Particle-hole Asymmetry Research Articles

Coexistence of linear and non-linear thermoelectricity in graphene-superconductor tunnel junctions

We theoretically analyze the electronic transport properties of a monolayer graphene/insulator/superconductor (GIS) tunnel junction subject to a temperature gradient. For intrinsic graphene, the system shows always dissipative charge transport even in the presence of an electronic temperature difference between the two leads. Differently, the GIS produces a thermoelectric response when the graphene electrochemical potential is lifted to energies comparable to the zero-temperature gap of the superconductor, i.e., the system is particle–hole asymmetric. Indeed, the thermally biased GIS system is able to produce both a short-circuit Peltier current and an open-circuit Seebeck voltage. This thermoelectric effect is made of a linear conventional component, due to the intrinsic particle–hole asymmetry of the system, and a non-linear contribution, due to a further spontaneous particle–hole symmetry breaking. In most of the thermal and charge configurations of the GIS system, the linear component prevails. Concluding, the GIS system could be employed in the design of thermometers, electromagnetic radiation sensors, and heat engines with profound influence in superconducting quantum technologies.

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice.

We present experimental findings on electron-electron scattering in two-dimensional moiré heterostructures with a tunable Fermi wave vector, reciprocal lattice vector, and band gap. We achieve this in high-mobility aligned heterostructures of bilayer graphene (BLG) and hBN. Around the half-full point, the primary contribution to the resistance of these devices arises from Umklapp electron-electron (Uee) scattering, making the resistance of graphene/hBN moiré devices significantly larger than that of non-aligned devices (where Uee is forbidden). We find that the strength of Uee scattering follows a universal scaling with Fermi energy and is nonmonotonically dependent on the superlattice period. The Uee scattering can be tuned with the electric field and is affected by layer polarization of BLG. It has a strong particle-hole asymmetry; the resistance when the chemical potential is in the conduction band is significantly lower than when it is in the valence band, making the electron-doped regime more practical for potential applications.

Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor.

Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.

Magnetic Field as an Important Tool in Exploring the Strongly Correlated Fermi Systems and Their Particle–Hole and Time-Reversal Asymmetries

In this review, we consider the impact of magnetic field on the properties of strongly correlated heavy-fermion compounds such as heavy-fermion metals and frustrated insulators with quantum spin liquid. Magnetic field B can be considered a universal tool, allowing the exploration of the physics controlling the remarkable properties of heavy-fermion compounds. These vivid properties are T/B scaling, exhibited under the application of magnetic field B and at fixed temperature T, and the emergence of Landau Fermi liquid behavior under the application of magnetic field. We analyze the influence of quasiparticle–hole asymmetry on the properties of heavy-fermion (HF) compounds such as the universal scaling behavior of the thermopower S/T exhibited under the application of magnetic field B. We show that universal scaling is demonstrated by different HF compounds such as β-YbAlB4, YbRh2Si2, and strongly correlated layered cobalt oxide [BiBa0.66K0.36O2]CoO2. Analyzing YbRh2Si2, we show that the T/B scaling behavior of S/T is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ρ0 and the density of states N0 experience jumps at the AF transition, causing two jumps in the thermopower and its sign reversal. Our consideration is based on the flattening of the single-particle spectrum that strongly affects ρ0 and N0 and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part Δσd(V) of tunneling differential conductivity σd(V), Δσd(V)=σd(V)−σd(−V), where V is the voltage bias. We demonstrate that in the presence of magnetic field, the quasiparticle–hole asymmetry vanishes, the LFL behavior is restored, and the asymmetry disappears. Our calculations of the mentioned properties of HF compounds, based on the fermion condensation theory, are in good agreement with the experiment and support our conclusion that the fermion condensation theory is capable of describing the properties of HF compounds, including those exhibited under the application of magnetic field.

Thermodynamic properties of the 2D generic helical edge states with quadrangular potential effects

We theoretically studied the generic helical edge state (GHES) with quadrangular potential in the two-dimensional (2D) HgTe/CdTe quantum well (QW) structure. We have specified the thermodynamic properties of the GHES with and without the external geometric potential. On the one hand, we first revealed the heat capacity dependence of the edge modes on the optimum temperatures. It is found that the model offers distorted Fermi lines of edge states but does not vary with the behavior of the heat capacity. In addition, we showed that the quadrangular potential term distorts the Fermi surface and contributes to particle-hole asymmetry.

Interference effects in polarization-controlled Rayleigh scattering in twisted bilayer graphene

We calculate the \tco{polarization}-controlled Rayleigh scattering response of twisted bilayer graphene (tBLG) based on the continuum electronic band model developed by Bistritzer and MacDonald while considering its refinements which address the effects of structural corrugation, doping-dependent Hartree interactions and particle-hole asymmetry. The dominant wave vectors for the Rayleigh scattering process emanate from various regions of the Moir\'e Brillouin zone (MBZ) in contrast to single-layer graphene (SLG) and AB-stacked bilayer graphene (AB-BLG), where the dominant contributions always stem from the vicinity of the $\bm{K}$ point for optical laser energies and below. Compared to SLG, the integrated Rayleigh intensity is strongly enhanced for small twist angles (\emph{e.g.}, at a twist angle $ \theta = 1.2^{\circ} $, the integrated Rayleigh intensity at laser energy $ E_l=2~\si{\electronvolt} $ enhances by a factor of $\sim $ 100 for the case of parallel \tco{polarization}). While for the case of cross-\tco{polarization}, it exhibits a markedly complex \tco{behavior} suggestive of strong interference effects mediated by the optical matrix elements. We find that at small twist angles, \emph{e.g.}, $ \theta = 1.05^{\circ} $, the corrugation effects strongly enhances the ratio $ \bm{R}_A = \frac{ \text{integrated Rayleigh intensity for parallel \tco{polarization}}}{\text{integrated Rayleigh intensity for cross-\tco{polarization}}} $ by $ \sim $ $ 1300 $ times \emph{viz a viz} SLG or AB-BLG.

Asymmetry effects on the phases of RKKY-coupled two-impurity Kondo systems

In a related work [arXiv:2106.07519] we have shown that in the two-impurity Anderson (2iA) model with two hosts coupled by spin exchange in the most symmetric case there are either two phase transitions or none. The phases comprise the conventional Kondo and RKKY regimes and a novel one, interpreted as a Kondo-stabilized, metallic quantum spin liquid (QSL). Here we analyze how various types of asymmetry affect this picture. We demonstrate that the transitions are robust against the coupling and particle-hole asymmetries, provided charge transfer is forbidden. This holds true despite the scattering phase shift at each impurity taking non-universal values. Finally, for an extended model including charge transfer between the hosts and a small Coulomb interaction at the host sites directly coupled to impurities, we show that the presence of charge transfer changes the phase transitions into crossovers. Provided the inter-host hopping is sufficiently small, this leads to qualitatively the same physics at non-zero temperature. The relevance of this model for rare-earth atoms in a metallic host is discussed and potential experimental setups for observing our findings are proposed.

Pseudomagnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamiltonians of twisted bilayer graphene

Using the method developed in the companion paper, we construct the effective continuum theories for two different microscopic tight binding models of the twisted bilayer graphene at the twist angle of $1.05^\circ$, one Slater-Koster based and the other ab-initio Wannier based. The energy spectra obtained from the continuum theory -- either for rigid twist or including lattice relaxation -- are found to be in nearly perfect agreement with the spectra from the tight binding models when the gradient expansion is carried out to second order, demonstrating the validity of the method. We also analyze the properties of the Bloch states of the resulting narrow bands, finding non-negligible particle-hole symmetry breaking near the $\Gamma$ point in our continuum theory constructed for the ab-initio based microscopic model due to a term in the continuum theory that was previously overlooked. This reveals the difference with all existing continuum models where the particle-hole symmetry of the narrow band Hilbert space is nearly perfect.

Kondo screening of single magnetic impurity doped type-II Ising superconductors

We theoretically study the Kondo effect in type-II Ising superconductors with a single magnetic impurity. Type-II Ising superconductivity was found in two-dimensional centrosymmetric materials with multiple degenerate orbitals, such as in few-layer stanene [Falson et al., Science 367, 1454 (2020)] and ultrathin ${\mathrm{PdTe}}_{2}$ films [Liu et al., Nano Lett. 20, 5728 (2020)]. The type-II Ising spin-orbit coupling (SOC) in these materials generates out-of-plane effective Zeeman fields orienting opposite directions for opposing orbitals, which strongly protects the interorbital superconducting pairing states against in-plane magnetic fields. We show that the SOC-induced band splitting and the chemical potential significantly influence the formation of a localized magnetic moment, with particle-hole asymmetry in the phase boundary between magnetic and nonmagnetic states. The behaviors of spin-induced Yu-Shiba-Rusinov bound states and low-temperature magnetic susceptibility demonstrate that the SOC suppresses the Kondo screening of the magnetic moment, while the interorbital mixing weakens the SOC at finite momentum, then enhances the Kondo effect. The quantum phase transition between magnetic doublet and Kondo singlet ground states can be tuned through chemical potential in experiments.

Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering

The mechanism of the pseudogap observed in hole-doped cuprates remains one of the central puzzles in condensed matter physics. We analyze this phenomenon via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which would open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry trigger a very different mechanism: a large imaginary part of the spin-fermion vertex promotes damping of antinodal fermions and, at the same time, protects the nodal Fermi arcs (antidamping). Our analysis naturally explains puzzling features of the pseudogap observed in experiments, such as Fermi arcs being cut off at the antiferromagnetic zone boundary and the subordinate role of hot spots.

Microscopic Origin of the Effective Spin-Spin Interaction in a Semiconductor Quantum Dot Ensemble

We present a microscopic model for a singly charged quantum dot (QD) ensemble to reveal the origin of the long-range effective interaction between the electron spins in the QDs. Wilson's numerical renormalization group (NRG) is used to calculate the magnitude and the spatial dependency of the effective spin-spin interaction mediated by the growth-induced wetting layer. Surprisingly, we found an antiferromagnetic Heisenberg coupling for very short inter-QD distances that is caused by the significant particle-hole asymmetry of the wetting layer band at very low filling. Using the NRG results obtained from realistic parameters as input for a semiclassical simulation for a large QD ensemble, we demonstrate that the experimentally reported phase shifts in the coherent spin dynamics between single- and two-color laser pumping can be reproduced by our model, solving a long-standing open problem of the microscopic origin of the inter-QD electron spin-spin interaction.

High-frequency transport and zero-sound in an array of SYK quantum dots

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T \gg T_{FL}T≫TFL. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric \sigma(\omega,p)σ(ω,p) and thermal \kappa(\omega,p)κ(ω,p) conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter \mathcal{E}ℰ. At low-frequencies \omega \ll Tω≪T we find the Lorenz ratio L = \kappa(0,0)/T\sigma(0,0)L=κ(0,0)/Tσ(0,0) to be non-universal and temperature-dependent. At \omega \gg Tω≫T the conductivity \sigma(\omega,p)σ(ω,p) contains a pole with nearly linear dispersion \omega \approx sp\sqrt{\ln\frac{\omega}{T}}ω≈splnωT reminiscent of the “zero-sound”, known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.

Erratum: Nonlinear sigma model with particle-hole asymmetry for the disordered two-dimensional electron gas [Phys. Rev. B 103, 125422 (2021)

Erratum: Nonlinear sigma model with particle-hole asymmetry for the disordered two-dimensional electron gas [Phys. Rev. B 103, 125422 (2021)

Critical metallic phase in the overdoped random t-J model

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-M limit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t-J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev-Ye-Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-T resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

Universal transparency and asymmetric spin splitting near the Dirac point in HgTe quantum wells

Spin-orbit coupling in thin HgTe quantum wells results in a relativistic-like electron band structure, making it a versatile solid state platform to observe and control nontrivial electrodynamic phenomena. Here we report an observation of universal terahertz (THz) transparency determined by fine-structure constant $\ensuremath{\alpha}\ensuremath{\approx}1/137$ in 6.5-nm-thick HgTe layer, close to the critical thickness separating phases with topologically different electronic band structure. Using THz spectroscopy in a magnetic field we obtain direct evidence of asymmetric spin splitting of the Dirac cone. This particle-hole asymmetry facilitates optical control of edge spin currents in the quantum wells.

Doped Mott insulators in the triangular-lattice Hubbard model

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\delta$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\delta\lesssim 10\%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $\delta \approx 10\%\sim 20\%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\delta \gtrsim 20\%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

Subgap states spectroscopy in a quantum dot coupled to gapped hosts: Unified picture for superconductor and semiconductor bands

We present a unified theory of quantum phase transitions for half-filled quantum dots (QDs) coupled to gapped host bands. We augment the bands by an additional weakly coupled metallic lead, which allows us to analyze the system by using standard numerical renormalization-group techniques. The ground-state properties of the systems without the additional metallic lead are then extrapolated in a controlled way from the broadened subgap spectral functions. We show that a broad class of narrow-gap-semiconductor tunneling densities of states (TDOSs) support the existence of two distinct phases known from their superconducting counterpart: the 0 phase, which is marked by the singlet ground state, and the $\ensuremath{\pi}$ phase regime with the doublet ground state. To keep a close analogy with the superconducting case, we focus on the influence of particle-hole asymmetry of the TDOS on the subgap spectral features. Nevertheless, we also discuss the possibility of inducing singlet-doublet quantum phase transitions in experimental setups by varying the filling of the QD. In addition, for gapped TDOS functions with smoothed gap edges, we demonstrate that all subgap peaks may leak out of the gap into the continuous part of the spectrum, an effect that has no counterpart in the superconducting Anderson model.

Planckian metal at a doping-induced quantum critical point

We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi liquid phase with a large Fermi surface volume and a low-doping phase with local moments ordering into a spin-glass. We show that this quantum critical point has non-Fermi liquid properties characterized by $T$-linear Planckian behavior, $\omega/T$ scaling and slow spin dynamics of the Sachdev-Ye-Kitaev (SYK) type. The $\omega/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a `skewed' non-Fermi liquid.

Particle–hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films

Intrinsically broken symmetries in the bulk of topological insulators (TIs) are manifested in their surface states. Despite particle–hole asymmetry in TIs, it has often been assumed that their surface states are characterized by a particle–hole symmetric Dirac energy dispersion. In this work, we demonstrate that the effect of particle–hole asymmetry is essential to correctly describe the energy spectrum and the magneto-optical response in TIs thin-films. In thin-films of TIs with a substantial degree of particle–hole symmetry breaking, such as Sb2Te3, the longitudinal optical conductivity displays absorption peaks arising from optical transitions between bulk and surface Landau levels for low photon energies. The transition energies between the bulk and surface Landau levels exhibit clearly discernable signatures from those between surface Landau levels due to their distinct magnetic field dependence. Bulk contributions to the magneto-optical conductivity in a TI thin-film are enhanced via one type of doping while being suppressed by the other. This asymmetric dependence on the type of doping aids in revealing the particle–hole asymmetry in TI thin-films.

Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors

Clapping modes, which are relative amplitude and phase modes between two chiral components of Cooper pairs, are bosonic collective modes inherent to chiral superconductors. These modes behave as long-lived bosons with masses smaller than the threshold energy, $2|\Delta|$, for decay into unbound fermion pairs. Here, we clarify that the real/imaginary clapping modes in chiral superconductors directly couple to acoustic wave propagation when the weak particle-hole asymmetry of the normal state quasiparticle dispersion is taken into account. The clapping modes driven by an acoustic wave generate an alternating electric current, that is, the acoustoelectric effect in superconductors. Significantly, the clapping modes give rise to a transverse electric current. When the sound velocity is comparable to the Fermi velocity, as in heavy fermion compounds, the transverse current is resonantly enhanced at energy below the threshold for continuum excitations. This resonance provides a smoking-gun evidence of chiral superconductivity.