Motivated by recent experiments on Kondo insulators, we theoretically study quantum oscillations from disorder-induced in-gap states in small-gap insulators. By solving a non-Hermitian Landau level problem that incorporates the imaginary part of electron's self-energy, we show that the oscillation period is determined by the Fermi surface area in the absence of the hybridization gap, and derive an analytical formula for the oscillation amplitude as a function of the indirect band gap, scattering rates, and temperature. Over a wide parameter range, we find that the effective mass is controlled by scattering rates, while the Dingle factor is controlled by the indirect band gap. We also show the important effect of scattering rates in reshaping the quasiparticle dispersion in connection with angle-resolved photoemission measurements on heavy fermion materials.
We investigate disorder effects on Landau levels in Dirac electron systems with the use of a non-Hermitian quasiparticle Hamiltonian formalism. This formalism reveals that spin-dependent scattering rates induce the spectrum collapse of Landau levels, i.e., the disappearance of the energy gaps between n-th and -n-th levels under a finite external magnetic field. The spectrum collapse occurs in both weak and strong magnetic field regimes, thus showing a reentrant behavior. Particularly, in the strong magnetic field regime, in contrast to naive expectation, the increase of a magnetic field stabil…
The Lindhard function represents the basic building block of many-body physics and accounts for charge response, plasmons, screening, Friedel oscillation, RKKY interaction etc. Here we study its non-Hermitian version in one dimension, where quantum effects are traditionally enhanced due to spatial confinement, and analyze its behavior in various limits of interest. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wavenumber and vanishes identically for all other wavenumbers at zero temperature. Consequently, no Friedel …
We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These `zero Landau level' quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes, and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a `s…
We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of…
A new family of the low-buckled Dirac materials which includes silicene, germanene, etc. is expected to possess a more complicated sequence of Landau levels than in pristine graphene. Their energies depend, among other factors, on the strength of the intrinsic spin-orbit (SO) and Rashba SO couplings and can be tuned by an applied electric field $E_z$. We studied the influence of the intrinsic Rashba SO term on the energies of Landau levels using both analytical and numerical methods. The quantum magnetic oscillations of the density of states are also investigated. A specific feature of the osc…
We report the observation of novel magnetoresistance oscillations induced by the resonant inter-subband absorption in nondegenerate 2D electrons bound to the surface of liquid helium. The oscillations are periodic in 1/B and originate from the scattering-mediated transitions of the excited electrons into the Landau states of the first subband. The structure of the oscillations is affected by the collision broadening of the Landau levels and by many-electron effects.
Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically …
Non-Hermitian materials can not only exhibit exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is not clear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functio…
Nodal line semimetals (NLSM) exhibit interesting quantum oscillation characteristics when acted upon by a strong magnetic field. We study the combined effect of strong direct (dc) and alternating (ac) magnetic field, perpendicular to the nodal plane in an untilted NLSM in order to probe the behavior of the low lying Landau level (LL) states that can periodically become gapless for suitably chosen field parameters. The oscillatory field variation, as opposed to a steady one, has interesting impact on the quantum oscillation phenomena with the Landau tubes crossing the Fermi surface extremally t…
Bloch-Zener oscillations (BZO), i.e. the interplay between Bloch oscillations and Zener tunneling in two-band lattices under an external dc force, are ubiquitous in different areas of wave physics, including photonics. While in Hermitian systems such oscillations are rather generally aperiodic and only accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition from aperiodic to periodic as a NH parameter in the system is varied. Remarkably, the phase transition can be either smooth or sharp, contrary to other types of NH phase transitions which are universally sharp. A dis…
We analyze the spectrum of electron density oscillations in an interacting one-dimensional electron system with an impurity. The system's inhomogeneity is characterized by different values of Fermi wave vectors $k_F=k_{L/R}$ on left/right side of the scatterer, leading to a Landauer dipole formation. We demonstrate, that while in the noninteracting system the Friedel oscillations possess only one periodicity related to the local $k_F$, say $k_L$ on the left side, the interplay of the interactions and the Landauer dipole generates an additional peak in the spectrum of density oscillations at th…
Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the …
Bloch oscillations (BOs), i.e. the oscillatory motion of a quantum particle in a periodic potential, are one of the most striking effects of coherent quantum transport in the matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called 'acceleration' theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shap…
We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level ($ν= 1/2$) that result from the presence of a periodic one-dimensional electrostatic potential. We use the Dirac composite fermion theory of Son [Phys. Rev. X 5 031027 (2015)], where the $ν=1/2$ state is described by a $(2+1)$-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger--Dy…
Landau and fractionalized theories of periodically driven intertwined orders
ITAMP, Center for Astrophysics | Harvard & Smithsonian（哈佛大学-史密森尼天体物理中心）；Department of Physics, Harvard University（哈佛大学物理系）；Center for Computational Quantum Physics, Flatiron Institute（平托研究所计算量子物理中心）；Max Planck Institute for Solid State Research（马克斯·普朗克固态研究所）
In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, charge-neutral fermions, e.g., spinons and fermionic excitons, that result in neutral Fermi surfaces and Landau quantization in an insulator. While previous experiments in quantum spin liquids, topological Kondo insulators, and quantum Hall systems have hinted at charge-neutral Fermi surfaces, evidence for their existence remains far from conclusive. Here we report experimental observation of Landau quantization in a two dimensional (2D…
We show that Shubnikov-de Haas oscillations in the interlayer resistivity of the organic superconductor $β''$-(BEDT-TTF)$_{2}$SF$_{5}$ CH$_{2}$CF$_{2}$SO$_{3}$ become very pronounced in magnetic fields $\sim$~60~T. The conductivity minima exhibit thermally-activated behaviour that can be explained simply by the presence of a Landau gap, with the quasi-one-dimensional Fermi surface sheets contributing negligibly to the conductivity. This observation, together with complete suppression of chemical potential oscillations, is consistent with an incommensurate nesting instability of the quasi-one-d…
Motivated by recent experiments on Pr2Ir2O7, we provide a theory of quantum oscillations in the Luttinger model with quadratic band touching, modelled for the spin-orbit-coupled conduction electrons in pyrochlore iridates. The magneto- and Hall resistivities are computed for electron- and hole-doped systems, and the corresponding Shubnikov de Haas (SdH) signals are investigated. The SdH signals are characterized by aperiodic behaviors that originate from the unconventional Landau level structures of the Luttinger model near the neutrality point, such as the inter-Landau level crossing, nonunif…
The normal-state energy spectrum of the two-dimensional $t$-$J$ model in a homogeneous perpendicular magnetic field is investigated. The density of states at the Fermi level as a function of the inverse magnetic field $\frac{1}{B}$ reveals oscillations in the range of hole concentrations $0.08<x<0.18$. The oscillations have both high- and low-frequency components. The former components are connected with large Fermi surfaces, while the latter with van Hove singularities in the Landau subbands, which traverse the Fermi level with changing $B$. The singularities are related to bending the Landau…
The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a metod due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density matrix renormalization group result is obtained.
Quantum oscillations have long been regarded as the manifestation of the Fermi surface in metals. However, they were recently observed in Kondo insulators. We examine the Kondo screening due to Landau levels in Kondo insulators. It is shown that even for large Kondo insulating gaps, appreciable amplitudes of quantum oscillations that are consistent with experimental observations are present both in magnetization and resistivity. Specifically, we show that due to the periodic alignment between the Landau levels in the conduction and the f-orbit electrons, the Kondo screening itself undergoes os…
We describe the lowest Landau level of a quantum electron star in AdS4. In the presence of a suitably strong magnetic field, the dynamics of fermions in the bulk is effectively reduced from four to two dimensions. These two-dimensional fermions can subsequently be treated using the techniques of bosonization and the difficult many-body problem of building a gravitating, charged quantum star is reduced to solving the sine-Gordon model coupled to a gauge field and a metric. The kinks of the sine-Gordon model provide the holographic dual of the lowest Landau levels of the strongly-coupled d=2+1 d…
Motivated by the recent advances in modelling the pseudo-Hermitian Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum dynamics subject to a small time-dependent perturbation. In particular, We develop the linear response theory formulation suitable for application to various pHH systems and compare it to the ones available in the literature. We derive analytical expressions for the generalized temporal quantum-mechanical correlation function $C(t)$ and the time-dependent dynamic susceptibility $χ(t) \propto \text{Im} ~C(t)$. We apply our results to two \textit{PT}-…
