States In Two-dimensional Electron Systems Research Articles

Investigation of spin stiffness in spin-depolarized states of two-dimensional electron systems with time-resolved Kerr rotation

An experimental technique based on time-resolved Kerr rotation allows a comparison of the spin stiffnesses of different spin-polarized and depolarized states in a two-dimensional electron system. With this technique, a new spin-correlated phase that has no known analogues was discovered. The new spin-depolarized phase is characterized by high spin stiffness equal to that of a spin-polarized quantum Hall ferromagnet.

Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene

Competition between liquid and solid states in two-dimensional electron systems is an intriguing problem in condensed matter physics. We have investigated competing Wigner crystal and fractional quantum Hall (FQH) liquid phases in atomically thin suspended graphene devices in Corbino geometry. Low-temperature magnetoconductance and transconductance measurements along with IV characteristics all indicate strong charge density dependent modulation of electron transport. Our results show unconventional FQH phases which do not fit the standard Jain’s series for conventional FQH states, instead they appear to originate from residual interactions of composite fermions in partially filled Landau levels. Also at very low charge density with filling factors nu ,lesssim, 1/5, electrons crystallize into an ordered Wigner solid which eventually transforms into an incompressible Hall liquid at filling factors around ν ≤ 1/7. Building on the unique Corbino sample structure, our experiments pave the way for enhanced understanding of the ordered phases of interacting electrons.

Nature of localized states in two-dimensional electron systems in the quantum Hall regime: Acoustic studies

We review our work on high-frequency conductance in two-dimensional high-mobility electronic systems in wide n-AlGaAs/GaAs/AlGaAs quantum wells. Using simultaneous measurements of the attenuation and velocity of a surface acoustic wave we obtained both real and imaginary components of the complex high-frequency conductance. Based on the experimental results and their analysis we conclude that close to the filling factor ν = 1/5, as well as in the interval 0.18 > ν > 0.125, a Wigner crystal pinned by disorder is formed. Both the melting temperature and the correlation length of the pinning-induced domains in the Wigner crystal were found. In close vicinities of ν = 1 and 2, transitions from single-electron localization to a Wigner crystal were observed.

Microwave-induced zero-resistance state in two-dimensional electron systems with unidirectional periodic modulation

In this study we fabricated lateral superlattices (LSLs) based on the selectively doped GaAs/AlAs heterostructures with a high-mobility two-dimensional (2D) electron gas. The LSLs were formed using the electron-beam lithography and lift-off techniques, which produced a set of metallic strips on top of a heterojunction. The amplitude of the 2D electron gas modulation in the LSL was controlled by the gate voltage applied to the metallic strips. The LSLs with two different periods (a = 200 nm and 500 nm) were used to investigate the influence of microwave radiation with the frequency of 110–150 GHz on the 2D electron transport at the temperature T = 1.6 K in the magnetic field B < 1 T. We have found that zero-resistance states (ZRSs) appear under the microwave radiation in the 2D systems with a unidirectional periodic modulation. These ZRSs are located at the minima of commensurability oscillations.

Comment on “Theory of microwave-induced zero-resistance states in two-dimensional electron systems” and on “Microwave-induced zero-resistance states and second-harmonic generation in an ultraclean two-dimensional electron gas”

Recent papers by S. A. Mikhailov [Phys. Rev. B 83, 155303 (2011) and Phys. Rev. B 89, 045410 (2014)] claim to explain ``all experimental facts'' pertinent to microwave-induced resistance oscillations and zero-resistance states in terms of ``the ponderomotive force theory.'' This Comment shows that the analysis of the results obtained in the above-mentioned papers, in fact, leads to opposite conclusions, i.e., that they cannot explain even the most basic experimental facts.

Reply to “Comment on ‘Theory of microwave-induced zero-resistance states in two-dimensional electron systems’ and on ‘Microwave-induced zero-resistance states and second-harmonic generation in an ultraclean two-dimensional electron gas’ ”

We show that all questions raised in the Comment can be easily answered within the theory formulated in the commented papers. It is also shown that the bulk theory promoted by the commenter fails to explain the most important fundamental features of the discussed phenomenon.

Spin polarization of composite fermions and particle-hole symmetry breaking

We study the critical spin-polarization energy ($\alpha_{\rm C}$) above which fractional quantum Hall states in two-dimensional electron systems confined to symmetric GaAs quantum wells become fully spin-polarized. We find a significant decrease of $\alpha_{\rm C}$ as we increase the well-width. In systems with comparable electron layer thickness, $\alpha_{\rm C}$ for fractional states near Landau level filling $\nu=3/2$ is about twice larger than those near $\nu=1/2$, suggesting a broken particle-hole symmetry. Theoretical calculations, which incorporate Landau level mixing through an effective three-body interaction, and finite layer thickness, capture certain qualitative features of the experimental results.

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].

Full tilt

An in-plane magnetic field usually destroys the isotropic fractional quantum Hall states of two-dimensional electron systems, and gives rise to anisotropic liquid-crystal-like states. An unexpected observation of the coexistence of both states at once suggests the emergence of a new quantum phase of matter.

Interface states in two-dimensional electron systems with spin–orbital interaction

Interface states at a boundary between regions with different spin–orbit interactions (SOIs) in two-dimensional (2D) electron systems are investigated within the one-band effective mass method with generalized boundary conditions for envelope functions. We have found that the interface states unexpectedly exist even if the effective interface potential equals zero. Depending on the system parameters, the energy of these states can lie in either or both forbidden and conduction bands of bulk states. The interface states have chiral spin texture similar to that of the edge states in 2D topological insulators. However, their energy spectrum is more sensitive to the interfacial potential, the largest effect being produced by the spin-dependent component of the interfacial potential. We have also studied the size quantization of the interface states in a strip of 2D electron gas with SOI and found an unusual (non-monotonic) dependence of the quantization energy on the strip width.

Microwave-induced resistance oscillations and zero-resistance states in two-dimensional electron systems with two occupied subbands

We report on theoretical studies of recently discovered microwave-induced resistance oscillations and zero resistance states in Hall bars with two occupied subbands. In the same results, resistance presents a peculiar shape which appears to have a built-in interference effect not observed before. We apply the microwave-driven electron orbit model, which implies a radiation-driven oscillation of the two-dimensional electron system. Thus, we calculate different intra and inter-subband electron scattering rates and times that are revealing as different microwave-driven oscillations frequencies for the two electronic subbands. Through scattering, these subband-dependent oscillation motions interfere giving rise to a striking resistance profile. We also study the dependence of irradiated magnetoresistance with power and temperature. Calculated results are in good agreement with experiments.

Theory of microwave-induced zero-resistance states in two-dimensional electron systems

The phenomena of the microwave induced zero resistance states (MIZRS) and the microwave induced resistance oscillations (MIRO) were discovered in the ultraclean two-dimensional electron systems in 2001 -- 2003 and have attracted great interest of researchers. In spite of numerous theoretical efforts the true origin of these effects remains unknown so far. We show that the MIRO/ZRS phenomena are naturally explained by the influence of the ponderomotive forces which arise in the near-contact regions of the two-dimensional electron gas under the action of microwaves. The proposed analytical theory is in agreement with all experimental facts accumulated so far and provides a simple and self-evident explanation of the microwave frequency, polarization, magnetic field, mobility, power and temperature dependencies of the observed effects.

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.

Synthetic magnetic fields for ultracold neutral atoms

Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation-a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall effect in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, which is evident from the appearance of vortices in our Bose-Einstein condensate. Our approach uses a spatially dependent optical coupling between internal states of the atoms, yielding a Berry's phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems. With a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.

Nonlinear transport theory for negative-differential resistance states of two-dimensional electron systems in strong magnetic fields

We present a model to describe the nonlinear response to a direct dc current applied to a two-dimensional electron system in a strong magnetic field. The model is based on the solution of the von Neumann equation incorporating the exact dynamics of two-dimensional damped electrons in the presence of arbitrarily strong magnetic and dc electric fields, while the effects of randomly distributed impurities are perturbatively added. From the analysis of the differential resistivity and the longitudinal voltage we observe the formation of negative differential resistivity states (NDRS) that are the precursors of the zero differential resistivity states (ZDRS). The theoretical predictions correctly reproduce the main experimental features provided that the inelastic scattering rate obey a $T^2$ temperature dependence, consistent with electron-electron interaction effects.

Evanescent states in two-dimensional electron systems with spin-orbit interaction and spin-dependent transmission through a barrier

We find that the total spectrum of electron states in a bounded two-dimensional electron gas with spin-orbit interaction contains two types of evanescent states lying in different energy ranges. The first-type states fill in a gap, which opens in the band of propagating spin-splitted states if tangential momentum is nonzero. They are described by a pure imaginary wave vector. The states of second type lie in the forbidden band. They are described by a complex wave vector. These states give rise to unusual features of the electron transmission through a lateral potential barrier with spin-orbit interaction, such as an oscillatory dependence of the tunneling coefficient on the barrier width and electron energy. However, of most interest is the spin polarization of an unpolarized incident electron flow. Particularly, the transmitted electron current acquires spin polarization even if the distribution function of incident electrons is symmetric with respect to the transverse momentum. The polarization efficiency is an oscillatory function of the barrier width. Spin filtering is most effective if the Fermi energy is close to the barrier height.

Temperature effects on microwave-induced resistivity oscillations and zero-resistance states in two-dimensional electron systems

In this work we address theoretically a key issue concerning microwave-induced longitudinal resistivity oscillations and zero resistance states, namely, temperature. In order to explain the strong temperature dependence of the longitudinal resistivity and the thermally activated transport in two-dimensional electron gas, we have developed a microscopic model based on the damping suffered by the microwave-driven electronic orbit dynamics by interactions with the lattice ions yielding acoustic phonons. Recent experimental results show a reduction in the amplitude of the longitudinal resistivity oscillations and a breakdown of zero resistance states as the radiation intensity increases. In order to explain it we have included in our model the electron heating due to large microwave intensities and its effect on the longitudinal resistivity.

Microwave photoconductivity of two-dimensional electron systems with unidirectional periodic modulation

Motivated by the recently discovered microwave-induced ``zero-resistance'' states in two-dimensional electron systems, we study the microwave photoconductivity of a two-dimensional electron gas (2DEG) subject to a unidirectional static periodic potential. The combination of this potential, the classically strong magnetic field, and the microwave radiation may result in an anisotropic negative conductivity of the 2DEG. Similar to the case of a smooth random potential, two mechanisms contribute to the negative photoconductivity. The displacement mechanism arises from electron transitions due to disorder-assisted microwave absorption and emission. The distribution-function mechanism arises from microwave-induced changes in the electron distribution. However, the replacement of a smooth random potential by the unidirectional one, leads to different relative strengths of the two contributions to the photoconductivity. The distribution function mechanism dominates the photoconductivity in the direction of the static potential modulation, while both mechanisms contribute equally strongly to the photoconductivity in the perpendicular direction. The unidirectionality of the static potential simplifies greatly the evaluation of the photoconductivities, which follow directly from Fermi's golden rule.

Absolute negative conductivity and zero-resistance states in two-dimensional electron systems: A plausible scenario

We present a model that provides a plausible explanation of the effect of zero-resistance and zero-conductance states in two-dimensional electron systems subjected to a magnetic field and irradiated with microwaves observed in a number of experiments and of the effect’s main features. The model is based on the concept of absolute negative conductivity associated with photon-assisted scattering of electrons on impurities. It is shown that the main features of the effect can be attributed to the interplay of different electron scattering mechanisms.

Period and phase of microwave-induced resistance oscillations and zero-resistance states in two-dimensional electron systems

We present phenomenological analysis of the period and the phase of microwave-induced resistance oscillations (MIRO) and ``zero-resistance'' states (ZRS) recently observed in two-dimensonal electron systems. While MIRO are found to be well described by a ``1/4-cycle shift,'' we find that as MIRO evolve into ZRS with increasing magnetic field B, the phase becomes progressively smaller, decreasing roughly as $1/B.$ As a result, both maxima and minima in the ZRS regime form periodic in $1/B$ sequences, without a 1/4-cycle shift. A simple model based on oscillatory density of states is found to provide a unified description of the period/phase of MIRO/ZRS and leads to an interpretation of previously reported fine structures in terms of multiphoton processes.