We consider a fixed impurity immersed in a Fermi gas at finite temperature. We take the impurity to have two internal spin states, where the $uparrow$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, w
hile the $downarrow$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states therefore allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity Greens functions with a variational approach to treat the Rabi driven dynamics, we find that the system features Rabi oscillations whose frequency scales as a non-trivial power of the Rabi drive at low temperatures. This reflects the power law of the Fermi-edge singularity and, importantly, this behavior is qualitatively different from the case of a mobile impurity quasiparticle where the scaling is linear. We therefore argue that the scaling law serves as an experimentally implementable probe of the orthogonality catastrophe. We additionally simulate rf spectroscopy beyond linear response, finding a remarkable agreement with an experiment using heavy impurities [Kohstall $textit{et al.}$, Nature $textbf{485}$, 615 (2012)], thus demonstrating the power of our approach.
We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi o
scillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is determined by many-body dephasing within the upper repulsive branch rather than by the metastability of the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.
We study the phase diagram of the interacting two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit coupling, which for weak coupling gives rise to the well-known persistent spin-helix phase. We construct the full Hartree-F
ock phase diagram using a classical Monte-Carlo method analogous to that used in Phys.Rev.B 96, 235425 (2017). For the 2DEG with only Rashba spin-orbit coupling, it was found that at intermediate values of the Wigner-Seitz radius rs the system is characterized by a single Fermi surface with an out-of-plane spin polarization, while at slightly larger values of rs it undergoes a transition to a state with a shifted Fermi surface and an in-plane spin polarization. The various phase transitions are first-order, and this shows up in discontinuities in the conductivity and the appearance of anisotropic resistance in the in-plane polarized phase. In this work, we show that the out-of-plane spin-polarized region shrinks as the strength of the Dresselhaus spin-orbit interaction increases, and entirely vanishes when the Rashba and Dresselhaus spin-orbit coupling strengths are equal. At this point, the system can be mapped onto a 2DEG without spin-orbit coupling, and this transformation reveals the existence of an in-plane spin-polarized phase with a single, displaced Fermi surface beyond rs > 2.01. This is confirmed by classical Monte-Carlo simulations. We discuss experimental observation and useful applications of the novel phase, as well as caveats of using the classical Monte-Carlo method.
We investigate the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermis golden rule that introducing (or injecting) an impurity into the medium is equ
ivalent to ejecting an impurity that is initially interacting with the medium, since the injection and ejection spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using a range of theoretical methods, including variational approaches. We use this property to compute the finite-temperature equation of state and Tan contact of the Fermi polaron. Our results for the contact of a mobile impurity are in excellent agreement with recent experiments and we find that the finite-temperature behavior is qualitatively different compared to the case of infinite impurity mass.
We present a theory of radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. By working in the canonical ensemble of a single impurity, we show that the impurity spectral response is directly connected to th
e finite-temperature equation of state (free energy) of the impurity. We consider two different response protocols: injection, where the impurity is introduced into the medium from an initially non-interacting state; and ejection, where the impurity is ejected from an initially interacting state with the medium. We show that there is a simple mapping between injection and ejection spectra, which is connected to the detailed balance condition in thermal equilibrium. To illustrate the power of our approach, we specialize to the case of the Fermi polaron, corresponding to an impurity atom that is immersed in a non-interacting Fermi gas. For a mobile impurity with a mass equal to the fermion mass, we employ a finite-temperature variational approach to obtain the impurity spectral response. We find a striking non-monotonic dependence on temperature in the impurity free energy, the contact, and the radio-frequency spectra. For the case of an infinitely heavy Fermi polaron, we derive exact results for the finite-temperature free energy, thus generalizing Fumis theorem to arbitrary temperature. We also determine the exact dynamics of the contact after a quench of the impurity-fermion interactions. Finally, we show that the injection and ejection spectra obtained from the variational approach compare well with the exact spectra, thus demonstrating the accuracy of our approximate method.
We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium
to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Greens function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on $^{40}$K atoms in a $^6$Li Fermi gas [M.~Cetina et al., Science textbf{354}, 96 (2016)]. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.
Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglecte
d. Here we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In TIs, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional HLN formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In WSM thin films having intermediate to large values of the quasiparticle mass extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. We discuss implications for experiments and provide a brief comparison with transition metal dichalcogenides.
Spin-orbit coupling is a single-particle phenomenon known to generate topological order, and electron-electron interactions cause ordered many-body phases to exist. The rich interplay of these two mechanisms is present in a broad range of materials,
and has been the subject of considerable ongoing research and controversy. Here we demonstrate that interacting two-dimensional electron systems with strong spin-orbit coupling exhibit a variety of time reversal symmetry breaking phases with unconventional spin alignment. We first prove that a Stoner-type criterion can be formulated for the spin polarization response to an electric field, which predicts that the spin polarization susceptibility diverges at a certain value of the electron-electron interaction strength. The divergence indicates the possibility of unconventional ferromagnetic phases even in the absence of any applied electric or magnetic field. This leads us, in the second part of this work, to study interacting Rashba spin-orbit coupled semiconductors in equilibrium in the Hartree-Fock approximation as a generic minimal model. Using classical Monte-Carlo simulations we construct the complete phase diagram of the system as a function of density and spin-orbit coupling strength. It includes both an out-of-plane spin polarized phase and in-plane spin-polarized phases with shifted Fermi surfaces and rich spin textures, reminiscent of the Pomeranchuk instability, as well as two different Fermi-liquid phases having one and two Fermi surfaces, respectively, which are separated by a Lifshitz transition. We discuss possibilities for experimental observation and useful application of these novel phases, especially in the context of electric-field-controlled macroscopic spin polarizations.
Topological semimetals have been at the forefront of experimental and theoretical attention in condensed matter physics. Among these, recently discovered Weyl semimetals have a dispersion described by a three-dimensional Dirac cone, which is at the r
oot of exotic physics such as the chiral anomaly in magnetotransport. In a time reversal symmetric (TRS) Weyl semimetal film, the confinement gap gives the quasiparticles a mass, while TRS is preserved by having an even number of valleys with opposite masses. The film can be tuned through a topological phase transition by a gate electric field. In this work, we present a theoretical study of the quantum corrections to the conductivity of a topological semimetal thin film, which is governed by the complex interplay of the chiral band structure, mass term, and scalar and spin-orbit scattering. We study scalar and spin-orbit scattering mechanisms on the same footing, demonstrating that they have a strong qualitative and quantitative impact on the conductivity correction. We show that, due to the spin structure of the matrix Greens functions, terms linear in the extrinsic spin-orbit scattering are present in the Bloch and momentum relaxation times, whereas previous works had identified corrections starting from the second order. In the limit of small quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to a potentially observable density dependence in the weak antilocalization correction. Moreover, when the mass term is around 30 percent of the linear Dirac terms, the system is in the unitary symmetry class with zero quantum correction and switching the extrinsic spin-orbit scattering drives the system to the weak antilocalization. We discuss the crossover between the weak localization and weak antilocalization regimes in terms of the singlet and triplet Cooperon channels, tuning the spin-orbit scattering strength.
Dirac fermions are actively investigated, and the discovery of the quantized anomalous Hall effect of massive Dirac fermions has spurred the promise of low-energy electronics. Some materials hosting Dirac fermions are natural platforms for interlayer
coherence effects such as Coulomb drag and exciton condensation. Here we determine the role played by the anomalous Hall effect in Coulomb drag in massive Dirac fermion systems. We focus on topological insulator films with out-of plane magnetizations in both the active and passive layers. The transverse response of the active layer is dominated by a topological term arising from the Berry curvature. We show that the topological mechanism does not contribute to Coulomb drag, yet the longitudinal drag force in the passive layer gives rise to a transverse drag current. This anomalous Hall drag current is independent of the active-layer magnetization, a fact that can be verified experimentally. It depends non-monotonically on the passive-layer magnetization, exhibiting a peak that becomes more pronounced at low densities. These findings should stimulate new experiments and quantitative studies of anomalous Hall drag.
