S-wave pairing in a two-orbital t-J model on triangular lattice: possible application to Pb10−x_{10-x}Cux_x(PO4_4)6_6O

Recently room temperature superconductor was claimed in Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O (also known as LK-99) with $x\in (0.9,1.1)$. Density functional theory (DFT) calculations suggest that the conduction electrons are from the doped Cu atoms with valence close to $d^{9}$. Motivated by this picture, we build a two-orbital Hubbard model on a triangular lattice formed by the $d_{xz}$ and $d_{yz}$ orbitals with total hole density (summed over spin and orbital) $n=1-p$. When $p=0$, the system is in a Mott insulator within this model. When $p>0$, we derive a $t-J$ model and perform a self-consistent slave boson mean field calculation. Interestingly we find a s-wave pairing in contrast to the one-orbital t-J model which favors $d+id$ pairing. S wave pairing should be more robust to disorder and may lead to high Tc superconductor with sufficiently large values of $t$ and $J$. However, the DFT calculations predict a very small value of $t$ and then the $T_c$ is expected to be small. If LK99 is really a high Tc superconductor, ingredients beyond the current model are needed. We conjecture that the doped Cu atoms may distort the original lattice and form local clusters with smaller Cu -Cu distance and thus larger values of $t$ and $J$. Within these clusters, we may locally apply our t-J model calculation and expect high Tc s-wave superconductor. Then the superconducting islands couple together, which may eventually become a global superconductor, an insulator or even an anomalous metal depending on sample details.Comment: 6 pages, 2 figure

Type II t-J model and shared antiferromagnetic spin coupling from Hund's rule in superconducting La3_3Ni2_2O7_7

Recently a 80 K superconductor was observed in La$_3$Ni$_2$O$_7$ under high pressure. Density function theory (DFT) calculations identify $d_{x^2-y^2}$ and $d_{z^2}$ as two active orbitals and a bilayer square lattice structure. The averange valence of Ni is $d^{8-x}$ with $x=0.5$ per site. Naively one may expect a description in terms of a two-orbital t-J model. However, there should be significant inter-orbital repulsion $U'$ and Hund's coupling $J_H$ larger than the bare value of $t$ and $J$. Especially the Hund's coupling can share the inter-layer super-exchange $J_\perp$ of $d_{z^2}$ to $d_{x^2-y^2}$, an effect beyond any perturbative and mean field treatment. In the limit that $d_{z^2}$ is Mott localized, we integrate it out and deal with a bialyer t-J model for $d_{x^2-y^2}$ only. We find strong inter-layer pairing due to the transmitted $J_\perp$ which can survive to $50\%$ hole doping relevant to the experiment. In real system we expect that $d_{z^2}$ orbital will also be slightly hole doped and can not be simply ignored. To deal with this situation, we take the $J_H\rightarrow +\infty$ limit and propose a type II t-J model with four singlon ($d^7$) states and three spin-triplet doublon ($d^8$) states. Through a parton mean field treatment of the constrained Hilbert space, we derive the bilayer one-orbital t-J model for an emergent `$d_{x^2-y^2}$' orbital with significant $J_\perp$, justifying our phenomenological treatment. The type II t-J model can also describe the regime where the $d_{z^2}$ orbital is also slightly hole doped through tuning an orbital energy splitting $\Delta$. From our calculation the pairing strength decreases with the hole doping $x$ and $x=0.5$ is likely larger than the optimal doping. We propose future experiments to electron dope the system to further enhance $T_c$.Comment: 5 pages, 2 figures, 1 tabl

Strong pairing from small Fermi surface beyond weak coupling: Application to La3_3Ni2_2O7_7

The studies of high-temperature superconductors raise a fundamental question: Can a small Fermi surface phase, which violates the Luttinger theorem, exist and give rise to superconductivity? Our work provides a positive answer through a controlled theory based on a bilayer model with strong inter-layer spin-spin coupling ($J_\perp$) but no inter-layer hopping ($t_\perp$). Then small hole doping of the rung-singlet insulator with two electrons per rung naturally leads to small hole pockets with Fermi surface volume per flavor smaller than the free fermion result by $1/2$ of the Brillouin zone(BZ). We construct a new t-J model on a bilayer square lattice, so called ESD t-J model and employ a generalized slave boson theory, which captures this small Fermi surface phase at small hole doping $x$. This metallic state is an intrinsically strongly correlated Fermi liquid beyond weak coupling theory, violating the perturbative Luttinger theorem but consistent with the Oshikawa's non-perturbative proof. We further show that it transitions into an inter-layer paired $s'$-wave superconductor at lower temperature through Feshbach resonance with a virtual Cooper pair, with a surprising doping-induced crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) at higher hole doping levels. This leads to a superconducting dome centered around $x=0.5$, with the normal state changing from the conventional Fermi liquid in the $x>0.5$ to the unusual small Fermi surface state in the $x<0.5$ side. Our theoretical findings including phase diagrams are also confirmed by density matrix renormalization group (DMRG) simulation in quasi one dimension. Applying our theoretical framework, we provide a plausible scenario for the recently found nickelate La$_3$Ni$_2$O$_7$ materials.Comment: 11+13 pages, 8+13 figur

Extended states in 1D lattices: application to quasiperiodic copper-mean chain

The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [ You et al. (1991)] : we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.Comment: 10 pages + 2 figures available on request; LaTeX version 2.0

Duality and Enhanced Gauge Symmetry in 2+1 Dimensions

We investigate the enlarged CP(N) model in 2+1 dimensions. This is a hybrid of two CP(N) models coupled with each other in a dual symmetric fashion, and it exhibits the gauge symmetry enhancement and radiative induction of the finite off-diagonal gauge boson mass as in the 1+1 dimensional case. We solve the mass gap equations and study the fixed point structure in the large-N limit. We find an interacting ultraviolet fixed point which is in contrast with the 1+1 dimensional case. We also compute the large-N effective gauge action explicitly.Comment: 26 pags, latex, 5 .eps figures, typos corrected. To appear in J. Phys.

Prospects for terahertz imaging the human skin cancer with the help of gold-nanoparticles-based terahertz-to-infrared converter

The design is suggested, and possible operation parameters are discussed, of an instrument to inspect a skin cancer tumour in the terahertz (THz) range, transferring the image into the infrared (IR) and making it visible with the help of standard IR camera. The central element of the device is the THz-to-IR converter, a Teflon or silicon film matrix with embedded 8.5 nm diameter gold nanoparticles. The use of external THz source for irradiating the biological tissue sample is presumed. The converter's temporal characteristics enable its performance in a real-time scale. The details of design suited for the operation in transmission mode (in vitro) or on the human skin in reflection mode {in vivo) are specified.Comment: To be published in the proceedings of the FANEM2018 workshop - Minsk, 3-5 June 201

Effects of the field modulation on the Hofstadter's spectrum

We study the effect of spatially modulated magnetic fields on the energy spectrum of a two-dimensional (2D) Bloch electron. Taking into account four kinds of modulated fields and using the method of direct diagonalization of the Hamiltonian matrix, we calculate energy spectra with varying system parameters (i.e., the kind of the modulation, the relative strength of the modulated field to the uniform background field, and the period of the modulation) to elucidate that the energy band structure sensitively depends on such parameters: Inclusion of spatially modulated fields into a uniform field leads occurrence of gap opening, gap closing, band crossing, and band broadening, resulting distinctive energy band structure from the Hofstadter's spectrum. We also discuss the effect of the field modulation on the symmetries appeared in the Hofstadter's spectrum in detail.Comment: 7 pages (in two-column), 10 figures (including 2 tables

Gauge Symmetry Enhancement and Radiatively Induced Mass in the Large N Nonlinear Sigma Model

We consider a hybrid of nonlinear sigma models in which two complex projective spaces are coupled with each other under a duality. We study the large N effective action in 1+1 dimensions. We find that some of the dynamically generated gauge bosons acquire radiatively induced masses which, however, vanish along the self-dual points where the two couplings characterizing each complex projective space coincide. These points correspond to the target space of the Grassmann manifold along which the gauge symmetry is enhanced, and the theory favors the non-Abelian ultraviolet fixed point.Comment: 11 pages, REVTEX, typos are corrected, version to appear in Phys. Rev.

Persistent Current From the Competition Between Zeeman Coupling and Spin-Orbit Interaction

Applying the non-adiabatic Aharonov-Anandan phase approach to a mesoscopic ring with non-interacting many electrons in the presence of the spin-orbit interaction, Zeeman coupling and magnetic flux, we show that the time-reversal symmetry breaking due to Zeeman coupling is intrinsically different from that due to magnetic flux. We find that the direction of the persistent currents induced by the Zeeman coupling changes periodically with the particle number, while the magnetic flux determines the direction of the induced currents by its sign alone.Comment: 5 pages, ReVTeX, including 3 figures on request,Submitted to Phys.Rev.Let

Astrometry of Water Maser Sources in Nearby Molecular Clouds with VERA - II. SVS 13 in NGC 1333

We report on the results of multi-epoch VLBI observations with VERA (VLBI Exploration of Radio Astrometry) of the 22 GHz H2O masers associated with the young stellar object SVS 13 in the NGC 1333 region. We have carried out phase-referencing VLBI astrometry and measured an annual parallax of the maser features in SVS 13 of 4.25+/-0.32 mas, corresponding to the distance of 235+/-18 pc from the Sun. Our result is consistent with a photometric distance of 220 pc previously reported. Even though the maser features were detectable only for 6 months, the present results provide the distance to NGC 1333 with much higher accuracy than photometric methods. The absolute positions and proper motions have been derived, revealing that the H2O masers with the LSR (local standard of rest) velocities of 7-8 km s-1 are most likely associated with VLA4A, which is a radio counterpart of SVS 13. The origin of the observed proper motions of the maser features are currently difficult to attribute to either the jet or the rotating circumstellar disk associated with VLA4A, which should be investigated through future high-resolution astrometric observations of VLA4A and other radio sources in NGC 1333.Comment: 9 pages, 5 figures. PASJ, in press (2008, Vol. 60, No. 1