Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p_x+ip_y. Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p_x+ip_y-wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a “nonrelativistic defect conformal field theory (CFT)”. The reduced Schrödinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.     

Exact results of a dimerized S=1 Ising chain with single-ion anisotropy

The dimerized spin-1 Ising chain with both longitude and transverse single-ion anisotropies D_z and D_x is solved exactly by means of a mapping to the spin- Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles’ spectra Λ_k, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole, and the ground-state energy E_g are obtained. The phase diagram of the ground state is also given. The results show that the system exhibits a series of quantum phase transitions depending on the dimerization strength of the crystal fields, while the quantum critical points are determined exactly.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

d-Wave superconductivity via buckling-like phonon mode

We follow the classic strong-coupling theory of superconductivity through electron-phonon interaction with a buckling-like phonon mode. We find a nonzero d-wave order parameter in the sense of the Eliashberg theory. We derive a zero temperature gap Δ(0,π) at the gap edge versus the electron-phonon coupling strength g² relation. We find that large enough value for Δ(0,π) as compared to those of high-T_c superconductors cannot be realized in the electron-buckling-like-phonon coupling on the CuO₂ planes.     

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.     

Coulomb repulsion-induced hyperbolic pairing as a mechanism of high-T c superconductivity

The hyperbolic metric of the dispersion law (the effective mass tensor components of carriers are opposite in sign) in the vicinity of the Fermi contour in high-T _c superconducting cuprates in the case of repulsive interaction gives rise to a superconducting state characterized by the condensate of pairs with a large total momentum (hyperbolic pairing). The gain in the energy of the superconducting state over the normal state is due to the fact that a change in the kinetic energy of pairs (because of the negative light component of the effective mass) dominates over the change in the potential energy (corresponding to energy loss). The shift of the chemical potential upon the transition to the superconducting phase is substantial in this case. With increasing repulsive interaction, the superconducting gap δ_K increases and the resulting gain in energy changes to an energy loss at a certain critical value of the repulsive potential. The low temperature T _c of the superconducting transition and the large value of δ _K in this region of potential values are the reasons for the high value of the 2δ_K/T _c ratio and for the developed quantum fluctuations that are observed in underdoped cuprate superconductors.     

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ(ω) = (iωL)^?1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ^?1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.     

Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.     

Renormalization group approach to a p-wave superconducting model

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.     

ZN Gauge theories on a lattice and quantum memory

In the present paper we shall study (2+1)-dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev’s model for quantum memory and quantum computations. Then we study effects of random gauge couplings (RGC) which are identified with noise and errors in quantum computations by Kitaev’s model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Cubic helimagnets in magnetic field and at pressure

Cubic helimagnets with B20 structure display several unusual properties such as anisotropy of the spin-wave spectrum al small momenta q, rotation of the helix vector k in magnetic field and quantum phase transition at pressure. We demonstrate that first two phenomena are a result of umklapp processes mixing excitations with momenta q, q+k and q−k. At very low magnetic field perpendicular to k the helical structure remains stable due to spin-wave gap Δ. Its square is sum of two parts. The first one is a result of the magnon interaction and the second negative part stems from magneto-elastic interaction. It is suggested that competition between these parts leads to the quantum phase transition observed in MnSi and FeGe. For MnSi from rough estimations at ambient pressure was shown that both parts are comparable with the experimentally observed gap. The magneto-elastic interaction is also responsible for 2k modulation of the lattice and contributes to the magnetic anisotropy. Experimental observation by X-ray and neutron scattering of this lattice modulation allows to determine the strength of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.     

Microscopic origin of collective exponentially small resistance states

The formation of ‘zero’ (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and subjected to strong microwave (MW) radiation has attracted great theoretical interest. These states appear to be associated with a new kind of energy gap Δ. Here I show that the energy gap Δ is explained by a microscopic quantum model that involves the Prime Number Theorem, hitherto reserved for only mathematical contexts. The model also contains the zeroes of the zeta function, and explains the physical origin of the Riemann hypothesis.     

Temperature and junction-type dependency of Andreev reflection in MgB2

We studied the voltage and temperature dependency of the dynamic conductance of normal metal-MgB₂ junctions obtained either with the point-contact technique (with Au and Pt tips) or by making Ag-paint spots on the surface of MgB₂ samples. The fit of the conductance curves with the generalized BTK model gives evidence of pure s-wave gap symmetry. The temperature dependency of the gap, measured in Ag-paint junctions (dirty limit), follows the standard BCS curve with 2Δ/k_BT_c=3.3. In out-of-plane, high-pressure point-contacts we obtained almost ideal Andreev reflection characteristics showing a single small s-wave gap Δ=2.6±0.2 meV (clean limit).     

A pilgrimage through superheavy valley

We searched for the shell closure proton and neutron numbers in the superheavy region beyond Z = 82 and N = 126 within the framework of non-relativistic Skryme–Hartree–Fock (SHF) with FITZ, SIII, SkMP and SLy4 interactions. We have calculated the average proton pairing gap Δ_p, average neutron pairing gap Δ_n, two-nucleon separation energy S _2q and shell correction energy E _shell for the isotopic chain of Z = 112–126. Based on these observables, Z = 120 with N = 182 is suggested to be the magic numbers in the present approach.     

Impurity induced resonance states at the superconducting interface LaAlO3/SrTiO3

Motivated by the recent discovery of superconductivity on the heterointerface LaAlO₃/SrTiO₃, we theoretically investigate the impurity-induced resonance states with coexisting spin singlet s- and triplet p-wave pairing symmetries by considering the influence of Rashba-type spin-orbit interaction (RSOI). Due to the nodal structure of the mixed gap function, we find single nonmagnetic impurity-induced resonance peaks appearing in the local density of state. We also analyze the evolutions of density of states and local density of states with the weight of triplet pairing component determined by the strength of RSOI, which will be widely observed in thin films of superconductors with surface or interface-induced RSOI, or various noncentrosymmetric superconductors in terms of point contact tunneling and scanning tunneling microscopy, and thus shed light on the admixture of the spin singlet and RSOI-induced triplet superconducting states.     

High-resolution photoemission study of FeSr2YCu2O7+δ

We have performed high-resolution photoemission spectroscopy (PES) on FeSr₂YCu₂O_7+δ, of which superconductivity of T_c=49 K was recently reported. We clearly observed opening of a d-wave-like superconducting gap and estimated the maximum gap value (Δ_max) to be 10 meV at 15 K. This gap value gives 2Δ_max/k_BT_c∼5, suggesting a strong-coupling nature of superconductivity in FeSr₂YCu₂O_7+δ. Comparative PES study with superconducting and insulating samples shows that the valence band is rigidly shifted as a function of doping without evolution of additional states within the insulating gap.     

Electronic structure of BN nanotubes with intrinsic defects NB and BN and isoelectronic substitutional impurities PN, AsN, SbN, InB, GaB, and AlB

The effect of intrinsic defects and isoelectronic substitutional impurities on the electronic structure of boron-nitride (BN) nanotubes is investigated using a linearized augmented cylindrical wave method and the local density functional and muffin-tin approximations for the electron potential. In this method, the electronic spectrum of a system is governed by a free movement of electrons in the interatomic space between cylindrical barriers and by a scattering of electrons from the atomic centers. Nanotubes with extended defects of substitution N_B of a boron atom by a nitrogen atom and, vice versa, nitrogen by boron B_N with one defect per one, two, and three unit cells are considered. It is shown that the presence of such defects significantly affects the band structure of the BN nanotubes. A defect band π(B, N) is formed in the optical gap, which reduces the width of the gap. The presence of impurities also affects the valence band: the widths of s, sp, and p_π bands change and the gap between s and sp bands is partially filled. A partial substitution of the N by P atoms leads to a decrease in the energy gap, to a separation of the Ds(P) band from the high-energy region of the s(B, N) band, as well as to the formation of the impurity Dπ(P) and Dπ*(P) bands, which form the valence-band top and conduction-band bottom in the doped system. The influence of partial substitution of N atoms by the As atom on the electronic structure of BN nanotubes is qualitatively similar to the case of phosphorus, but the optical gap becomes smaller. The optical gap of the BN tubule is virtually closed due to the effect of one Sb atom impurity per translational unit cell, in contrast to the weak indium-induced perturbation of the band structure of the BN nanotube. Introduction of the one In, Ga or Al atom per three unit cells of the (5, 5) BN nanotube results in 0.6 eV increase of the optical gap. The above effects can be detected by optical and photoelectron spectroscopy methods, as well as by measuring electrical properties of the pure and doped BN nanotubes. They can be used to design electronic devices based on BN nanotubes.     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.