Unitary Limit Research Articles

Influence of the impurity scattering on charge transport in unconventional superconductor junctions

We study the influence of non-magnetic impurity scatterings on the tunneling conductance of a junction consisting of a normal metal and a disordered unconventional superconductor by solving the quasiclassical Eilenberger equation self-consistently. We find that the impurity scatterings in both the Born and unitary limits affect the formation of the Andreev bound states and modify strongly the tunneling spectra around zero bias. Our results are interpreted well by the appearance of odd-frequency Cooper pairs near the interface and by the divergent behavior of the impurity self-energy. The present paper provides a useful tool to identify the pairing symmetry of unconventional superconductors in experiments.

Matching universal behavior with potential models

Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed.

Thermodynamics of the First Order Phase Transition of Quark-Gluon Plasma at RHIC

The quark-gluon plasma in thermodynamic equilibrium is reviewed. The phase diagram of quark hadron phase transition and the color superconducting phases of quark-gluon matter are discussed. The lattice QCD results on the order of the phase transition. We discuss some aspects of atomic Fermi gas in the unitary limit in the first order transition. We consider the equation of state and the critical temperature for pair condensation. The strongly interacting phase transition (Quark-Hadron phase transition) also discussed.

Hypernuclei in halo/cluster effective field theory

The light double [Formula: see text] hypernuclei, [Formula: see text] and [Formula: see text], are studied as three-body [Formula: see text] and [Formula: see text] cluster systems in halo/cluster effective field theory at leading order. We find that the [Formula: see text] system in spin-0 channel does not exhibit a limit cycle whereas the [Formula: see text] system in spin-1 channel and the [Formula: see text] system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the [Formula: see text] system in the spin-0 channel we estimate the scattering length [Formula: see text] for [Formula: see text]-wave [Formula: see text] hyperon–hypertriton scattering as [Formula: see text][Formula: see text]fm. We also discuss that studying the cutoff dependences in the [Formula: see text] and [Formula: see text] systems, the bound state of [Formula: see text] is not an Efimov state but formed due to a high energy mechanism whereas that of [Formula: see text] may be regarded as an Efimov state.

Effective theory of 3H and 3He

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order (LO) the spin-singlet nucleon–nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron–deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse scattering lengths converges rapidly. Using a new systematic treatment of the proton–proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the – binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the LO is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting .

Effects of vorticity and impurity on NMR relaxation rate in chiral p-wave superconductors

In order to study site-selective NMR in chiral p-wave superconductors, we calculate local nuclear relaxation rate T1−1 in the vortex lattice state by Eilenberger theory with and without non-magnetic impurity scattering in the Born limit and unitary limit. The local T1−1 in the NMR resonance line shape is different between two chiral states p±, depending on whether the chirality is parallel or anti-parallel to the vorticity. In the p−-wave, anomalous suppression of local T1−1 occurs around the vortex core due to the negative coherence term coming from odd-frequency s-wave Cooper pair induced around the vortex. We especially examine the site dependence of the anomalous suppression of local T1−1, including the applied magnetic field dependence and the impurity effects.

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields.

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m_{π}∼450 and 806MeV in uniform, time-independent magnetic fields of strength |B|∼10^{19}-10^{20} G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems.

ДИФФУЗИОННАЯ МОДЕЛЬ КОСМОЛОГИЧЕСКОЙ ЭВОЛЮЦИИ ЧАСТИЦ СВЕРХВЫСОКИХ ЭНЕРГИЙ В УСЛОВИЯХ СКЕЙЛИНГА ФУНДАМЕНТАЛЬНЫХ ВЗАИМОДЕЙСТВИЙ В УНИТАРНОМ ПРЕДЕЛЕ

ДИФФУЗИОННАЯ МОДЕЛЬ КОСМОЛОГИЧЕСКОЙ ЭВОЛЮЦИИ ЧАСТИЦ СВЕРХВЫСОКИХ ЭНЕРГИЙ В УСЛОВИЯХ СКЕЙЛИНГА ФУНДАМЕНТАЛЬНЫХ ВЗАИМОДЕЙСТВИЙ В УНИТАРНОМ ПРЕДЕЛЕ

Efimov Physics with $${1/2}$$ 1 / 2 Spin-Isospin Fermions

The structure of few-fermion systems having $1/2$ spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum $L=0$ state and spin $S=0,1$ channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.

The BMS equation and c c ¯ $$ c\overline{c} $$ production; a comparison of the BMS and BK equations

We introduce two processes where the BMS equation appears in a context quite different from the original context of non-global jet observables. We note the strong similarities of the BMS equation to the BK and FKPP equations and argue that these, essentially identical equations, can be viewed either in terms of the probability, or amplitude, of something not happening or in terms of the nonlinear terms setting unitarity limits. Mostly analytic solutions are given for (i) the probability that no $c\bar{c}$ pairs be produced in a jet decay and (ii) the probability that no-$c\bar{c}$ pairs be produced in a high energy dipole nucleus scattering. Both these processes obey BMS equations, albeit with very different kernels.

Optimal interactions of light with magnetic and electric resonant particles

This work studies the limits of far and near-field electromagnetic response of sub-wavelength scatterers, like the unitary limit and of lossless scatterers, and the ideal absorption limit of lossy particles. These limit behaviors are described in terms of analytic formulas that approximate finite size effects while rigorously including radiative corrections. This analysis predicts the electric and/or magnetic limit responses of both metallic and dielectric nanoparticles while quantitatively describing near-field enhancements.

Combined Analysis of CP Properties of Higgs Boson in Effective Higgs Lagrangian**Supported by the National Natural Science Foundation of China under Grant No. 11105152

CP violation effects of the Higgs stem from not only the CP mixing state but also the CP-violation couplings to electroweak bosons. The two CPV sources are combinedly studied based on an effective Higgs Lagrangian. The constraints from unitarity limits for WW and ZZ scatterings are investigated. We classify free parameters into five cases to analyze CP properties of the Boson. The allowed ranges are shown from fitting results to the signal strengths of the Higgs measured by ATLAS and CMS.

Weakly bound states with spin-isospin symmetry

We discuss weakly bound states of a few-fermion system having spin-isospin symmetry. This corresponds to the nuclear physics case in which the singlet, $a_0$, and triplet, $a_1$, $n-p$ scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about $a_0/a_1\approx-4.31$. This value defines a plane in which $a_0$ and $a_1$ can be varied up to the unitary limit, $1/a_0=0$ and $1/a_1=0$, maintaining its ratio fixed. Using a spin dependant potential model we estimate the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three $1/2$-spin-isospin fermions.

Efimov correlations in strongly interacting Bose gases

We compute the virial coefficients, the contact parameters, and the momentum distribution of a strongly interacting three-dimensional Bose gas by means of a virial expansion up to third order in the fugacity, which takes into account three-body correlations exactly. Our results characterize the nondegenerate regime of the interacting Bose gas, where the thermal wavelength is smaller than the interparticle spacing but the scattering length may be arbitrarily large. We observe a rapid variation of the third virial coefficient as the scattering length is tuned across the three-atom and the atom-dimer thresholds. The momentum distribution at unitarity displays a universal high-momentum tail with a log-periodic momentum dependence, which is a direct signature of Efimov physics. We provide a quantitative description of the momentum distribution at high momentum as measured by P. Makotyn et al. [Nat. Phys. 10, 116 (2014)], and our calculations indicate that the lowest trimer state might not be occupied in the experiment. Our results allow for a spectroscopy of Efimov states in the unitary limit.

Universal range corrections to Efimov trimers for a class of paths to the unitary limit

Using potential models we analyze range corrections to the universal law dictated by the Efimov theory of three bosons. In the case of finite-range interactions we have observed that, at first order, it is necessary to supplement the theory with one finite-range parameter, $\Gamma_n^3$, for each specific $n$-level [Kievsky and Gattobigio, Phys. Rev. A {\bf 87}, 052719 (2013)]. The value of $\Gamma_n^3$ depends on the way the potentials is changed to tune the scattering length toward the unitary limit. In this work we analyze a particular path in which the length $r_B=a-a_B$, measuring the difference between the two-body scattering length $a$ and the energy scattering length $a_B$, results almost constant. Analyzing systems with very different scales, as atomic or nuclear systems, we observe that the finite-range parameter remains almost constant along the path with a numerical value of $\Gamma_0^3\approx 0.87$ for the ground state level. This observation suggests the possibility of constructing a single universal function that incorporate finite-range effects for this class of paths. The result is used to estimate the three-body parameter $\kappa_*$ in the case of real atomic systems brought to the unitary limit thought a broad Feshbach resonances. Furthermore, we show that the finite-range parameter can be put in relation with the two-body contact $C_2$ at the unitary limit.

The Impurity Effects on the Superconducting Gap in the High- T c Superconductor Bi2Sr2CaCu2−x Fe x O 8 + δ Investigated by STM/STS

We performed scanning tunneling microscopy/ spectroscopy (STM/STS) experiments to investigate Fe substitution effects on the superconductivity (SC) of overdoped Bi2212. The gap-edge peaks in STS spectrum at T≪T c become inhomogeneous strongly in Fe-doped Bi2212. The spectral weight around zero bias, namely the density of states (DOS) at ∼E F is partly recovered by substitution of Fe in every position. The recovery of the DOS at ∼E F can be explained in terms of impurity effects on d-wave SC in the unitarity limit. However, the strong inhomogeneity of gap-edge peaks would be ascribed to different effects due to Fe-substitution.

Perfect-fluid behavior of a dilute Fermi gas near unitary

We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength 1/ak_F from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for 1/ak_F approx 0.4, with a minimum value of (eta/s)_min approx 0.2 hbar/k_B, which is about twice as small as the value reported for experiments in quark-gluon plasma (eta/s)_QGP lesssim 0.4 hbar/k_B. The Fermi gas near unitarity thus emerges as the most "perfect fluid" observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory or larger (less than 10^9 atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.

Strong Coupling Effects on the Specific Heat of an Ultracold Fermi Gas in the Unitarity Limit

We investigate strong-coupling corrections to the specific heat $C_V$ in the normal state of an ultracold Fermi gas in the BCS-BEC crossover region. A recent experiment on a $^6$Li unitary Fermi gas [M. J. H. Ku, {\it et. al.}, Science {\bf 335}, 563 (2012)] shows that $C_V$ is remarkably amplified near the superfluid phase transition temperature $T_{\rm c}$, being similar to the well-known $\lambda$-structure observed in liquid $^4$He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that strong pairing fluctuations are sufficient to explain the anomalous behavior of $C_V$ observed in a $^6$Li unitary Fermi gas near $T_{\rm c}$. We also show that there is no contribution from {\it stable} preformed Cooper pairs to $C_V$ at the unitarity. This indicates that the origin of the observed anomaly is fundamentally different from the case of liquid $^{4}$He, where {\it stable} $^4$He Bose atoms induce the $\lambda$-structure in $C_V$ near the superfluid instability. Instead, the origin is the suppression of the entropy $S$, near $T_{\rm c}$, due to the increase of {\it metastable} preformed Cooper pairs. Our results indicate that the specific heat is a useful quantity to study the effects of pairing fluctuations on the thermodynamic properties of an ultracold Fermi gas in the BCS-BEC crossover region.

Spin Susceptibility and Effects of Inhomogeneous Strong Pairing Fluctuations in a Trapped Ultracold Fermi Gas

We theoretically investigate magnetic properties of a unitary Fermi gas in a harmonic trap. Including strong pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a trap potential within the local density approximation (LDA), we calculate the local spin susceptibility $\chi(T,r)$ above the superfluid phase transition temperature $T_{\rm c}$. We show that the formation of preformed singlet Cooper pairs anomalously suppresses $\chi(T,r)$ in the trap center near $T_{\rm c}$. We also point out that, in the unitarity limit, the spin-gap temperature in a uniform Fermi gas can be evaluated from the observation of the spatial variation of $\chi(T,r)$. Since a real ultracold Fermi gas is always in a trap potential, our results would be useful for the study of how this spatial inhomogeneity affects thermodynamic properties of an ultracold Fermi gas in the BCS-BEC crossover region.

OPE convergence in non-relativistic conformal field theories

Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NRCFT, in particular the mapping between operators and states in a non-relativistic "radial quantization" Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2,d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.