Two-dimensional Kondo Lattice Research Articles

Pseudogap state of two-dimensional Kondo lattice

The pseudogap behavior of spectral function A(k, ω) of charge carriers is considered in the weak doping regime for a 2D Kondo lattice with a strong spin-hole antiferromagnetic interaction. The scattering of carriers is described in terms of a local polaron according to the irreducible Green functions. The behavior of the carrier spectrum in the nodal and antinodal domains is considered. The resultant value of the pseudogap is in conformity with experimental data on photoemission with angular resolution.

Kondo Lattice Scenario in Disordered Semiconductor Heterostructures

We study nuclear relaxation in the presence of localized electrons in a two-dimensional electron gas in a disordered delta-doped semiconductor heterostructure and show that this method can reliably probe their magnetic interactions and possible long-range order. In contrast, we argue that transport measurements, the commonly employed tool, may not sometimes distinguish between spatial disorder and long-range order. We illustrate the utility of using the nuclear relaxation method to detect long-range order by analyzing a recent proposal made on the basis of transport measurements, on the spontaneous formation of a two-dimensional Kondo lattice in a 2D electron gas in a heterostructure.

Evolution of the Fermi Surface across a Magnetic Order-Disorder Transition in the Two-Dimensional Kondo Lattice Model: A Dynamical Cluster Approach

We use the dynamical cluster approximation, with a quantum Monte Carlo cluster solver on clusters of up to 16 orbitals, to investigate the evolution of the Fermi surface across the magnetic order-disorder transition in the two-dimensional doped Kondo lattice model. In the paramagnetic phase, we observe the generic hybridized heavy-fermion band structure with large Luttinger volume. In the antiferromagnetic phase, the heavy-fermion band drops below the Fermi surface giving way to hole pockets centered around k=(pi/2,pi/2) and equivalent points. In this phase Kondo screening does not break down, but the topology of the resulting Fermi surface is that of a spin-density wave approximation in which the localized spins are frozen.

Coherence and metamagnetism in the two-dimensional Kondo lattice model

We report the results of dynamical mean-field calculations for the metallic Kondo lattice model subject to an applied magnetic field. High-quality spectral functions reveal that the picture of rigid, hybridized bands, which are Zeeman shifted in proportion to the field strength, is qualitatively correct. We find evidence of a zero-temperature magnetization plateau whose onset coincides with the chemical potential entering the spin up hybridization gap. The plateau appears at the field scale predicted by a (static) large-$N$ mean-field theory and has a magnetization value consistent with that of $x=1\ensuremath{-}{n}_{c}$ spin-polarized heavy holes, where ${n}_{c}l1$ is the conduction band filling of the noninteracting system. We argue that the emergence of the plateau at a low temperature marks the onset of quasiparticle coherence.

Field-tunable magnetic phases in a semiconductor-based two-dimensional Kondo lattice

We show the existence of intrinsic localized spins in mesoscopic high-mobility GaAs/AlGaAs heterostructures. Non-equilibrium transport spectroscopy reveals a quasi-regular distribution of the spins, and indicates that the spins interact indirectly via the conduction electrons. The interaction between spins manifests itself in a characteristic zero-bias anomaly near the Fermi energy, and indicates gate voltage-controllable magnetic phases in high-mobility heterostructures. To address this issue further, we have also designed electrostatically tunable Hall devices, that allow a probing of Hall characteristics at the active region of the mesoscopic devices. We show that the zero field Hall coefficient has an anomalous contribution, which can be attributed to scattering by the localized spins. The anomalous contribution can be destroyed by an increase in temperature, source-drain bias, or field range.

Deconfined quantum criticality in the two-dimensional Kondo lattice model

We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.

Nonuniform phases in metals with local moments

The two-dimensional Kondo lattice model with both nearest and next-nearest neighbor exchange interactions is studied within a mean-field approach and its phase diagram is determined. In particular, we allow for lattice translation symmetry breaking. We observe that the usual uniform intersite order parameter is never realized, being unstable towards other more complex types of order. When the nearest neighbor exchange ${J}_{1}$ is ferromagnetic the flux phase is always the most stable state, irrespective of the value of the next-nearest-neighbor interaction ${J}_{2}$. For antiferromagnetic ${J}_{1,}$, however, either a columnar or a flux phase is realized, depending on conduction electron filling and the value of ${J}_{2}$.

Coherence scale of the two-dimensional Kondo lattice model

A doped hole in the two-dimensional half-filled Kondo lattice model with exchange $J$ and hopping $t$ has momentum $(\ensuremath{\pi},\ensuremath{\pi})$ irrespective of the coupling $J∕t$. The quasiparticle residue of the doped hole, ${Z}_{(\ensuremath{\pi},\ensuremath{\pi})}$, tracks the Kondo scale, ${T}_{K}$, of the corresponding single impurity model. Those results stem from high precision quantum Monte Carlo simulations on lattices up to $12\ifmmode\times\else\texttimes\fi{}12$. Accounting for small dopings away from half-filling within a rigid band approximation, this result implies that the effective mass of the charge carriers at the Fermi level tracks $1∕{T}_{K}$ or equivalently that the coherence temperature ${T}_{\mathrm{coh}}\ensuremath{\propto}{T}_{K}$. This results is consistent with the large-N saddle point of the $SU(N)$ symmetric Kondo lattice model.

Mechanism of unconventional superconductivity in strongly correlated electron systems

A mechanism of unconventional superconductivity is proposed in two-dimensional strongly correlated electron systems. We consider a two-dimensional Kondo lattice system or double-exchange system with spin–orbit coupling arising from buckling of the plane. Describing the spin fluctuations in terms of a gage field, we show that a Chern–Simons term is induced. Due to this Chern–Simons term, the carriers behave like skyrmion excitations that destroy magnetic long-range order. Depending on the interaction between the localized spins, the attractive interaction between skyrmions leads to p-wave or d-wave superconductivity. In particular, for the antiferromagnetic case, symmetry of the Cooper pair is d x 2− y 2 .

Mechanism of unconventional superconductivity induced by skyrmion excitations in two-dimensional strongly correlated electron systems

We propose a mechanism of unconventional superconductivity in two-dimensional strongly correlated electron systems. We consider a two-dimensional Kondo lattice system or double exchange system with spin-orbit coupling arising from buckling of the plane. We show that a Chern-Simons term is induced for a gauge field describing the phase fluctuations of the localized spins. Through the induced Chern-Simons term, carriers behave like skyrmion excitations that lead to a destruction mechanism of magnetic long-range order by carrier doping. After magnetic long-range order is destroyed by carrier doping, the Chern-Simons term plays a dominant role and the attractive interaction between skyrmions leads to unconventional superconductivity. For the case of the ferromagnetic interaction between the localized spins, the symmetry of the Cooper pair is p wave ${(p}_{x}\ifmmode\pm\else\textpm\fi{}{\mathrm{ip}}_{y}).$ For the case of the antiferromagnetic interaction between the localized spins, the symmetry of the Cooper pair is d wave ${(d}_{{x}^{2}\ensuremath{-}{y}^{2}}).$ Applications to various systems are discussed, in particular to the high-${T}_{c}$ cuprates.

Optical conductivity of the two-dimensional Kondo lattice in spin–polaron approach

In the framework of the two dimensional Kondo lattice model the optical conductivity spectrum σ( ω) is investigated. The calculations are based on the realistic energy spectrum of spin–polaron excitations to fit photoemission experiments in cuprates. The memory function approach is used for deriving σ( ω). Obtained optical transport damping, plasma frequency and conductivity demonstrate qualitative agreement with experimental data. It is pointed out the crucial importance of nested Fermi surface scattering by vector Q =(π,π) due to strong carrier coupling to a resonance structure of spin excitations with momenta close to Q .

Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model

We present a detailed numerical study of ground state and finite temperature spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. Our numerical results stem from auxiliary field quantum Monte Carlo simulations formulated in such a way that the sign problem is absent at half-band filling thus allowing us to reach lattice sizes up to $12\ifmmode\times\else\texttimes\fi{}12.$ At $T=0$ and antiferromagnetic couplings $J>0$ the competition between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect triggers a quantum phase transition between antiferromagnetically ordered and magnetically disordered insulators: ${J}_{c}/t=1.45\ifmmode\pm\else\textpm\fi{}0.05.$ At $J<0$ the system remains an antiferromagnetically ordered insulator and irrespective of the sign of J, the quasiparticle gap scales as $|J|.$ The dynamical spin structure factor $S(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ evolves smoothly from its strong-coupling form with spin gap at $\stackrel{\ensuremath{\rightarrow}}{q}=(\ensuremath{\pi},\ensuremath{\pi})$ to a spin-wave form. For $J>0,$ the single-particle spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ shows a dispersion relation following that of hybridized bands as obtained in the noninteracting periodic Anderson model. In the ordered phase this feature is supplemented by shadows, thus allowing an interpretation in terms of the coexistence of Kondo screening and magnetic ordering. In contrast, at $J<0$ the single-particle dispersion relation follows that of noninteracting electrons in a staggered external magnetic field. At finite temperatures spin ${T}_{S}$ and charge ${T}_{C}$ scales are defined by locating the maximum in the charge and spin uniform susceptibilities. For weak to intermediate couplings, ${T}_{S}$ marks the onset of antiferromagnetic fluctuations---as observed by a growth of the staggered spin susceptibility---and follows a ${J}^{2}$ law. At strong couplings ${T}_{S}$ scales as J. On the other hand ${T}_{C}$ scales as J both in the weak- and strong-coupling regime. At and slightly below ${T}_{C}$ we observe (i) the onset of screening of the magnetic impurities, (ii) a rise in the resistivity as a function of decreasing temperature, (iii) a dip in the integrated density of states at the Fermi energy, and finally (iv) the occurrence of hybridized bands in $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega}).$ It is shown that in the weak-coupling limit, the charge gap of order J is formed only at ${T}_{S}$ and is hence of magnetic origin. The specific heat shows a two-peak structure. The low-temperature peak follows ${T}_{S}$ and is hence of magnetic origin. Our results are compared to various mean-field theories.

Finite-temperature properties of the two-dimensional Kondo lattice model

Using recently developed Lanczos technique we study finite-temperature properties of the 2D Kondo lattice model at various fillings of the conduction band. At half filling the quasiparticle gap governs physical properties of the chemical potential and the charge susceptibility at small temperatures. In the intermediate coupling regime quasiparticle gap scales approximately linearly with Kondo coupling. Temperature dependence of the spin susceptibility reveals the existence of two different temperature scales. A spin gap in the intermediate regime leads to exponential drop of the spin susceptibility at low temperatures. Unusual scaling of spin susceptibility is found for temperatures above 0.6 J. Charge susceptibility at finite doping reveals existence of heavy quasiparticles. A new low energy scale is found at finite doping.

Spin-polaron excitations in the two-dimensional Kondo lattice with spin frustration

In the framework of the two-dimensional Kondo lattice model with hoppings between first-, second-, and third-nearest neighbors the spin-polaron spectrum is investigated. A complex structure of a spin-polaron and an increase of frustration in spin subsystem leads to the evolution in the excitation band close to the evolution on hole hopping which is given by ARPES experiments in HTSC.

Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model

The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.

One spin-polaron problem in the two-dimensional Kondo lattice

Using the spin-polaron concept and the spherically symmetric state for the antiferromagnetic spin background, one-particle motion is studied for the two-dimensional Kondo lattice. The elementary excitations are represented by a Bloch superposition of four one-site electron states: two local states - a bare electron state and a local spin-polaron of small radius -and two states of delocalized polarons which correspond to the coupling of local states to the antiferromagnetic spin wave with momentum Q = ( π, π), so-called Q-polarons. We show that the lowest band of elementary excitations is essentially determined by Q-polaron states in the strongly coupled regime. Taking into account Q-polarons shifts the band bottom from (π,π) to (0,0). The spectral weight of a bare particle in the lowest band states can greatly differ from 1. This may lead to a large Fermi surface for a relatively small particle concentration.

EXTINCTION OF SPIN INTERACTIONS IN THE 2D KONDO LATTICE

A two-dimensional Kondo lattice with inter-site interaction is studied using a canonical transformation to eliminate interactions. Our approach is patterned on Bardeen and Pines' elimination of electron–phonon interaction. It is shown that interactions are eliminated at nonzero temperatures in the thermodynamic limit, in a manner differing radically from the case of phonons.

Frustration effects in a Kondo lattice: a model for the coexistence of magnetic and non-magnetic Ce planes in CeSb

The coexistence of magnetic and non-magnetic planes, observed by neutron diffraction in CeSb, is described assuming that each Ce plane is a two-dimensional Kondo lattice, interacting with the neighbouring planes through RKKY interaction. We show that, when the Ce planes are close to the Kondo-ferromagnetic instability, such magnetic structures are stabilized if the interplane interactions are frustrated.