arXiv:cond-mat/0210569 · Journal of the Physical Society of Japan

Ground State Phase Diagram of 2D Electrons in High Magnetic Field

Naokazu Shibata, D. Yoshioka

Published Mar 15, 2003• 51 citations

Abstract

The ground state of 2D electrons in high magnetic field is studied by the density matrix renormalization group method. The ground state energy, excitation gap, and pair correlation functions are systematically calculated at various fillings in the lowest and the second lowest Landau levels. The ground state phase diagram, which consists of incompressible liquid state, compressible liquid state, stripe state, pairing state, and Wigner crystal is determined.

DOI: 10.1143/jpsj.72.664

Related papers

Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study

Naokazu Shibata, D. Yoshioka

arXiv:cond-mat/0101401Physical Review LettersJun 18, 2001148 citations

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method

Naokazu Shibata

arXiv:0906.1036Progress of Theoretical Physics SupplementJan 1, 20089 citations

Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

Naokazu Shibata, D. Yoshioka

arXiv:cond-mat/0403493Journal of the Physical Society of JapanAug 15, 200411 citations

Stripe State in the Lowest Landau Level

Naokazu Shibata, D. Yoshioka

The stripe state in the lowest Landau level is studied by the density matrix renormalization group (DMRG) method. The ground state energy and pair correlation functions are systematically calculated for various pseudopotentials in the lowest Landau level. We show that the stripe state in the lowest Landau level is realized only in a system whose width perpendicular to the two-dimensional electron layer is smaller than the order of magnetic length.

arXiv:cond-mat/0311213Journal of the Physical Society of JapanJan 15, 200415 citations

Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

Emil J. Bergholtz, A. Karlhede

arXiv:cond-mat/0304517Apr 23, 20033 citations

Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects

Xuejun Zhu, Steven G. Louie

arXiv:cond-mat/9505074Physical review. B, Condensed matterAug 15, 199558 citations

arXiv:cond-mat/0210569 · Journal of the Physical Society of Japan

Ground State Phase Diagram of 2D Electrons in High Magnetic Field

Naokazu Shibata, D. Yoshioka

Published Mar 15, 2003• 51 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsj.72.664

Related papers

Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study

Naokazu Shibata, D. Yoshioka

The ground-state phase diagram of 2D electrons in a high Landau level (index $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ ) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to $1/2$ . It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.The ground-state phase diagram of 2D electrons in a high Landau level (index $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to $1/2$. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.

arXiv:cond-mat/0101401Physical Review LettersJun 18, 2001148 citations

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method

Naokazu Shibata

The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.

arXiv:0906.1036Progress of Theoretical Physics SupplementJan 1, 20089 citations

Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

Naokazu Shibata, D. Yoshioka

The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.

arXiv:cond-mat/0403493Journal of the Physical Society of JapanAug 15, 200411 citations

Stripe State in the Lowest Landau Level

Naokazu Shibata, D. Yoshioka

arXiv:cond-mat/0311213Journal of the Physical Society of JapanJan 15, 200415 citations

Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

Emil J. Bergholtz, A. Karlhede

We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to the surface. For a thin cylinder, the ground state is for generic filling factors a charge density wave state, however, at $ν=1/2$ a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to the surface. For a thin cylinder, the ground state is for generic filling factors a charge density wave state, however, at $ν=1/2$ a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.

arXiv:cond-mat/0304517Apr 23, 20033 citations

Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects

Xuejun Zhu, Steven G. Louie

The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wave function of the strongly correlated solid. Exchange, correlation, and magnetic-field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from n doping to p doping in GaAs/ ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor \ensuremath{\nu}\ensuremath{\sim}1/5 to \ensuremath{\nu}\ensuremath{\sim}1/3. This lends strong support to the claim that the observed reentrant insulating phases around \ensuremath{\nu}=1/5 for n-doped and around \ensuremath{\nu}=1/3 for p-doped high-mobility samples are primarily caused by electron-electron interaction effects. We discuss the possible implications of our theoretical results for some recent experiments carried out in the quantum Hall regime in search of the electron solid.The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wave function of the strongly correlated solid. Exchange, correlation, and magnetic-field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from n doping to p doping in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor \ensuremath{\nu}\ensuremath{\sim}1/5 to \ensuremath{\nu}\ensuremath{\sim}1/3. This lends strong support to the claim that the observed reentrant insulating phases around \ensuremath{\nu}=1/5 for n-doped and around \ensuremath{\nu}=1/3 for p-doped high-mobility samples are primarily caused by electron-electron interaction effects. We discuss the possible implications of our theoretical results for some recent experiments carried out in the quantum Hall regime in search of the electron solid.

arXiv:cond-mat/9505074Physical review. B, Condensed matterAug 15, 199558 citations

The ground-state phase diagram of 2D electrons in a high Landau level (index

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to

1/2

. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.

ν=1/2

a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.

{\mathrm{Al}}_{\mathit{x}}

${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor \ensuremath{\nu}\ensuremath{\sim}1/5 to \ensuremath{\nu}\ensuremath{\sim}1/3. This lends strong support to the claim that the observed reentrant insulating phases around \ensuremath{\nu}=1/5 for n-doped and around \ensuremath{\nu}=1/3 for p-doped high-mobility samples are primarily caused by electron-electron interaction effects. We discuss the possible implications of our theoretical results for some recent experiments carried out in the quantum Hall regime in search of the electron solid.