also electron temperature independent. These results can be verified in a typical pump-probe experimental setting for graphene.

cond-mat.str-el↗

arXiv2017

A Novel Effect of Electron Spin Resonance on Electrical Resistivity

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.

cond-mat.str-el↗

arXiv2017

The Memory Function Formalism: A Review

An introduction to the Zwanzig-Mori-Götze-Wölfle 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 Götze-Wölfle 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.

cond-mat.str-el↗

arXiv2017

A comparative study of finite frequency scattering rate from Allen, Mitrović-Fiorucci, Shulga-Dolgov-Maksimov, Sharapov-Carbotte and Götze-Wölfle Memory Function formalisms

We report a comparative study of the scattering rates using different formalisms such as Allen\cite{allen_71}, Shulga et al.\cite{shulga_91}, Mitrović 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.

cond-mat.str-el↗

arXiv2017

The Kelvin Water Dropper: Converting a physics toy into an educational device

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.

physics.ed-ph↗

arXiv2016

Dynamical Conductivity of Dirac Materials

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- Grüneisen ($Θ_{BG}$) temperature and T linear in opposite case ($T>>Θ_{BG}$). 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 $ω^4 $ behavior at low frequencies ($ω<< k_B Θ_{BG}/ \hbar$) 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, $ω>>k_B Θ_{BG}/ \hbar$, and higher temperatures $T>>Θ_{BG}$, 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.

cond-mat.str-el↗

arXiv2016

Finite frequency Seebeck coefficient of metals: A memory function approach

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 ($ω\gg ω_{D}$, where $ω_{D}$ is the Debye frequency) and in the low frequency regime ($ω\ll ω_{D}$), 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.

cond-mat.str-el↗

arXiv2016

Theory of the Dynamical Thermal conductivity of Metals

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.

cond-mat.str-el↗

arXiv2016

Infrared properties of cuprates in the pseudogap state: A study of Mitrovic-Fiorucci and Sharapov-Carbotte scattering rates

Frequency dependent scattering rate of generalized Drude model contains important physics of the electronic structure and of scattering mechanisms. In the present investigation, we study the frequency dependent scattering rate of cuprates (Mitrovic-Fiorucci/ Sharapov-Carbotte scattering rate) in the pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ) density of states. First, with the energy dependent density of states, the scattering rate gives the picture of depression formation coming from the opening of the pseudogap. Second, the evolution of $1/τ(ω)$ with temperature shows the increase of scattering rate with the temperature at lower frequencies and the temperature independence of $1/τ(ω)$ at higher frequencies. Third, the signature of thresholds due to boson density of states and the electronic density of states also has been observed. These signatures are qualitatively in accord with the experiments.

cond-mat.supr-con↗

arXiv2016

Moment Expansion to the Memory Function for Generalized Drude Scattering rate

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.

cond-mat.str-el↗

arXiv2016

Impurity induced resistivity upturns in underdoped cuprates

Impurity induced low temperature upturns in both the ab-plane and the c-axis dc-resistivities of cuprates in the pseudogap state have been observed in experiments. We provide an explanation of this phenomenon by incorporating impurity scattering of the charge carriers within a phenomenological model by Yang-Rice-Zhang in this regime. The scattering between charge carriers and the impurity atom is considered within the lowest order Born approximation. Resistivity is calculated within Kubo formula using the impurity renormalized spectral functions. Using physical parameters for cuprates, we describe qualitative features of the upturn phenomena and its doping evolution that coincides with the experimental findings and we stress the role of strong electronic correlations.

cond-mat.str-el↗

arXiv2016

Generalized Drude Scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result

An explicit perturbative computation of the Mori's memory function was performed by Götze and Wölfle (GW) to calculate Generalized Drude scattering (GDS) rate for the case of electron-impurity and electron-phonon scattering in metals by assuming constant electronic density of states at the Fermi energy. In the present investigation, we go beyond this assumption and extend the GW formalism to the case in which there is a gap around the Fermi surface in electron density of states. The resulting GDS is compared with a recent one by Sharapov and Carbotte (SC) obtained through a different route. We find good agreement between the two at finite frequencies. However, we find discrepancies in the dc scattering rate. These are due to a crucial assumption made in SC namely $ω>> \vert Σ(ε+ω) - Σ^{*}(ε)\vert$. No such high frequency assumption is made in the memory function based technique.

cond-mat.supr-con↗

arXiv2016

Memory Function Approach to Correlated Electron Transport: A Comprehensive Review

Memory function formalism or projection operator technique is an extremely useful method to study the transport and optical properties of various condensed matter systems. A recent revival of its uses in various correlated electronic systems is being observed. It is being used and discussed in various contexts, ranging from non-equilibrium dynamics to the optical properties of various strongly correlated systems such as high temperature superconductors. However, a detailed discussion on this method, starting from its origin to its present day applications at one place is lacking. In this article we attempt a comprehensive review of the memory function approach focusing on its uses in studying the dynamics and the transport properties of correlated electronic systems.

cond-mat.str-el↗

arXiv2015

Hot electron relaxation in metals within the Götze-Wölfle memory function formalism

We consider non-equilibrium relaxation of electrons due to their coupling with phonons in a simple metal. In our model electrons are living at a higher temperature than that of the phonon bath, mimicking a non-equilibrium steady state situation. We study the relaxation of such hot electrons proposing a suitable generalization of the memory function formalism formulated by Götze and Wölfle[Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for both dc and optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies. An interesting feature, that the dc scattering rate at high temperatures and optical scattering rate at high frequencies, are independent of the temperature difference between the electrons and the phonons is found in this study. The present formalism forms a basis which can also be extended to study hot-electron relaxation in more complex situations

cond-mat.str-el↗

arXiv2014

Non-linear Nyquist theorem: A conjecture

Thermodynamics of equilibrium states is well established. However, in nonequilibrium few general results are known. One prime and important example is that of Nyquist theorem. It relates equilibrium tiny voltage fluctuations across a conductor with its resistance. In linear systems it was proved in its generality in a beautiful piece of work by Callen and Welton (in 1950s\cite{cw}). However Callen-Welton's formalism has not been extended to nonlinear systems up to now, although alternative methods exist (like Kubo's approach) that leads to formal and implicit expressions {\it at nonlinear order} with no practical consequence. Here--using a brute-force method--we conjecture "a non-linear Nyquist theorem". This is an explicit formula much like Nyquist's original one. Our conjecture is based upon tests of the conjectured explicit formula in specific systems. We conjecture that higher moments of {\it equilibrium} fluctuations bear a relation to {\it nonlinear} admittance very similar to Nyquist's relation. Thus one can easily compute nonlinear admittance from the character of {\it equilibrium} fluctuations. Our relation will have great practical applicability, for example for electronic devices that operate under nonlinear response.

cond-mat.stat-mech↗

arXiv2014

On the failure of mean-field theories near a critical point

It is well known that mean-field theories fail to reproduce the experimentally known critical exponents. The traditional argument which explain this failure of mean-field theories near a critical point is the Ginsburg criterion in which diverging fluctuations of the order parameter is the root cause. We argue, contrary to the above mentioned traditional view, that diverging fluctuations in real physical systems near a critical point are genuine consequence of the breakdown of the property of statistical independence, and are faithfully reproduced by the mean-field theory. By looking at the problem from the point of view of "statistical independence" the divergence of fluctuations in real physical systems near criticality becomes immediately apparent as a connection can be established between diverging correlation length and diverging fluctuations. To address the question of why mean-field theories, much successful qualitatively, fail to reproduce the known values of critical indices we argue, using the essential ideas of the Wilsonian renormalization group, that mean-field theories fail to capture the long length scale averages of an order parameter near a critical point.

cond-mat.stat-mech↗

arXiv2014

Thermodynamical Phase transitions, the mean-field theories, and the renormalization (semi)group: A pedagogical introduction

While analyzing second order thermodynamical phase transitions, Lev Landau (the famous Russian physicist) introduced a very vital concept, the concept of an "order parameter". This not only amalgamated the previous fragmentary theoretical understanding of phase transitions (an arsenal of mean-field theories) but also it put forward the important theory of "spontaneous symmetry breaking". Today, order parameter concept is a paradigm both in condensed matter physics and in high energy physics, and Landau theory is a pinnacle of all mean-field theories. Mean field theories are good qualitative descriptors of the phase transition behavior. But all mean-field theories (including Landau's theory) fail at the critical point (the problem of large correlation length). The problems with large correlation length in quantum many-body systems are the hardest problems known in theoretical physics (both in condensed matter and in particle physics). It was Ken Wilson's physical insights and his powerful mathematical skills that opened a way to the solution of such hard problems. This manuscript is a perspective on these issues. Starting with simple examples of phase transitions (like ice/water; diamond/graphite etc.) we address the following important questions: Why does non-analyticity (sharp phase transitions) arise when thermodynamical functions (i.e., free energies etc) are good analytic functions? How does Landau's program unify all the previous mean-field theories? Why do all the mean-field theories fail near the critical point? How does Wilson's program go beyond all the mean-field theories? What is the origin emergence and universality?

cond-mat.stat-mech↗