Single-particle Density Research Articles

Pseudogap Phenomena of an Ultracold Fermi Gas with a P-wave Feshbach Resonance

We investigate pseudogap phenomena in an ultracold Fermi gas with a p-wave tunable pairing interaction. Including p-wave pairing fluctuations within a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) above the superfluid transition temperature Tc. Starting from the weak-coupling regime, we show that, at first, a dip structure gradually appears to become remarkable in DOS with increasing the strength of the p-wave pairing interaction at Tc. However, this pseudogap structure again becomes less remarkable to eventually disappear, as one passes through the intermediate coupling regime to enter the strong-coupling region. This non-monotonic interaction dependence of the pseudogap is quite different from the s-wave case, where the pseudogap size simply increases with increasing a s-wave interaction strength. This difference is found to originate from the momentum dependence of the p-wave interaction. We also determine the pseudogap temperature below which the dip structure in DOS appears and identify the pseudogap regime in the phase diagram of a Fermi gas with respect to the temperature and p-wave interaction strength.

Penrose-Onsager Criterion Validation in a One-Dimensional Polariton Condensate

We perform quantum tomography on one-dimensional polariton condensates, spontaneously occurring in linear disorder valleys in a CdTe planar microcavity sample. By the use of optical interferometric techniques, we determine the first-order coherence function and the amplitude and phase of the order parameter of the condensate, providing a full reconstruction of the single particle density matrix for the polariton system. The experimental data are used as input to theoretically test the consistency of the Penrose-Onsager criterion for Bose-Einstein condensation in the framework of nonequilibrium polariton condensates. The results confirm the pertinence and validity of the criterion for a nonequilibrium condensed gas.

Multiphoton resonant excitation of Fermi-Dirac sea in graphene at the interaction with strong laser fields

In order to develop the microscopic theory of the multiphoton interaction of graphene with strong laser fields of arbitrary polarization, the analytical solution of established evolutionary equation for graphene single-particle density matrix was obtained revealing the generalized Rabi oscillations of Fermi-Dirac sea in the graphene. Creation of coherent superposition states of the particle-hole pairs in the graphene at the multiphoton resonant excitation by laser pulses of arbitrary polarizations and harmonics generation at the particle-hole annihilation from these superposition states are shown.

Effect of two-particle correlations on x-ray coherent diffractive imaging studies performed with continuum models

Coherent diffraction imaging (CDI) of single molecules at atomic resolution is a major goal for the x-ray free-electron lasers (XFELs). However, during an imaging pulse, the fast laser-induced ionization may strongly affect the recorded diffraction pattern of the irradiated sample. The radiation tolerance of the imaged molecule should then be investigated a priori with a dedicated simulation tool. The continuum approach is a powerful tool for modeling the evolution of irradiated large systems consisting of more than a few hundred thousand atoms. However, this method follows the evolution of average single-particle densities, and the experimentally recorded intensities reflect the spatial two-particle correlations. The information on these correlations is then inherently not accessible within the continuum approach. In this paper we analyze this limitation of continuum models and discuss the applicability of continuum models for imaging studies. We derive a formula to calculate scattered intensities (including both elastic and inelastic scattering) from the estimates obtained with a single-particle continuum model under conditions typical for CDI studies with XFELs. We demonstrate through numerical simulations that it describes the scattered signal with good accuracy. Two-particle correlation effects manifest themselves only in the region of low momentum transfers, together with the effects of the finite size of the sample. We also show that inelastic scattering on bound electrons can have a significant impact on the measured intensities: it contributes to the background that reduces the contrast of the recorded image. This effect is even more pronounced at larger momentum transfers. Therefore, whereas inelastic scattering can be neglected for nanocrystals, where Bragg scattering dominates, and in experiments imaging single objects at low resolution, it should be taken into account when planning atomic resolution imaging of nonperiodic samples. Finally, we show the effect of the electronic damage on the recorded total signal. Progressing damage does not change the positions of intensity peaks that correspond to the (fixed) positions of imaged ions. It only changes the contrast between intensity minima and maxima, which reduces the image contrast. Our results have implications for imaging-oriented studies of radiation damage performed with continuum models, as they define the limits of applicability of these models for CDI simulations.

Quantum Entanglement and Spin Control in Silicon Nanocrystal

Selective coherence control and electrically mediated exchange coupling of single electron spin between triplet and singlet states using numerically derived optimal control of proton pulses is demonstrated. We obtained spatial confinement below size of the Bohr radius for proton spin chain FWHM. Precise manipulation of individual spins and polarization of electron spin states are analyzed via proton induced emission and controlled population of energy shells in pure 29Si nanocrystal. Entangled quantum states of channeled proton trajectories are mapped in transverse and angular phase space of 29Si axial channel alignment in order to avoid transversal excitations. Proton density and proton energy as impact parameter functions are characterized in single particle density matrix via discretization of diagonal and nearest off-diagonal elements. We combined high field and low densities (1 MeV/92 nm) to create inseparable quantum state by superimposing the hyperpolarizationed proton spin chain with electron spin of 29Si. Quantum discretization of density of states (DOS) was performed by the Monte Carlo simulation method using numerical solutions of proton equations of motion. Distribution of gaussian coherent states is obtained by continuous modulation of individual spin phase and amplitude. Obtained results allow precise engineering and faithful mapping of spin states. This would provide the effective quantum key distribution (QKD) and transmission of quantum information over remote distances between quantum memory centers for scalable quantum communication network. Furthermore, obtained results give insights in application of channeled protons subatomic microscopy as a complete versatile scanning-probe system capable of both quantum engineering of charged particle states and characterization of quantum states below diffraction limit linear and in-depth resolution.PACS numbers: 03.65.Ud, 03.67.Bg, 61.85.+p, 67.30.hj

Coulomb Gap Triptych in a Periodic Array of Metal Nanocrystals

The Coulomb gap in the single-particle density of states (DOS) is a universal consequence of electron-electron interaction in disordered systems with localized electron states. Here we show that in arrays of monodisperse metallic nanocrystals, there is not one but three identical adjacent Coulomb gaps, which together form a structure that we call a "Coulomb gap triptych." We calculate the DOS and the conductivity in two- and three-dimensional arrays using a computer simulation. Unlike in the conventional Coulomb glass models, in nanocrystal arrays the DOS has a fixed width in the limit of large disorder. The Coulomb gap triptych can be studied via tunneling experiments.

Quantum Coulomb gap in low dimensions

We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two dimensions, which produce linear gaps in the density of states in both cases. We focus on the strong localization regime where the localization length is small but non-zero. We use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. We find that, with both methods, the inclusion of a finite hopping contribution does not change the linear character of the gap, but reduces its slope, widening the gap.

Atypical BCS-BEC crossover induced by quantum-size effects

Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow the size-dependent changes in the single-particle density of states. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size effects, overlooked previously. The many-body physics is revealed in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. Quantized perpendicular spectrum results in the formation of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both the BCS and BEC-like components.

Indirect Coulomb energy for two-dimensional atoms

In this paper we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.

Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave minigap in terms of the microscopic parameters of the contact. Second, we study temperature-dependence of the resistance near the superconducting transition and find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the single-particle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors. It is argued that to realize unpaired end Majorana modes, one does not necessarily need a half-metallic state, but a partial spin polarization may suffice. Finally, we propose yet another related class of material systems -- ferromagnetic semiconductor wires coupled to ferromagnetic superconductors -- where direct realization of Kitaev-Majorana model should be especially straightforward.

Elementary excitations and avalanches in the Coulomb glass

We study numerically the statistics of elementary excitations and charge avalanches in the classical Coulomb glass model of localized charges with unscreened Coulomb interaction and disorder. We compute the single-particle density of states with an energy minimization algorithm for systems of up to 1003 sites. The shape of the Coulomb gap is consistent with a power-law with exponent δ ≃ 2.4 and marginally consistent with exponential behavior. The results are also compared with a recently proposed self-consistent approach. We then analyze the size distribution of the charge avalanches produced by a small perturbation of the system. We show that the distribution decays as a power law in the limit of large system size, and explain this behavior in terms of the elementary excitations. Similarities and differences with the scale-free avalanches observed in mean-field spin glasses are discussed.

Wave chaos as signature for depletion of a Bose-Einstein condensate

We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), that is, the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as an indication for the onset of depletion of the BEC and the occupation of excited modes within a many-body description. Comparison between the multiconfigurational time-dependent Hartree for bosons method and the GPE reveals a close correspondence between the many-body effect of depletion and the mean-field effect of wave chaos for a wide range of single-particle external potentials. In the regime of wave chaos the GPE fails to account for the fine-scale quantum fluctuations because many-body effects beyond the validity of the GPE are non-negligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarse-grained expectation values of the single-particle density such as the overall width of the atomic cloud agree very well with the many-body simulations. The time-dependent depletion of the condensate could be investigated experimentally, for example, via decay of coherence of the expanding atom cloud.

Effect of nonlocal interactions on the disorder-induced zero-bias anomaly in the Anderson-Hubbard model

To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this anomaly responds to the addition of nonlocal electron-electron interactions. We use exact diagonalization to calculate the single-particle density of states of the extended Anderson-Hubbard model. We find that for weak nonlocal interactions the form of the zero-bias anomaly is qualitatively unchanged. The energy scale of the anomaly continues to be set by an effective hopping amplitude renormalized by the nonlocal interaction. At larger values of the nonlocal interaction strength, however, hopping ceases to be a relevant energy scale and higher energy features associated with charge correlations dominate the density of states.

Direct probe of the variability of Coulomb correlation in iron pnictide superconductors

We use core-valence-valence Auger spectra to probe the Coulomb repulsion between holes in the valence band of Fe pnictide superconductors. By comparing the two-hole final-state spectra to density functional theory calculations of the single-particle density of states, we extract a measure of the electron correlations that exist in these systems. Our results show that the Coulomb repulsion is highly screened and can definitively be considered as weak. We also find that there are differences between the 1111 and 122 families and even a small variation as a function of the doping $x$ in Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$. We discuss how the values of the hole-hole Coulomb repulsion obtained from our study relate to the onsite Coulomb parameter $U$ used in model and first-principles calculations based on dynamical mean field theory and establish an upper bound for its effective value. Our results impose stringent constraints on model-based phase diagrams that vary with the quantity $U$ or $U$/$W$ by restricting the latter to a rather small range of values.

Pseudogap phenomenon in an ultracold Fermi gas with ap-wave pairing interaction

We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a $T$-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature $T_{\rm c}$. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.

Theoretical interpretation of the systematics of effective single-particle level densities from (n,p) reactions at 14.8 MeV energy

The universal experimental data for the energy-integrated angular distribution and the angle-integrated energy spectra for protons emitted from the ($n$,$p$) reactions at 14.8 MeV incident energy were analyzed earlier using the computer code preco-d2, developed on the basis of Kalbach's semiempirical model for the preequilibrium reactions. The results of the analysis provided the semiempirical systematics of the single-particle level densities ${g}_{R}(\mathrm{exp})$ (effective in the residual nuclei) and ${g}_{c}(\mathrm{exp})$ (effective in the composite system). In order to interpret these results, we have carried out the theoretical calculations with Shlomo's theory developed on the basis of the Green's function approach. The theoretical values based on Shlomo's theory for ${g}_{Rn}^{Th}({\ensuremath{\varepsilon}}_{Rn})$ and ${g}_{Rp}^{Th}({\ensuremath{\varepsilon}}_{Rp})$ for the residual nucleus and ${g}_{cn}^{Th}({\ensuremath{\varepsilon}}_{cn})$ and ${g}_{cp}^{Th}({\ensuremath{\varepsilon}}_{cp})$ for the composite systems, respectively, were calculated at various excitation energies by using a reasonable single-particle nuclear potential strength ${V}_{0}$, available from systematics in literature. Here, ${\ensuremath{\varepsilon}}_{Rn}$ and ${\ensuremath{\varepsilon}}_{Rp}$ are the single-particle excitation energies for single-particle level densities for the residual nucleus, and ${\ensuremath{\varepsilon}}_{cn}$ and ${\ensuremath{\varepsilon}}_{cp}$ are the single-particle excitation energies of effective single-particle level densities for the composite system for neutrons and protons, respectively. The Coulomb interaction potential ${V}_{c}$ was included for protons over and above the nuclear potential ${V}_{0}$. The total theoretical values were taken as ${g}_{R}^{TTh}({\ensuremath{\varepsilon}}_{R})={g}_{Rn}^{Th}({\ensuremath{\varepsilon}}_{Rn})+{g}_{Rp}^{Th}({\ensuremath{\varepsilon}}_{Rp})$ for residual nuclei and ${g}_{c}^{TTh}({\ensuremath{\varepsilon}}_{c})={g}_{cn}^{Th}({\ensuremath{\varepsilon}}_{cn})+{g}_{cp}^{TTh}({\ensuremath{\varepsilon}}_{cp})$ for the composite system. ${\ensuremath{\varepsilon}}_{R}$ is the Fermi energy of the total effective single-particle level density for residual nuclei, and ${\ensuremath{\varepsilon}}_{c}$ is the excitation energy of the effective single-particle level density of the composite system. Careful comparison of theoretical and experimental results shows that ${g}_{R}(\mathrm{exp})$ matches with ${g}_{R}^{TTh}({\ensuremath{\varepsilon}}_{f})$ for ${V}_{0}^{i}=45\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}\phantom{\rule{4pt}{0ex}}\mathrm{where}\phantom{\rule{4pt}{0ex}}({\ensuremath{\varepsilon}}_{f})\phantom{\rule{4pt}{0ex}}\text{is}\phantom{\rule{4.pt}{0ex}}\text{the}\phantom{\rule{4.pt}{0ex}}\text{Fermi}\phantom{\rule{4.pt}{0ex}}\text{energy}.$ The theoretical values ${g}_{R}^{TTh}({\ensuremath{\varepsilon}}_{f})$ also nearly agree with the previously reported values by various groups, obtained through different approaches for a large number of cases. The values of ${g}_{c}(\mathrm{exp})$ always are found to be greater than ${g}_{R}(\mathrm{exp})$ and match with ${g}_{c}^{TTh}({\ensuremath{\varepsilon}}_{c})$ at effective excitation energies ${\ensuremath{\varepsilon}}_{c}$, which are found to be invariably much higher than the respective ${\ensuremath{\varepsilon}}_{f}$ and are positive and follow the nuclear shell model structure when plotted against $A$. This supports the concept that the values of effective ${g}_{c}(\mathrm{exp})$ are decided mainly by dominant transition, which occurs during initial stages of the multistep statistical direct preequilibrium process that involves unbound states. The values of ${g}_{R}(\mathrm{exp})$, on the other hand, are found to correspond to the effective ${\ensuremath{\varepsilon}}_{R}$ around the Fermi energies of the bound states of residual nuclei involved in the decay processes. The ratios of ${g}_{c}(\mathrm{exp})/{g}_{R}(\mathrm{exp})$ are found to follow the ${(\frac{\ensuremath{\langle}{\ensuremath{\varepsilon}}_{c}\ensuremath{\rangle}}{\ensuremath{\langle}{\ensuremath{\varepsilon}}_{f}\ensuremath{\rangle}})}^{1/\phantom{\rule{0.0pt}{0ex}}2}f$ description and to match Shlomo's theory.

A New Estimate on the Two-Dimensional Indirect Coulomb Energy

We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with a smaller constant, C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 < C_{LSY}= 192\sqrt{2 \pi} \approx 481.27, which also involves an additive gradient energy term of the single particle density.

Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation

Nonlinear dynamics of the establishment of electron-hole coherent superposition states in graphene by multiphoton resonant excitation of interband transitions in laser fields is considered. The single-particle time-dependent density matrix for such a quantized system is calculated in the multiphoton resonant approximation. The dependence of Rabi oscillations of the Fermi-Dirac sea in graphene on the time, momentum, and photon number at multiphoton laser excitation is analyzed.

Character of valence-band states in the Kondo surface alloys CeAgx/Ag(111) and CePt5/Pt(111)

The crystal and electronic structures of the CePt${}_{5}$ and CeAg${}_{x}$ surface alloys have been investigated by means of low-energy electron diffraction and angle-resolved photoelectron spectroscopy. From measurements performed near the $4d$-$4f$ absorption edge we were able to infer the weight of the $4f$-electron spectral function with respect to the single-particle density of states. While the typical Kondo features at the Fermi energy (Kondo resonance and spin-orbit partner) in the CePt${}_{5}$ surface alloy were observed, only the ${f}^{0}$ ionization structure and the spin-orbit partner were present in the CeAg${}_{x}$ case. From our experiments, and by comparison to model calculations, we were able to estimate the Kondo temperature in the two systems and investigate parameters contributing to the hybridization strength.

Observations of plasmarons in a two-dimensional system: Tunneling measurements using time-domain capacitance spectroscopy

Calculations of the single-particle density of states (SPDOS) of electron liquids have long predicted that there exist two distinct charged excitations: the usual quasiparticle consisting of an electron or hole, and a plasmaron consisting of a hole resonantly bound to real plasmons in the Fermi sea. Using tunneling spectroscopy to measure the SPDOS of a 2D electronic system, we demonstrate the detection of a plasmaron in a 2D system in which electrons have mass. With the application of a magnetic field we discover unpredicted magnetoplasmarons which resemble Landau levels with a negative index.