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Sudip Chakravarty

Publications and source records attributed to Sudip Chakravarty.

At least 55 records · Page 3Linked to original sources
arXiv2011

Magnetic breakdown and quantum oscillations in electron-doped high temperature superconductor $\mathrm{Nd_{2-x}Ce_{x}CuO_{4}}$

Recent more precise experiments have revealed both a slow and a fast quantum oscillation in the c-axis resistivity of nearly optimal to overdoped electron-doped high temperature superconductor $\mathrm{Nd_{2-x}Ce_{x}CuO_{4}}$. Here we study this problem from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula. In this method, neither quasiclassical approximations for magnetic breakdown, nor {\em ad ho}c broadening of Landau levels, are necessary to study the high field quantum oscillations. The underlying Hamiltonian is a mean field Hamiltonian that incorporates a two-fold commensurate Fermi surface reconsruction. While the specific mean field considered is the $d$-density wave, similar results can also be obtained by a model of a spin density wave, as was explicitly demonstrated earlier. The results are consistent with an interplay of magnetic breakdown across small gaps in the reconstructed Fermi surface and Shubnikov-de Haas oscillations.

cond-mat.supr-con↗
arXiv2010

Singlet versus triplet particle-hole condensates in quantum oscillations in cuprates

Quantum oscillations in a tilted magnetic field offer the possibility of distinguishing singlet versus triplet order parameters in the particle hole channel provided the measurements reflect a putative ``normal'' state of a density wave obtained by applying by high magnetic field at low temperatures. A theoretical analysis is given that compares spin density wave, a singlet $d$-density wave, and a triplet $d$-density wave. While the existence of a spin zero in the oscillation amplitude is a necessary consequence of a singlet order parameter, a triplet order parameter may or may not exhibit a spin zero, making it a quantitative issue that depends on the actual extremal orbits on the Fermi surface. Nonetheless, a theoretical analysis can shed light on the striking recent measurements in $\mathrm{YBa_{2}Cu_{3}O_{6+δ}}$.

cond-mat.supr-con↗
arXiv2010

Quantum oscillations in electron doped high temperature superconductors

Quantum oscillations in hole doped high temperature superconductors are difficult to understand within the prevailing views. An emerging idea is that of a putative normal ground state, which appears to be a Fermi liquid with a reconstructed Fermi surface. The oscillations are due to formation of Landau levels. Recently the same oscillations were found in the electron doped cuprate, $\mathrm{Nd_{2-x}Ce_{x}CuO_{4}}$, in the optimal to overdoped regime. Although these electron doped non-stoichiometric materials are naturally more disordered, they strikingly complement the hole doped cuprates. Here we provide an explanation of these observations from the perspective of density waves using a powerful transfer matrix method to compute the conductance as a function of the magnetic field.

cond-mat.supr-con↗
arXiv2010

Key issues in theories of high temperature superconductors

High temperature superconductivity in cuprate superconductors remains an unsolved problem in theoretical physics. The same statement can also be made about a number of other superconductors that have been dubbed unconventional. What makes these superconductors so elusive is an interesting question in itself. The present manuscript focuses on the recent magnetic oscillation experiments and how they fit into the broader picture. Many aspects of these experiments can be explained by Fermi liquid theory; the key issue is the extent to which this is true. If true, the entire paradigm developed over the past three decades must be reexamined. A critical analysis of this issue has necessitated a broader analysis of questions about distinct ground states of matter, which may be useful in understanding other unconventional superconductors.

cond-mat.supr-con↗
arXiv2010

Quantum Phase Transition, Dissipation, and Measurement

A selected set of topics in quantum phase transition is discussed. It includes dissipative quantum phase transitions, the role of disorder, and the relevance of quantum phase transition to measurement theory in quantum mechanics.

cond-mat.str-el↗
arXiv2010

Multiple quantum oscillation frequencies in $\mathrm{YBa_{2}Cu_{3}O_{6+δ}}$ and bilayer splitting

Experiments have revealed multiple quantum oscillation frequencies in underdoped high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6+δ}}$, corresponding to approximately 10% doping, which contain $\mathrm{CuO}$ bilayers in the unit cell. These unit cells are further coupled along the c-axis by a tunneling matrix element. A model of the energy dispersion that has its roots in the previously determined electronic structure, combined with two-fold commensurate density waves, reveals multiple electron and hole pockets. To the extent that quasiparticles of the reconstructed Fermi surface have finite residues, however small, the formation of Landau levels are the cause of these oscillations and the bilayer splitting and warping of the electronic dispersion along the direction perpendicular to the CuO-planes are firm consequences. We explore this possibility in detail and find overall consistency with experiments. An important conclusion is that bilayer splitting is severely renormalized from the value obtained from band structure calculations. It would be extremely interesting to perform these experiments for higher values of doping. We roughly expect the splitting of the frequencies to increase with doping, but the full picture may be more complex because the density wave order parameter is also expected to decrease with doping, vanishing around the middle of the superconducting dome.

cond-mat.supr-con↗
arXiv2010

Scaling of von Neumann entropy at the Anderson transition

Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two---a metal-insulator transition. This model also plays an important role in the plateau-to-plateu transition in the integer quantum Hall effect, which is also correctly captured by a scaling theory. Yet, in neither of these cases the ground state energy shows any non-analyticity as a function of a suitable tuning parameter, typically considered to be a hallmark of a quantum phase transition, similar to the non-analyticity of the free energy in a classical phase transition. Here we show that von Neumann entropy (entanglement entropy) is non-analytic at these phase transitions and can track the fundamental changes in the internal correlations of the ground state wave function. In particular, it summarizes the spatially wildly fluctuating intensities of the wave function close to the criticality of the Anderson transition. It is likely that all quantum phase transitions can be similarly described.

cond-mat.dis-nn↗
arXiv2010

Quasiparticle Nernst effect in the cuprate superconductors from the d-density wave theory of the pseudogap phase

We consider the Nernst effect in the underdoped regime of the cuprate high temperature superconductors within the d-density wave (DDW) model of the pseudogap phase. By a combination of analytical and numerical arguments, we show that there is a robust low-temperature positive peak (i.e., maximum) in the temperature dependence of the Nernst coefficient when the DDW state is ambipolar, i.e., when the broken symmetry supports the coexistence of both electron- and hole-like quasiparticles in the excitation spectrum, and the electron pocket dominates at the low temperatures. In contrast, the Nernst coefficient is negative and there is no such positive peak if the underlying state is non-ambipolar, i.e., when it supports only one type of quasiparticles. More generally, in the ambipolar state, the sign of the Nernst coefficient can be positive or negative depending on the dominance of the electron or hole pockets, respectively, in the low temperature thermoelectric transport. By modeling the pseudogap phase by a doping-dependent DDW order parameter with a Fermi surface topology that supports both hole and electron pockets, and assuming energy-independent transport scattering times, we analyze the evolution of the Nernst effect with doping concentration at low temperatures in the cuprate phase diagram.

cond-mat.str-el↗
arXiv2009

Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-$T_{c}$ superconductors

Recent quantum oscillation experiments in underdoped high temperature superconductors seem to imply two paradoxes. The first paradox concerns the apparent non-existence of the signature of the electron pockets in angle resolved photoemission spectroscopy (ARPES). The second paradox is a clear signature of a small electron pocket in quantum oscillation experiments, but no evidence as yet of the corresponding hole pockets of approximately double the frequency of the electron pocket. This hole pockets should be present if the Fermi surface reconstruction is due to a commensurate density wave, assuming that Luttinger sum rule relating the area of the pockets and the total number of charge carriers holds. Here we provide possible resolutions of these apparent paradoxes from the commensurate $d$-density wave theory. To address the first paradox we have computed the ARPES spectral function subject to correlated disorder, natural to a class of experiments relevant to the materials studied in quantum oscillations. The intensity of the spectral function is significantly reduced for the electron pockets for an intermediate range of disorder correlation length, and typically less than half the hole pocket is visible, mimicking Fermi arcs. Next we show from an exact transfer matrix calculation of the Shubnikov-de Haas oscillation that the usual disorder affects the electron pocket more significantly than the hole pocket. However, when, in addition, the scattering from vortices in the mixed state is included, it wipes out the frequency corresponding to the hole pocket. Thus, if we are correct, it will be necessary to do measurements at higher magnetic fields and even higher quality samples to recover the hole pocket frequency.

cond-mat.supr-con↗
arXiv2009

Glassy states in fermionic systems with strong disorder and interactions

We study the competition between interactions and disorder in two dimensions. Whereas a noninteracting system is always Anderson localized by disorder in two dimensions, a pure system can develop a Mott gap for sufficiently strong interactions. Within a simple model, with short-ranged repulsive interactions, we show that, even in the limit of strong interaction, the Mott gap is completely washed out by disorder for an infinite system for dimensions $D\le 2$. The probability of a nonzero gap falls onto a universal curve, leading to a glassy state for which we provide a scaling function for the frequency dependent susceptibility.

cond-mat.str-el↗
arXiv2008

Quantum oscillations in graphene in the presence of disorder and interactions

Quantum oscillations in graphene is discussed. The effect of interactions are addressed by Kohn's theorem regarding de Haas-van Alphen oscillations, which states that electron-electron interactions cannot affect the oscillation frequencies as long as disorder is neglected and the system is sufficiently screened, which should be valid for chemical potentials not very close to the Dirac point. We determine the positions of Landau levels in the presence of potential disorder from exact transfer matrix and finite size diagonalization calculations. The positions are shown to be unshifted even for moderate disorder; stronger disorder, can, however, lead to shifts, but this also appears minimal even for disorder width as large as one-half of the bare hopping matrix element on the graphene lattice. Shubnikov-de Haas oscillations of the conductivity are calculated analytically within a self-consistent Born approximation of impurity scattering. The oscillatory part of the conductivity follows the widely invoked Lifshitz-Kosevich form when certain mass and frequency parameters are properly interpreted.

cond-mat.mes-hall↗
arXiv2008

Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high temperature superconductors

We consider incommensurate $d$-density wave order in underdoped high temperature superconductors. We find that Fermi surface reconstruction can correctly capture the phenomenology of the recent quantum oscillation experiments that suggest incommensurate order. The predicted frequencies are a frequency around 530 T arising from the electron pocket, a hole frequency at around 1650 T, and a new low frequency from a smaller hole pocket at 250 T for which there are some indications that require further investigation. The oscillation corresponding to the electron pocket will be further split due to bilayer coupling but the splitting is sufficiently small to require more refined measurements. The truly incommensurate $d$-density wave breaks both time reversal and inversion but the product of these two symmetry operations is preserved. There is some similarity of our results with the spiral spin density wave order, which, as pointed out by Overhauser, also breaks time reversal and inversion. Calculations corresponding to higher order commensuration produces results similar to anti-phase spin stripes, but appear to us to be an unlikely explanation of the experiments. The analysis of the Gorkov equation in the mixed state shows that the oscillation frequencies are unshifted from the putative normal state and the additional Dingle factor arising from the presence of the mixed state can provide a subtle distinction between the spiral spin density wave and the $d$-density wave.

cond-mat.supr-con↗
arXiv2008

Hidden order revealed in quantum oscillations in cuprate superconductors

We follow the line of reasoning that hidden broken symmetries are the root of quantum oscillations observed in underdoped superconductors and examine the role of bilayer splitting and incommensuration. This is a view that eschews the notion of a featureless Mott liquid as the source of complexity. Instead, our view is grounded in a conventional Fermi surface and quasiparticles. We show that bilayer splitting and/or incommensurate $d$-density wave order can lead to many interesting results, in particular a splitting of the main frequency of the quantum oscillations.

cond-mat.supr-con↗
arXiv2008

Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors

Recent quantum oscillation measurements in high temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here we explain the observations with the theory that the alleged normal state exhibits a hidden order, the $d$-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle $π/2$, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but also touch upon the consequences if the order were to incommensurate. It is shown that while commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.

cond-mat.supr-con↗
arXiv2008

Universality of transition temperatures in families of copper-oxide superconductors: interlayer tunneling redux

We revisit the interlayer tunneling theory of high temperature superconductors and formulate it as a mechanism by which the striking systematics of the transition temperature within a given homologous series can be understood. We pay attention not only to the enhancement of pairing, as was originally suggested, but also to the role of competing order parameters that tend to suppress superconductivity, and to the charge imbalance between inequivalent outer and inner CuO2 planes in a unit cell. Calculations based on a generalized Ginzburg-Landau theory yield results that bear robust and remarkable resemblance to experimental observations.

cond-mat.supr-con↗
arXiv2008

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance $σ_\mathrm{xy}$ and the longitudinal conductance $σ_\mathrm{xx}$ are computed. We demonstrate that bond disorder can produce a plateau-like feature centered at $ν=0$, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between $\pm E_{c}$, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be $2.47\pm 0.04$. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between $\sim 1.0$ and $\sim 7/3$.

cond-mat.mes-hall↗
arXiv2008

Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points

We give a heuristic argument for disorder rounding of a first order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the the N-color quantum Ashkin-Teller model in one spatial dimension, we find that for $N \geq 3$, the first order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to N-decoupled pure Ising models.

cond-mat.dis-nn↗