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Physical review. B./Physical review. B

Spin stiffness of a Fermi liquid in the ν=1 quantum Hall regime

A. B. Van'kov, Игорь Владимирович Кукушкин

Published Dec 21, 2020• 9 citations
Publisher

Abstract

Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter ${r}_{s}>6$. The spin stiffness is extracted directly from the quadratic $k$ dispersion of spin excitons at $\ensuremath{\nu}=1$ probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs---spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.

DOI
10.1103/physrevb.102.235424

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•Jan 1, 2014•0 citations
Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter rs>6{r}_{s}>6rs​>6. The spin stiffness is extracted directly from the quadratic kkk dispersion of spin excitons at \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=1 probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs---spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.
Collective spin excitations were utilized to probe many-particle energies of strongly correlated quantum Hall ferromagnets (FMs) at $\frac{1}{3}\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}1$. For this purpose, experiments on inelastic light scattering and polarized photoluminescence (PL) were performed on a MgZnO/ZnO heterostructure, containing a high-mobility two-dimensional electron system with the Wigner-Seitz parameter ${r}_{s}\ensuremath{\approx}11$. The dispersion of the Larmor spin exciton was utilized to extract the spin stiffness, which was found to have maxima at $\ensuremath{\nu}=\frac{1}{3}, \ensuremath{\nu}=1$, and to be strongly suppressed at intermediate filling factors. Measurements of circularly polarized PL helped to confirm a FM configuration of the system. In the close vicinity of $\ensuremath{\nu}=\frac{1}{3}$, a hybrid spin-density excitation was discovered, the energy of which enables us to probe the correlation energy of the Laughlin liquid. The measured correlation and exchange energies at $\ensuremath{\nu}=\frac{1}{3}$ and ${r}_{s}\ensuremath{\gg}1$ turned out to be much less suppressed by the Landau level mixing than the exchange energy at integer filling factors. The same answer follows from the calculations performed using the exact diagonalization method.
We derive analytical expressions for the quasiparticle lifetime $\ensuremath{\tau}$, the effective mass m∗{m}^{*}m∗, and the Green's function renormalization factor ZZZ for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index $\ensuremath{\rho}$, and occur in second order of the spin-orbit coupling $\ensuremath{\alpha}$. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small $\ensuremath{\alpha}$.
We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.
Electrons in two-dimensional (2D) layers at semiconductor interfaces may be driven to a solid phase by reducing their density. Understandmg of this electron liquid-solid transition at mK-temperatures and the origin of the 2D electron solid phase remain challenging. The experimental system under study is subject to strong interactions and disorder. Charge transport in the electron solid phase demonstrates many features anticipated for the pinned crystal, though no direct imaging of a spatial charge- or magnetic-ordering is available by now. Rich information has been recently obtained for dilute electron liquid phase on strong renormalization of the Pauli spin susceptibility, magnetization, and the effective mass. These data provide a set of the Fermi-liquid coupling parameters for densities down to and at the transition. The steep density dependence of the susceptibility is intriguing because it might indicate a developing magnetic transition, though it is more likely reflects a tendency to crystallization.
Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.
In this dissertation, we investigate the edge spin excitations and reconstructions of quantum Hall (QH) liquids. Edge spin reconstructions reflect the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of QH liquids. The main method used in this dissertation is the exact diagonalization calculation for finite size systems. The QH liquids studied in this dissertation are classified into three kinds, based on their topological properties and statistics of quasiparticles (quasiholes). The first kind of QH liquids is spin-polarized QH liquids. The QH liquids with filling factors ν = 1 and 1/3 are studied in this kind. We find the low-energy excitations of the ν = 1 and 1/3 are bosonic edge spin waves. Instabilities of these ferromagnetic state with altering confinement strength result from the softening of these spin waves and formation of edge spin textures. A microscopic trial wave function is used to study the edge instabilities of larger systems with particle number up to 40, and the obtained results are consistent to the ones calculated by exact diagonalization. The second kind of QH liquids is spin-unpolarized QH liquids. The liquids with ν = 2, 2/5 and 2/3 are studied in this kind. When ν = 2, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appearing between two compact states are their edge spin waves. The initial ν = 2 instability is toward the compact state with total spin 1. At ν = 2/5, the edge instabilities is also triggered by softening of the edge spin waves with smoother confinement. The situation of ν = 2/3 unpolarized QH liquids is a little different, because it has one backward-moving edge spin wave mode and one forward-moving magnetoplasmon mode. There is no mystery about what kind of instability would occur with stronger or smoother confinement. The exact diagonalization calculation of finite systems can reproduce the instability induced by edge spin wave at the stronger confinement side and gives an estimate about the critical value of confining potential. But instability due to edge magnetoplasmon mode can not be realized in small size systems because of the high velocity of this mode. The last kind is the non-Abelian QH liquid (at ν = 5/2). Its edge instability triggered by softening of edge magnetoplasmon excitations with smoother confinement. Three different confinements are compared in the study of integer QH liquids in finite size systems. And some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit. The effect of Zeeman splitting to the edge instabilities is also considered in this dissertation.