arXiv subjects

Rok Zitko

Publications and source records attributed to Rok Zitko.

At least 19 recordsLinked to original sources

arXiv2021

Electrical conductivity in the Hubbard model: orbital effects of magnetic field

Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and translational invariance, and that in the DMFT the vertex corrections cancel regardless of the magnetic field. We present the DMFT results for the spectral function and both the longitudinal and Hall conductivity in several regimes of parameters. We analyze thoroughly the quantum oscillations of the longitudinal conductivity and identify a high-frequency oscillation component, arising as a combined effect of scattering and temperature, in line with recent experimental observations in moir\'e systems.

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arXiv2021

Universal magnetic oscillations of DC conductivity in the incoherent regime of correlated systems

Using the dynamical mean field theory we investigate the magnetic field dependence of DC conductivity in the Hubbard model on the square lattice, fully taking into account the orbital effects of the field introduced via the Peierls substitution. In addition to the conventional Shubnikov-de Haas quantum oscillations, associated with the coherent cyclotron motion of quasiparticles and the presence of a well-defined Fermi surface, we find an additional oscillatory component with a higher frequency that corresponds to the total area of the Brillouin zone. These paradigm-breaking oscillations appear at elevated temperature. This finding is in excellent qualitative agreement with the recent experiments on graphene superlattices. We elucidate the key roles of the off-diagonal elements of the current vertex and the incoherence of electronic states, and explain the trends with respect to temperature and doping.

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arXiv2019

Aharonov-Bohm and Aharonov-Casher effects for local and nonlocal Cooper pairs

We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreeev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively.

cond-mat.mes-hall↗

arXiv2019

Aharonov-Bohm and Aharonov-Casher effects in double quantum dot Josephson junction

We analyze a Josephson junction between two superconductors interconnected through a normal-state nanostructure made of two parallel nanowires with embedded quantum dots. We study the influence of interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases for local and nonlocal (split) Cooper pairs. In the AB effect the phase of electron is affected by magnetic flux, while in the AC effect the phase of the electron in solid state can be modified due to the Rashba spin-orbit coupling. In the low-transmission regime the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively. We demonstrate that by the addition of the quantum dots the Cooper pair splitting can be made perfectly efficient, and that the AC phase is different for non-spin-flip and spin-flip transport processes.

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arXiv2019

Non-Fermi-liquid fixed point in multi-orbital Kondo impurity model relevant for Hund's metals

Due to the separation between the spin and the orbital screening scales, the normal state of Hund's metals at ambient temperature can be loosely characterized as a partially coherent state with fluctuating spins and quenched orbital moments. With the aim to characterize this situation more precisely, we investigate the Kondo-Kanamori impurity model that describes the low-energy local physics of three-orbital Hund's metals occupied by two or four electrons. Within this model one can diminish the mixed spin-orbital terms and thereby enhance the separation between the two screening scales, allowing a more precise investigation of the intermediate state. Using the numerical renormalization group we calculate the impurity entropy as well as the temperature and frequency dependence of the spin and the orbital susceptibilities. We uncover a non-Fermi-liquid two-channel overscreened SU(3) fixed point that controls the behavior in the intermediate regime. We discuss its fingerprints in the frequency dependence of local orbital susceptibility and the shape of the spectral function.

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arXiv2019

Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results and the question of the exact solution for the conductivity in the Hubbard model remained open. In this letter we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity, and identify the best available result to be compared to experiment. We find that at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size $4\times 4$ and the corresponding Lanczos diagonalization result is therefore close to the exact result in the thermodynamic limit.

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arXiv2019

Superconducting quantum dot and the sub-gap states

Quantum dots are nanostructures made of semiconducting materials that are engineered to hold a small amount of electric charge (a few electrons) that is controlled by external gate and may hence be considered as tunable artificial atoms. A quantum dot may be contacted by conductive leads to become the active part of a single-electron transistor, a device that is highly conductive only at very specific gate voltages. In recent years a significant attention has been given to more complex hybrid devices, in particular superconductor-semiconductor heterostructures. Here I review the theoretical and experimental studies of small quantum-dot devices contacted by one or several superconducting leads. I focus on the research on the low-lying localized electronic excitations that exist inside the superconducting gap (Yu-Shiba-Rusinov states) and determine the transport properties of these devices. The sub-gap states can be accurately simulated using the numerical renormalization group technique, often providing full quantitative understanding of the observed phenomena.

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arXiv2018

A comparative study of nonequilibrium insulator-to-metal transitions in electron-phonon systems

We study equilibrium and nonequilibrium properties of electron-phonon systems described by the Hubbard-Holstein model using the dynamical mean-field theory. In equilibrium, we benchmark the results for impurity solvers based on the one-crossing approximation and slave-rotor approximation against non-perturbative numerical renormalization group reference data. We also examine how well the low energy properties of the electron-boson coupled systems can be reproduced by an effective static electron-electron interaction. The one-crossing and slave-rotor approximations are then used to simulate insulator-to-metal transitions induced by a sudden switch-on of the electron-phonon interaction. The slave-rotor results suggest the existence of a critical electron-phonon coupling above which the system is transiently trapped in a non-thermal metallic state with coherent quasiparticles. The same quench protocol in the one-crossing approximation results in a bad metallic state.

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arXiv2017

Spin-orbit coupling in three-orbital Kanamori impurity model and its relevance for transition-metal oxides

We investigate the effects of the spin-orbit coupling (SOC) in a three-orbital impurity model with Kanamori interaction using the numerical renormalization group method. We focus on the impurity occupancy $N_d=2$ relevant to the dynamical mean-field theory studies of Hund's metals. Depending on the strength of SOC $λ$ we identify three regimes: usual Hund's impurity for $|λ|<λ_c$, van-Vleck non-magnetic impurity for $λ> λ_c$, and a $J=2$ impurity for $λ< -λ_c$. They all correspond to a Fermi liquid but with very different quasiparticle phase shifts and different physical properties. The crossover between these regimes is controlled by an emergent scale, the orbital Kondo temperature, $λ_c =T_K^\mathrm{orb}$ that drops with increasing interaction strength. This implies that oxides with strong electronic correlations are more prone to the effects of the spin-orbit coupling.

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arXiv2017

A new high-temperature quantum spin liquid with polaron spins

The existence of a quantum spin liquid (QSL) in which quantum fluctuations of spins are sufficiently strong to preclude spin ordering down to zero temperature was originally proposed theoretically more than 40 years ago, but its experimental realisation turned out to be very elusive. Here we report on an almost ideal spin liquid state that appears to be realized by atomic-cluster spins on the triangular lattice of a charge-density wave (CDW) state of 1T-TaS$_2$. In this system, the charge excitations have a well-defined gap of $\sim 0.3$ eV, while nuclear magnetic quadrupole resonance and muon spin relaxation experiments reveal that the spins show gapless quantum spin liquid dynamics and no long range magnetic order down to 70~mK. Canonical $T^{2}$ power-law temperature dependence of the spin relaxation dynamics characteristic of a QSL is observed from 200~K to $T_f= 55$ K. Below this temperature we observe a new gapless state with reduced density of spin excitations and high degree of local disorder signifying new quantum spin order emerging from the QSL.

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arXiv2017

Magnetic impurities in spin-split superconductors

Hybrid semiconductor-superconductor quantum dot devices are tunable physical realizations of quantum impurity models for a magnetic impurity in a superconducting host. The binding energy of the localized sub-gap Shiba states is set by the gate voltages and external magnetic field. In this work we discuss the effects of the Zeeman spin splitting which is generically present both in the quantum dot and in the (thin-film) superconductor. The unequal $g$-factors in semiconductor and superconductor materials result in respective Zeeman splittings of different magnitude. We consider both classical and quantum impurities. In the first case we analytically study the spectral function and the sub-gap states. The energy of bound states depends on the spin-splitting of the Bogoliubov quasiparticle bands as a simple rigid shift. For the case of collinear magnetization of impurity and host, the Shiba resonance of a given spin polarization remains unperturbed when it overlaps with the branch of the quasiparticle excitations of the opposite spin polarization. In the quantum case, we employ numerical renormalization group calculations to study the effect of the Zeeman field for different values of the $g$-factors of the impurity and of the superconductor. We find that in general the critical magnetic field for the singlet-doublet transition changes non-monotonically as a function of the superconducting gap, demonstrating the existence of two different transition mechanisms: Zeeman splitting of Shiba states or gap closure due to Zeeman splitting of Bogoliubov states. We also study how in the presence of spin-orbit coupling, modeled as an additional non-collinear component of the magnetic field at the impurity site, the Shiba resonance overlapping with the quasiparticle continuum of the opposite spin gradually broadens and then merges with the continuum.

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arXiv2016

Scaling of sub-gap excitations in a superconductor-semiconductor nanowire quantum dot

A quantum dot coupled to a superconducting contact provides a tunable artificial analogue of a magnetic atom in a superconductor, a paradigmatic quantum impurity problem. We realize such a system with an InAs semiconductor nanowire contacted by an Al-based superconducting electrode. We use an additional normal-type contact as weakly coupled tunnel probe to perform tunneling spectroscopy measurements of the elementary sub-gap excitations, known as Andreev bound states or Yu-Shiba-Rusinov states. We demonstrate that the energy of these states, $ζ$, scales with the ratio between the Kondo temperature, $T_K$, and the superconducting gap, $Δ$. $ζ$ vanishes for $T_K/Δ\approx 0.6$, denoting a quantum phase transition between spin singlet and doublet ground states. By further leveraging the gate control over the quantum dot parameters, we determine the singlet-doublet phase boundary in the stability diagram of the system. Our experimental results show remarkable quantitative agreement with numerical renormalization group calculations.

cond-mat.mes-hall↗

arXiv2016

Kondo effect at low electron density and high particle-hole asymmetry in 1D, 2D, and 3D

Using the perturbative scaling and the NRG, we study the characteristic energy scales in the Kondo impurity problem as a function of the exchange coupling constant $J$ and the conduction electron density. We discuss the relation between the impurity binding energy $ΔE$ and the Kondo temperature $T_K$. We find that the two are proportional only for large values of $J$, whereas in the weak-coupling limit the energy gain is quadratic in $J$, while the Kondo temperature is exponentially small. The exact relation between the two quantities depends on the detailed form of the density of states of the band. In the limit of low electron density the Kondo screening is affected by the strong particle-hole asymmetry due to the presence of the band-edge van Hove singularities. We consider the cases of 1D, 2D, and 3D tight-binding lattices with inverse-square-root, step function, and square-root onsets of the density of states that are characteristic of the respective dimensionalities. We always find two different regimes depending on whether $T_K$ is higher or lower than $μ$, the chemical potential measured from the bottom of the band. For 2D and 3D, we find a sigmoidal cross-over between the large-$J$ and small-$J$ asymptotics in $ΔE$, and a clear separation between $ΔE$ and $T_K$ for $T_K < μ$. For 1D, there is in addition a sizable intermediate-$J$ regime where the Kondo temperature is quadratic in $J$ due to the diverging density of states at the band edge. Furthermore, we find that in 1D the particle-hole asymmetry leads to a large decrease of $T_K$ compared to the standard result obtained by approximating the density of states to be constant (flat-band approximation), while in 3D the opposite is the case; this is due to the non-trivial interplay of the exchange and potential scattering renormalization in the presence of particle-hole asymmetry.

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arXiv2016

Low-energy physics of three-orbital impurity model with Kanamori interaction

We discuss the low-energy physics of the three-orbital Anderson impurity model with the Coulomb interaction term of the Kanamori form which has orbital SO(3) and spin SU(2) symmetry and describes systems with partially occupied $t_{2g}$ shells. We focus on the case with two electrons in the impurity that is relevant to Hund's metals. Using the Schrieffer-Wolff transformation we derive an effective Kondo model with couplings between the bulk and impurity electrons expressed in terms of spin, orbital, and orbital quadrupole operators. The bare spin-spin Kondo interaction is much smaller than the orbit-orbit and spin-orbital couplings or is even ferromagnetic. Furthermore, the perturbative scaling equations indicate faster renormalization of the couplings related to orbital degrees of freedom compared to spin degrees of freedom. Both mechanisms lead to a slow screening of the local spin moment. The model thus behaves similarly to the related quantum impurity problem with a larger SU(3) orbital symmetry (Dworin-Narath interaction) where this was first observed. We find that the two problems actually describe the same low-energy physics since the SU(3) symmetry is dynamically established through the renormalization of the splittings of coupling constants to zero. The perturbative renormalization group results are corroborated with the numerical-renormalization group (NRG) calculations. The dependence of spin Kondo temperatures and orbital Kondo temperatures as a function of interaction parameters, the hybridization, and the impurity occupancy is calculated and discussed.

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arXiv2016

Spectral properties of Shiba sub-gap states at finite temperatures

Using the numerical renormalization group (NRG), we analyze the temperature dependence of the spectral function of a magnetic impurity described by the single-impurity Anderson model coupled to superconducting contacts. With increasing temperature the spectral weight is gradually transferred from the $δ$-peak (Shiba/Yu-Shiba-Rusinov/Andreev bound state) to the continuous sub-gap background, but both spectral features coexist at any finite temperature, i.e., the $δ$-peak itself persists to temperatures of order $Δ$. The continuous background is due to inelastic exchange scattering of Bogoliubov quasiparticles off the impurity and it is thermally activated since it requires a finite thermal population of quasiparticles above the gap. In the singlet regime for strong hybridization (charge-fluctuation regime) we detect the presence of an additional sub-gap structure just below the gap edges with thermally activated behavior, but with an activation energy equal to the Shiba state excitation energy. These peaks can be tentatively interpreted as Shiba bound states arising from the scattering of quasiparticles off the thermally excited sub-gap doublet Shiba states, i.e., as high-order Shiba states.

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arXiv2015

Evolution of the density of states at the Fermi level across the metal-to-insulator crossover in alkali doped zeolite

We report a systematic nuclear magnetic resonance investigation of the $^{23}$Na spin-lattice relaxation rate, $1/T_1$, in sodium loaded low-silica X (LSX) zeolite, Na$_n$/Na$_{12}$-LSX, for various loading levels of sodium atoms $n$ across the metal-to-insulator crossover. For high loading levels of $n \geq 14.2$, $1/T_1T$ shows nearly temperature-independent behavior between 10 K and 25 K consistent with the Korringa relaxation mechanism and metallic ground state. As the loading levels decrease below $n \leq 11.6$, the extracted density of states (DOS) at the Fermi level sharply decreases, although a residual DOS at Fermi level is still observed even in samples that lack the metallic Drude-peak in the optical reflectance. The observed crossover is a result of a complex loading-level dependence of electric potential felt by the electrons confined to zeolite cages, where the electronic correlations and disorder both play an important role.

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arXiv2015

$Z_2$-gauge theory description of the Mott transition in infinite dimensions

The infinite dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a $Z_2$ gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local $Z_2$ gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.

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arXiv2015

Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate

We contrast the transport properties (dc resistivity, Seebeck coefficient), optical conductivity, spectral functions, dynamical magnetic susceptibility, and the NMR $1/T_1$ spin-lattice relaxation rate of the repulsive and attractive infinite-dimensional Hubbard models in the paramagnetic phase for a generic band filling. The calculations are performed in a wide temperature interval using the dynamical mean-field theory with the numerical renormalization group as the impurity solver. The attractive case exhibits significantly more complex temperature dependences which can be explained by the behavior of the half-filled Hubbard model in external magnetic field with constant magnetization, to which the attractive Hubbard model maps through the partial particle-hole transformation. The resistivity is non-monotonous for strongly attractive case: it peaks significantly above the MIR value at a temperature $T_\mathrm{max}$ where the quasiparticle band disappears. For both signs of $U$ we find particle-hole asymmetry in the self-energy at low energies, but with the opposite kind of excitations having longer lifetime. This leads to a strong suppression of the slope of the Seebeck coefficient in the attractive case, rather than an enhancement as in the repulsive case. The spin-lattice relaxation rate in the strongly attractive case has a non-monotonic temperature dependence, thereby revealing the pairing fluctuations.

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