arXiv subjects

Mohit Randeria

Publications and source records attributed to Mohit Randeria.

At least 73 records · Page 4Linked to original sources

arXiv2011

Fermions in 3D Optical Lattices: Cooling Protocol to Obtain Antiferromagnetism

A major challenge in realizing antiferromagnetic (AF) and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling, but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an AF Mott phase.

cond-mat.quant-gas↗

arXiv2010

Viscosity of strongly interacting quantum fluids: spectral functions and sum rules

The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of \emph{non-relativistic} quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $ζ(ω)$ and $η(ω)$ respectively, to derive exact, non-perturbative results. Our results include: a microscopic connection between the shear viscosity $η$ and the normal fluid density $ρ_n$; sum rules for $ζ(ω)$ and $η(ω)$ and their evolution through the BCS-BEC crossover; universal high-frequency tails for $η(ω)$ and the dynamic structure factor $S({\bf q}, ω)$. We use our sum rules to show that, at unitarity, $ζ(ω)$ is identically zero and thus relate $η(ω)$ to density-density correlations. We predict that frequency-dependent shear viscosity $η(ω)$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.

cond-mat.quant-gas↗

arXiv2010

Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases

We show that the universal $1/k^4$ tail in the momentum distribution of dilute Fermi gases implies that the spectral function $A(\kk,ω)$ must have weight below the chemical potential for large momentum $k \gg k_F$, with observable consequences in RF spectroscopy experiments. We find that this incoherent spectral weight is centered about $ω\simeq - ε(\kk)$ in a range of energies of order $v_F k$. This "bending back" in the dispersion, while natural for superfluids, is quite surprising for normal gases. This universal structure is present in the hard-sphere gas as well as the Fermi liquid ground state of the highly imbalanced, attractive gas near unitarity. We argue that, even in the BCS superfluid, this bending back at large $k$ is dominated by interaction effects which do not reflect the pairing gap.

cond-mat.quant-gas↗

arXiv2009

BCS-BEC crossover with unequal mass fermions

We investigate the crossover from BCS pairing to molecular BEC in an atomic gas with two fermion species with masses $m_\up \ne m_\dn$ tuned through a Feshbach resonance. We present results for the T=0 equation of state as a function of the scattering length including the effects of Gaussian fluctuations about the mean field ground state. We compute the ground state energy as a function of $m_\up/m_\dn$ at unitarity and find excellent agreement with the quantum Monte Carlo result for $m_\up/m_\dn = 6.67$ for a $^{40}$K-$^6$Li mixture. We show that the dimer scattering length in the BEC limit as a function of $m_\up/m_\dn$ compares well with exact four-body results of Petrov {\it et al}. We also derive the condition for trapping frequencies to obtain an unpolarized gas in a harmonic trap.

cond-mat.quant-gas↗

arXiv2009

Fermions in 2D Optical Lattices: Temperature and Entropy Scales for Observing Antiferromagnetism and Superfluidity

One of the major challenges in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine constraints on the entropy for observing these phases in two-dimensional Hubbard models. We investigate antiferromagnetic correlations in the repulsive model at half filling and superfluidity of s-wave pairs in the attractive case away from half filling using determinantal quantum Monte Carlo simulations that are free of the fermion sign problem. We find that an entropy per particle ~log(2) is sufficient to observe the charge gap in the repulsive Hubbard model or the pairing pseudogap in the attractive case. Observing antiferromagnetic correlations or superfluidity in 2D systems requires a further reduction in entropy by a factor of three or more. In contrast to higher dimensions, we find that adiabatic cooling is not useful to achieve the required low temperatures. We also show that double occupancy measurements are useful for thermometry for temperatures greater than the nearest-neighbor hopping.

cond-mat.quant-gas↗

arXiv2009

Theory of Radio Frequency Spectroscopy of Polarized Fermi Gases

We present two exact results for singular features in the radio frequency intensity $I(ω)$ for ultracold Fermi gases. First, in the absence of final state interactions, $I(ω)$ has a universal high frequency tail $ Cω^{-3/2}$ for \emph{all} many-body states, where $C$ is Tan's contact. Second, in a \emph{normal} Fermi liquid at T=0, $I(ω)$ has a jump discontinuity of $Z/(1 - m/m^{*})$, where $Z$ is the quasiparticle weight and $m^*/m$ the mass renormalization. We then describe various approximations for $I(ω)$ in polarized normal gases. We show why an approximation that is exact in the $n_\dn=0$ limit, fails qualitatively for $n_{\dn} > 0$: there is no universal tail and sum rules are violated. The simple ladder approximation is qualitatively correct for very small $n_{\dn}$, but not quantitatively.

cond-mat.other↗

arXiv2008

Competition between antiferromagnetism and superconductivity, electron-hole doping asymmetry and "Fermi Surface" topology in cuprates

We investigate the asymmetry between electron and hole doping in a 2D Mott insulator, and the resulting competition between antiferromagnetism (AF) and d-wave superconductivity (SC), using variational Monte Carlo for projected wave functions. We find that key features of the T = 0 phase diagram, such as critical doping for SC-AF coexistence and the maximum value of the SC order parameter, are determined by a single parameter which characterises the topology of the "Fermi surface" at half filling defined by the bare tight-binding parameters. Our results give insight into why AF wins for electron doping, while SC is dominant on the hole doped side. We also suggest using band structure engineering to control the parameter for enhancing SC.

cond-mat.str-el↗

arXiv2008

Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover

We determine the effects of quantum fluctuations about the T=0 mean field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground state energy, the gap, the speed of sound and the Landau critical velocity. At unitarity, we find excellent agreement with quantum Monte Carlo and experimental results. In the BCS limit, we show analytically that we obtain Fermi liquid interaction corrections to thermodynamics including the Hartree shift. In the BEC limit, we show that the theory leads to an approximate description of the reduction of the scattering length for bosonic molecules and also obtain quantum depletion of the Lee-Yang form. At the end of the paper, we describe a method to include feedback of quantum fluctuations into the gap equation, and discuss the problems of self-consistent calculations in satisfying Goldstone's theorem and obtaining ultraviolet finite results at unitarity.

cond-mat.other↗

arXiv2007

Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films

A central issue in the physics of high temperature superconductors is to understand superconductivity within a single copper-oxide layer or bilayer, the fundamental structural unit in the cuprates, and how it is lost with underdoping. As mobile holes are removed from the CuO_2 planes, the transition temperature T_C and superfluid density n_S decrease in a surprisingly correlated fashion in crystals and thick films. We seek to elucidate the intrinsic physics of bilayers in the strongly underdoped regime, near the critical doping level where superconductivity disappears. We report measurements of n_S(T) in films of Y_{1-x}Ca_xBa_2Cu_3O_{7-δ} as thin as two copper-oxide bilayers with T_C's as low as 3 K. In addition to seeing the two-dimensional (2D) Kosterlitz-Thouless-Berezinski transition at T_C, we observe a remarkable scaling of T_C with n_S(0) that demonstrates that the disappearance of superconductivity with underdoping is due to quantum fluctuations near a T = 0 2D quantum critical point.

cond-mat.supr-con↗

arXiv2007

Breakdown of the Thomas Fermi approximation for polarized Fermi gases

We use Bogoliubov de-Gennes theory to show that the commonly used Thomas-Fermi approximation (TFA) can fail in describing polarized unitary gases in anisotropic harmonic traps. We find a magnetized superfluid region inside the trap, with order parameter oscillations, even though there is no such stable bulk phase. This leads to magnetization profiles that deviate from contours of constant potential energy. We determine how this violation scales with trap anisotropy and number of particles, and show that we are able to account for important differences between the MIT and Rice experiments.

cond-mat.supr-con↗

arXiv2006

Can one determine the underlying Fermi surface in the superconducting state of strongly correlated superconductors?

The question of determining the underlying Fermi surface (FS) that is gapped by superconductivity (SC) is of central importance in strongly correlated systems, particularly in view of angle-resolved photoemission experiments. Here we explore various definitions of the FS in the superconducting state using the zero-energy Green's function, the excitation spectrum and the momentum distribution. We examine (a) d-wave SC in high Tc cuprates, and (b) the s-wave superfluid in the BCS-BEC crossover. In each case we show that the various definitions agree, to a large extent, but all of them violate the Luttinger count and do not enclose the total electron density. We discuss the important role of chemical potential renormalization and incoherent spectral weight in this violation.

cond-mat.supr-con↗

arXiv2006

Strong correlations lead to protected low energy excitations in disordered d-wave superconductors

We show that strong correlations play a vital role in protecting low energy excitations in disordered high temperature superconductors. The impurity-induced low-energy density of states (DOS) is greatly reduced in the strongly correlated superconductor compared to d-wave Bogoliubov-deGennes theory. The gapless nodal quasiparticles, and the resulting `V' in the low-energy DOS, are much more robust against disorder compared to the large-gap antinodal excitations. We discuss the relevance of our results to angle-resolved photoemission and scanning tunneling spectroscopy experiments.

cond-mat.str-el↗

arXiv2005

Can correlations drive a band insulator metallic?

We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but non-zero insulating gap for all finite U.

cond-mat.str-el↗

arXiv2005

BCS - BEC crossover at T=0: A Dynamical Mean Field Theory Approach

We study the T=0 crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory(DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field theory, usually used to describe this crossover, and to explore physics beyond it. Quantum fluctuations are incorporated using iterated perturbation theory as the DMFT impurity solver. We find that these fluctuations lead to large quantitative effects in the intermediate coupling regime leading to a reduction of both the superconducting order parameter and the energy gap relative to the HFB results. A qualitative change is found in the single-electron spectral function, which now shows incoherent spectral weight for energies larger than three times the gap, in addition to the usual Bogoliubov quasiparticle peaks.

cond-mat.supr-con↗

arXiv2004

Particle-Hole Asymmetry in Doped Mott Insulators: Implications for Tunneling and Photoemission Spectroscopies

In a system with strong local repulsive interactions it should be more difficult to add an electron than to extract one. We make this idea precise by deriving various exact sum rules for the one-particle spectral function independent of the details of the Hamiltonian describing the system and of the nature of the ground state. We extend these results using a variational ansatz for the superconducting ground state and low lying excitations. Our results shed light on the striking asymmetry in the tunneling spectra of high Tc superconductors and should also be useful in estimating the local doping variations in inhomogeneous materials.

cond-mat.str-el↗

arXiv2004

High Tc Superconductors -- A Variational Theory of the Superconducting State

We use a variational approach to gain insight into the strongly correlated d-wave superconducting state of the high Tc cuprates at T=0. We show that strong correlations lead to qualitatively different trends in pairing and phase coherence: the pairing scale decreases monotonically with hole doping while the SC order parameter shows a non-monotonic dome. We obtain detailed results for the doping-dependence of a large number of experimentally observable quantities, including the chemical potential, coherence length, momentum distribution, nodal quasiparticle weight and dispersion, incoherent features in photoemission spectra, optical spectral weight and superfluid density. Most of our results are in remarkable quantitative agreement with existing data and some of our predictions, first reported in Phys. Rev. Lett. {\bf 87}, 217002 (2001), have been recently verified.

cond-mat.supr-con↗

arXiv2003

Nodal Quasiparticle Dispersion in Strongly Correlated d-wave Superconductors

We analyze the effects of a momentum-dependent self-energy on the photoemission momentum distribution curve (MDC) lineshape, dispersion and linewidth. We illustrate this general analysis by a detailed examination of nodal quasiparticles in high Tc cuprates. We use variational results for the nodal quasiparticle weight Z (which varies rapidly with hole doping x) and the low energy Fermi velocity $v_F^{low}$ (which is independent of x), to show that the high energy MDC dispersion $v_{high} = v_F^{low}/Z$, so that it is much larger than the bare (band structure) velocity and also increases strongly with underdoping. We also present arguments for why the low energy Fermi velocity and the high energy dispersion are independent of the bare band structure at small x. All of these results are in good agreement with earlier and recent photoemission data [Zhou et al, Nature 423, 398 (2003)].

cond-mat.supr-con↗

arXiv2003

Fractionalization in Spin Liquid Mott Insulators: Vison Wavefunctions and Gaps

We study fractionalization in a spin-liquid Mott insulator defined by a Gutzwiller projected BCS state |0> at half-filling. We construct a trial vison (Z2 vortex) state |V> by projecting an hc/2e vortex and determine when it is orthogonal to |0>. Using a combination of analytical arguments and Monte Carlo calculations we show that generically the spin-liquid is Z2 fractionalized. For microscopic parameters appropriate for high Tc cuprates, we estimate that the vison gap Ev << J, consistent with recent experimental bounds, due to proximity to the bipartite symmetric point where Ev = 0.

cond-mat.str-el↗