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We theoretically investigate the resonant inelastic X-ray scattering (RIXS) spectra in a quasi-1D chain of weakly coupled frustrated spin-1/2 trimers, as realized in Na$_{2}$Cu$_{3}$Ge$_{4}$O$_{12}$, with Cu $d^{9}$ 1/2 spins. We compute multi-spin correlations contributing to spin-conserving (SC) and spin non-conserving (NSC) RIXS cross-sections using ultra-short core-hole lifetime expansion within the Kramer-Heisenberg formalism. These excitations involve flipping spins of up to three spin-1/2 trimers and include the inelastic neutron scattering (INS) single spin-flip excitations in the lowest order of the NSC channel. We identify the fractionalization of two coupled frustrated trimers in terms of spinons, doublons, and quartons in the spectra evaluated using exact diagonalization, complementing prior studies single spin-spin flip excitation in inelastic neutron scattering. Specifically, we uncover two new high-energy modes at $\omega \approx 2.4J_1$ and $3.0 J_1$ in the NSC and SC channels that are accessible at the Cu $K$-edge and $L$-edge RIXS spectra, which were missing in the INS study. This, therefore, provides pathways to uncover all the possible excitations in coupled trimers. Our work opens new opportunities for understanding the nature of fractionalization and RIXS spectra of frustrated, low-dimensional spin chains.

Understanding the interplay of strong correlation and temperature in nodal-line semimetals can offer novel ways to control spin currents. Here we consider the 3d-5d double-perovskite Ba$_{2}$CoWO$_{6}$, which features mirror-symmetry-protected nodal-lines, strong Co-site interactions, and spin-orbit coupling (SOC) at W sites. Our first principles and exact diagonalization results reveal a half-metallic ground state with high-spin Co and topologically non-trivial bands. We demonstrate that SOC gaps out nodal points, causes band-inversion and generates anomalous Hall response. A semi-classical Monte Carlo finite-temperature simulation of five-orbital Hubbard model uncovers an emergent Co-spin scalar chirality and colossal positive transverse-magnetoresponse. We predict the temperature and magnetic field scales for the tunability of scalar-chirality and magnetoresponse.

Using unbiased Monte Carlo simulations and variational analysis, we present the ground state and finite temperature phase diagrams of an exactly solvable spin-orbital model with Kitaev-type interactions on a square lattice. We show that an array of new gapped and gapless vison crystals -- characterized by the periodic arrangement of $\mathbb{Z}_2$ flux excitations -- can be stabilized as a function of external magnetic field and exchange anisotropy. In particular, we discover a variety of `quarter phases' wherein new sixteen-site periodic patterns emerge, with only a quarter of the fluxes adopting 0-flux configurations. In contrast, the rest remain in $\pi$-flux configurations. Vison crystals break translational symmetry and undergo finite temperature phase transitions. We investigate the finite temperature properties of these phases and report the corresponding critical and crossover temperatures. Our results reveal an array of novel phases in exactly solvable extensions of the Kitaev model, wherein local and topological orders can coexist.

Resonant inelastic x-ray spectroscopy (RIXS) has emerged as an important tool to explore magnetism in two-dimensional (2D) antiferromagnet realized in strongly correlated materials. Here we consider the Heisenberg model with nearest and next nearest neighbor hopping relevant to the study of magnetic excitations of the cuprate family. We compute the RIXS cross-section within the ultra-short core-hole lifetime (UCL) expansion of the Kramers-Heisenberg scattering amplitude that allows perturbative solution within linear spin wave theory (LSWT). We report detailed results for both spin-conserving and non-conserving channels. Apart from the widely discussed single magnon and bimagnon contributions, we show that three-magnon contributions in the spin non-conserving channel are useful to explain certain features of the RIXS data for two-dimensional cuprates. We confirm the qualitative correctness of the LSWT conclusions for the three-magnon excitation with exact diagonalization. Our work puts constraints on the dispersion of the three-magnon in the Brillouin zone, opening new avenues for realizing higher modes of quasiparticles using RIXS.

A fundamental roadblock to the exact numerical solution of many-fermion problems is the exponential growth of the Hilbert space with system size. It manifests as extreme dynamical memory and computation-time requirements for simulating many-fermion processes. Here we construct a novel reorganization of the Hilbert space to establish that the exponential growth of dynamical-memory requirement is suppressed inversely with system size in our approach. Consequently, the state-of-the-art resolvent computation can be performed with substantially less memory. The memory-efficiency does not rely on Hamiltonian symmetries, sparseness, or boundary conditions and requires no additional memory to handle long-range density-density interaction and hopping. We provide examples calculations of interacting fermion ground state energy, the many-fermion density of states and few-body excitations in interacting ground states in one and two dimensions.

We investigate the impact of site dilution by setting the on-site repulsion strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach first to recover the zero dilution (undiluted $x=1$) properties, including $U$ dependence of insulator to metal crossover temperature scale $T^*$ and long-range staggered antiferromagnetic ordering temperature ($T_N$). For the non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of $T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At $x \leq 0.7$, $T^*$ and $T_N$ coincide and are suppressed together with further increase in site-dilution. Finally, the system loses the magnetic order and the insulating state for $x=0.15$, significantly below the classical percolation threshold $x_p^{sc} (\sim 0.31$). We show that the induced moments on $U=0$ sites drive the magnetic order below the classical percolation limit by studying local moment systematics and finite-size analysis of magnetic order. At the end, we show that either increasing $U$ to large values or raising temperature beyond a $U$ dependent critical value, suppresses the induced local moments of the $U=0$ sites and recovers the classical percolation threshold., Comment: 7 pages including supplementary information

As a minimal model to study charge transfer effects in a transition metal (TM) and Oxygen (OX) chain, we consider a one-dimensional chain with spinless fermion with an alternating motif of site-pairs with nearest neighbor (NN) repulsion $U$ and uncorrelated site-pairs, separated by a charge transfer gap $\Delta$. We first show that while two holes added in a filled band of NN interacting fermion in one dimension can stabilize to a two-hole bound pair, the bound pair delocalizes with a $U$-dependent bandwidth. In contrast, we establish that the bandwidth of two holes added on a TM site-pair in a filled band is dramatically suppressed, realizing a `local' two-hole resonance (L2HR) at the same TM site-pair mimicking the AES phenomenology. Employing a memory-efficient exact numerical scheme and standard Lanczos-based diagonalization, we then study two-hole spectra for holes added at TM site-pairs in partially filled bands. We analyze the multiple features that arise in the two-hole spectra at partial filling of the ground state. We uncover that in the strong $U$ limit, there is a filling-dependent $\Delta_{crit}$ above which the L2HR remains stable for any band-filling greater than 75\%. In this regime, the energy location of the L2HR provides a direct estimate of the correlation strength at TM site-pairs for partial filling and is reminiscent of the Cini-Sawatzky theory for the filled band case. At 75\% band-filling, an abrupt redistribution of two-hole spectral weight destroys the L2HR regardless of $U$ or $\Delta$ values. We discuss the relevance of these nonperturbative results, obtained with full lattice symmetry, for understanding AES of partially filled bands in terms of the local-two-hole spectrum.

Sustaining exotic quantum mechanical phases at high temperatures is a long-standing goal of condensed matter physics. Among them, half-metals are spin-polarized conductors that are essential for realizing room-temperature spin current sources. However, typical half-metals are low-temperature phases whose spin polarization rapidly deteriorates with temperature increase. Here, we first show that a low-temperature insulator with an unequal charge gap for the two spin channels can arise from competing Mott and band insulating tendencies. We establish that thermal fluctuations can drive this insulator to a half-metal through a first-order phase transition by closing the charge gap for one spin channel. This half-metal has 100% spin polarization at the onset temperature of metallization. Further, varying the strength of electron repulsion can enhance the onset temperature while preserving spin polarization. We outline experimental scenarios for realizing this tunable finite temperature half-metal., Comment: Published version

A triangular lattice with onsite Coulomb interaction $U$ present only on one sub-lattice, is periodically driven by electromagnetic field with a frequency $\Omega \gg (t,~U)$ at half filling. In this high frequency limit, the electromagnetic vector potential, with an amplitude $A$, modifies the bare hopping and generates new next nearest neighbour hopping parameters. For $U=0$, the driving acts like an emergent intrinsic spin-orbit coupling term and stabilises three dispersive bands with the lower and upper bands having non zero Chern numbers. Within a slave rotor mean field theory, we show that while $U$ freezes out charge fluctuations on the interacting sub-lattice, it does not open up a charge gap without the external drive. In presence of the drive, and small $U$, the system exhibits repeated metal insulator transitions as a function of the amplitude $A$. For large $U$, we establish that the freezing of charge fluctuations on the interacting sub-lattice stabilizes an emergent, low energy \textit{half filled non-interacting Kane-Mele model}, whose band gaps can be tuned by varying $A$. In this limit, we show that the external drive provides an handle to engineer periodic band inversions at specific values of $A$ accompanied by topological phase transitions that are characterised by swapping of band Chern numbers., Comment: This is the published version

The Lieb lattice possesses three bands and with intrinsic spin orbit coupling $\lambda$, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction $U$ on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength ($U_{crit}$), creating a correlated flat band insulator. Beyond $U_{crit}$, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of $U$ introduced only on one sublattice where $\lambda=0$, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator., Comment: This is the published version

We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction ($U$), in presence of (frustrating) next nearest neighbor hopping ($t^{\prime}$) using a semiclassical approximation scheme. We show that introduction of $t^{\prime}$ results in a finite temperature pseudogapped (PG) phase that separates the small $U$ Fermi liquid and large $U$ Mott insulator. We map out the PG to normal metal crossover temperature scale ($T^*$) as a function of $U$ and $t^\prime$. We demonstrate that in the PG phase, the quadratic dependence of resistivity on temperature is violated due to thermally induced spin fluctuations. We conclude with exact diagonalization calculations, that complement our finite temperature results, and indicate the presence of a frustration driven PG state between the Fermi liquid and the Mott insulator at zero temperature as well.

We propose the concept of "hybridization-switching induced Mott transition" which is relevant to a broad class of ABO$_3$ perovskite materials including BiNiO$_3$ and PbCrO$_3$ which feature extended $6s$ orbitals on the A-site cation (Bi or Pb), and A-O covalency induced ligand holes. Using {\it ab initio} electronic structure and slave rotor theory calculations, we show that such systems exhibit a breathing phonon driven A-site to oxygen hybridization-wave instability which conspires with strong correlations on the B-site transition metal ion (Ni or Cr) to induce a Mott insulator. These Mott insulators with active A-site orbitals are shown to undergo a pressure induced insulator to metal transition accompanied by a colossal volume collapse due to ligand hybridization switching., Comment: 6 pgs, 4 figs, published version

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation ($U$) and disorder ($V$) strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling $T^{\alpha}$ for this metal reveals non Fermi liquid characteristics. Moreover, a continuous dependence of $\alpha$ on $U$ and $V$ from linear to nearly quadratic was observed. We argue that these exotic results arise from a systematic change with $U$ and $V$ of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

Employing a recently developed many-body technique that allows for the incorporation of thermal effects, the rich phase diagram of a two dimensional two orbital (degenerate $d_{xz}$ and $d_{yz}$) Hubbard model is presented varying temperature and the repulsion $U$. Our main result is the finding at intermediate $U$ of a novel antiferromagnetic orbital selective state where an effective dimensional reduction renders one direction insulating and the other metallic. Possible realizations of this state are discussed. In addition we also study nematicity above the N\'eel temperature. After a careful finite-size scaling analysis the nematicity temperature window appears to survive in the bulk limit although it is very narrow.

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically refereed to as the "spins", are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED+MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "Traveling Cluster Approximation" (TCA) is a real space variant of the ED+MC method that allows to solve spin-fermion problems on lattice sizes with up to $10^3$ sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on $10^4$ lattice sites and with some effort on $10^5$ lattice sites, representing the record lattice sizes studied for this family of models.

The canonical one-band Hubbard model is studied using a computational method that mixes the Monte Carlo procedure with the mean field approximation. This technique allows us to incorporate thermal fluctuations and the development of short-range magnetic order above ordering temperatures, contrary to the crude finite-temperature Hartree-Fock approximation, which incorrectly predicts a N\'eel temperature $T_N$ that grows linearly with the Hubbard $U/t$. The effective model studied here contains quantum and classical degrees of freedom. It thus belongs to the "spin fermion" model family widely employed in other contexts. Using exact diagonalization, supplemented by the traveling cluster approximation, for the fermionic sector, and classical Monte Carlo for the classical fields, the Hubbard $U/t$ vs. temperature $T/t$ phase diagram is studied employing large three and two dimensional clusters. We demonstrate that the method is capable of capturing the formation of local moments in the normal state without long-range order, the non-monotonicity of $T_N$ with increasing $U/t$, the development of gaps and pseudogaps in the density of states, and the two-peak structure in the specific heat. Extensive comparisons with determinant quantum Monte Carlo results suggest that the present approach is qualitatively, and often quantitatively, accurate, particularly at intermediate and high temperatures. Finally, we study the Hubbard model including plaquette diagonal hopping (i.e. the $t-t^\prime$ Hubbard model) in two dimensions and show that our approach allows us to study low temperature properties where determinant quantum Monte Carlo fails due to the fermion sign problem. Future applications of this method include multi-orbital Hubbard models such as those needed for iron-based superconductors.

Using Monte Carlo simulations with a tunable uniaxial strain, for the first time the nematic susceptibility of a model for the pnictides is calculated. The results are in good agreement with the experiments by J-H. Chu {\it et al.}, Science {\bf 337}, 710 (2012). Via a Ginzburg-Landau analysis, our study suggests a nematicity in pnictides primarily originating on magnetism, but with the lattice/orbital boosting up critical temperatures and separating the structural $T_S$ and N\'eel $T_N$ transitions. At $T>T_S$, Curie-Weiss behavior is observed with the characteristic temperature $T^*$ unveiled by Chu {\it et al.} being the $T_N$ of the purely electronic system. In this temperature regime, short-range magnetic order with wavevectors $(\pi,0)-(0,\pi)$ induce local nematic fluctuations and a density-of-states pseudogap, compatible with several experiments.

We study a model for the metal-insulator (MI) transition in the rare-earth nickelates RNiO$_3$, based upon a negative charge transfer energy and coupling to a rock-salt like lattice distortion of the NiO$_6$ octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with ground state of predominantly $d^8\ligand$ character, where $\ligand$ denotes a ligand hole. For sufficiently large distortions ($\delta d_{\rm Ni-O} \sim 0.05 - 0.10\AA$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $(d^8\ligand^2)_{S=0}(d^8)_{S=1}$ character, where $S$ is the total spin. Thus the MI transition may be viewed as being driven by an internal volume "collapse" where the NiO$_6$ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2,1/2,1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of a new type of charge ordering achieved without any actual movement of the charge., Comment: 7 pages with supplement. Submitted to PRL

We propose a novel variational method to calculate the two-hole propagators relevant for Auger spectroscopy in transition metal oxides. This method can be thought of as an intermediary step between the full solution (which is difficult to generalize to systems with partially filled bands) and the impurity approximation. Like the former, our solution has full translational invariance, and like the latter, it can be generalized to certain types of systems with partially filled bands. Here we compare both our variational approximation and the impurity approximation against the exact solution for a simple one-dimensional model with filled bands. We show that when the energies of the eigenstates residing primarily on the transition metal ions do not overlap with those of the eigenstates residing primarily on Oxygen ions, both approximations are valid but the variational approach is superior., Comment: 12 pages, 11 figures

Double perovskites like Sr$_2$FeMoO$_6$ are materials with half-metallic ground states and ferrimagnetic T$_{\rm{c}}$'s well above room temperature. This paper is the second of our comprehensive theory for half metallic double perovskites. Here we derive an effective Hamiltonian for the Fe core spins by "integrating out" the itinerant Mo electrons and obtain an unusual double square-root form of the spin-spin interaction. We validate the classical spin Hamiltonian by comparing its results with those of the full quantum treatment presented in the companion paper "Theory of Half-Metallic Double Perovskites I: Double Exchange Mechanism". We then use the effective Hamiltonian to compute magnetic properties as a function of temperature and disorder and discuss the effect of excess Mo, excess Fe, and anti-site disorder on the magnetization and T$_{\rm{c}}$. We conclude with a proposal to increase T$_{\rm{c}}$ without sacrificing carrier polarization.

The double perovskite material \SFMO has the rare and desirable combination of a half-metallic ground state with 100% spin polarization and ferrimagnetic \Tc$\simeq 420$K, well above room temperature. In this two-part paper, we present a comprehensive theoretical study of the magnetic and electronic properties of half metallic double perovskites. In this paper we present exact diagonalization calculations of the "fast" Mo electronic degrees coupled to "slow" Fe core spin fluctuations treated by classical Monte Carlo techniques. From the temperature dependence of the spin-resolved density of states, we show that the electronic polarization at the chemical potential is proportional to magnetization as a function of temperature. We also consider the effects of disorder and show that excess Fe leaves the ground state half-metallic while anti-site disorder greatly reduces the polarization. In a companion paper titled "Theory of Half-Metallic Double Perovskites II: Effective Spin Hamiltonian and Disorder Effects", we derive an effective classical spin Hamiltonian that provides a new framework for understanding the magnetic properties of half-metallic double perovskites including the effects of disorder. Our results on the dependence of the spin polarization on temperature and disorder has important implications for spintronics.

We show that applying strain on half-doped manganites makes it possible to tune the system to the proximity of a metal-insulator transition and thereby generate a colossal magnetoresistance (CMR) response. This phase competition not only allows control of CMR in ferromagnetic metallic manganites but can be used to generate CMR response in otherwise robust insulators at half-doping. Further, from our realistic microscopic model of strain and magnetotransport calculations within the Kubo formalism, we demonstrate a striking result of strain engineering that, under tensile strain, a ferromagnetic charge-ordered insulator, previously inaccessible to experiments, becomes stable.

We present a comprehensive theory of the temperature- and disorder-dependence of half-metallic ferrimagnetism in the double perovskite Sr$_2$FeMoO$_6$ (SFMO) with $T_c$ above room temperature. We show that the magnetization $M(T)$ and conduction electron polarization $P(T)$ are both proportional to the magnetization $M_S(T)$ of localized Fe spins. We derive and validate an effective spin Hamiltonian, amenable to large-scale three-dimensional simulations. We show how $M(T)$ and $T_c$ are affected by disorder, ubiquitous in these materials. We suggest a way to enhance $T_c$ in SFMO without sacrificing polarization.

We study the effect of A site disorder on magnetic field induced melting of charge order (CO) in half doped manganites using a Monte-Carlo technique. Strong A-site disorder destroys CO even without an applied field. At moderate disorder, the zero field CO state survives but has several intriguing features in its field response. Our spatially resolved results track the broadening of the field melting transition due to disorder and explain the unusual dependence of the melting scales on bandwidth and disorder. In combination with our companion paper on field melting of charge order in clean systems we provide an unified understanding of CO melting across all half doped manganites., Comment: 9 pages, pdflatex, 10 embedded png figs

We study the melting of charge order in the half doped manganites using a model that incorporates double exchange, antiferromagnetic superexchange, and Jahn-Teller coupling between electrons and phonons. We primarily use a real space Monte Carlo technique to study the phase diagram in terms of applied field $(h)$ and temperature $(T)$, exploring the melting of charge order with increasing $h$ and its recovery on decreasing $h$. We observe hysteresis in this response, and discover that the `field melted' high conductance state can be spatially inhomogeneous even without extrinsic disorder. The hysteretic response plays out in the background of field driven equilibrium phase separation. Our results, exploring $h$, $T$, and the electronic parameter space, are backed up by analysis of simpler limiting cases and a Landau framework for the field response. This paper focuses on our results in the `clean' systems, a companion paper studies the effect of cation disorder on the melting phenomena., Comment: 16 pages, pdflatex, 11 png figs

The field induced switching of conductance in the charge ordered half-doped manganites is controlled by the combination of metastability, an inhomogeneous high field state, and cation disorder. We study this non-equilibrium problem via real space Monte Carlo on a disordered strong coupling model appropriate to the manganites. We reproduce the variation of the switching fields with the mean ionic radius r_A and cation disorder \sigma_A, and demonstrate how the experimental features arise from the proximity of several phases in the Landau free energy landscape. Our prediction for the field melted state is consistent with a growing body of experimental evidence., Comment: 5 pages, pdflatex, 5 png figures To appear in Europhys. Lett

Disorder on the active d element site is usually very disruptive for conduction and long range order in perovskite transition metal oxides. However, in the background of phase competition such `B site' dopants also act to promote one ordered phase at the expense of another. This occurs either through valence change of the transition metal or via creation of `defects' in the parent magnetic state. We provide a framework for understanding the complex variety of phenomena observed in B site doped manganites and identify the key parameters that control the physics. Using a spatially resolved analysis of B ions in various manganite phases we explain the existing data and predict new situations where highly polarisable phase separated states can be created., Comment: 5 pages, pdflatex, 5 png figures

We study the two orbital double-exchange model in two dimensions in the presence of antiferromagnetic (AF) superexchange, strong Jahn-Teller coupling, and substitutional disorder. At hole doping x=0.5 we explore the `bicritical' regime where the energy of a ferromagnetic metal and a charge and orbital ordered (CO-OO) CE state are closely balanced, and compare the impact of weak homogeneous disorder to that of a low density of strong scatterers. Even moderate homogeneous disorder suppresses the CE-CO-OO phase and leads to a glass with nanoscale correlations. Dilute strong scatterers of comparable strength, however, convert the CE-CO-OO phase to a phase separated state with ferromagnetic and AF-CO-OO clusters. We provide the first spatial description of these phenomena and compare our results in detail to experiments on the half-doped manganites., Comment: 4 pages pdflatex, 4 jpg figs, published

We study adiabatic charge pumping through a quantum dot placed at the junction of $N$ quantum wires. We explicitly map out the pattern of pumped charge as a function of the time-varying tunneling parameters coupling the wires to the dot and the phase between any two time varying parameters controlling the shape of the dot. We find that with $N-2$ time-independent well-coupled leads, the maximum pumped charge in the remaining two leads is strongly suppressed with increasing $N$, leading to the possibility of tuning of the pumped charge, by modulating the coupling of the $N-2$ leads., Comment: 5 pages, 6 figures, version to be published in PRB