Recent experiments indicate the presence of new anisotropic fractional quantum Hall states at regimes not anticipated before. These experiments raise many fundamental questions regarding the inner nature of the electronic system that leads to such anisotropic states. Interplay between electron mass anisotropy and electron-electron correlation effects in a magnetic field can create a rich variety of possibilities. Several anisotropic electronic states ranging from anisotropic quantum Hall liquids to anisotropic Wigner solids may stabilize due to such effects. The electron mass anisotropy in a two-dimensional electron gas effectively leads to an anisotropic Coulomb interaction potential between electrons. An anisotropic interaction potential may strongly influence the stability of various quantum phases that are close in energy since the overall stability of an electronic system is very sensitive to local order. As a result there is a possibility that various anisotropic electronic phases may emerge even in the lowest Landau level in regimes where one would not expect them. In this work we study the state with filling factor 1/6 in the lowest Landau level, a state which is very close to the critical filling factor where the liquid-solid transition takes place. We investigate whether an anisotropic Coulomb interaction potential is able to stabilize an anisotropic electronic liquid state at this filling factor. We describe such an anisotropic state by means of a liquid crystalline wave function with broken rotational symmetry which can be adiabatically connected to the actual wave function for the corresponding isotropic phase. We perform quantum Monte Carlo simulations in a disk geometry to study the properties of the anisotropic electronic liquid state under consideration. The findings indicate stability of liquid crystalline order in presence of an anisotropic Coulomb interaction potential. The results are consistent with the existence of an anisotropic electronic liquid state in the lowest Landau level.Recent experiments indicate the presence of new anisotropic fractional quantum Hall states at regimes not anticipated before. These experiments raise many fundamental questions regarding the inner nature of the electronic system that leads to such anisotropic states. Interplay between electron mass anisotropy and electron-electron correlation effects in a magnetic field can create a rich variety of possibilities. Several anisotropic electronic states ranging from anisotropic quantum Hall liquids to anisotropic Wigner solids may stabilize due to such effects. The electron mass anisotropy in a two-dimensional electron gas effectively leads to an anisotropic Coulomb interaction potential between electrons. An anisotropic interaction potential may strongly influence the stability of various quantum phases that are close in energy since the overall stability of an electronic system is very sensitive to local order. As a result there is a possibility that various anisotropic electronic phases may emerge even in the lowest Landau level in regimes where one would not expect them. In this work we study the state with filling factor 1/6 in the lowest Landau level, a state which is very close to the critical filling factor where the liquid-solid transition takes place. We investigate whether an anisotropic Coulomb interaction potential is able to stabilize an anisotropic electronic liquid state at this filling factor. We describe such an anisotropic state by means of a liquid crystalline wave function with broken rotational symmetry which can be adiabatically connected to the actual wave function for the corresponding isotropic phase. We perform quantum Monte Carlo simulations in a disk geometry to study the properties of the anisotropic electronic liquid state under consideration. The findings indicate stability of liquid crystalline order in presence of an anisotropic Coulomb interaction potential. The results are consistent with the existence of an anisotropic electronic liquid state in the lowest Landau level.

AIP AdvancesDec 22, 201610 citations

Anisotropic Quantum Hall Liquids at Intermediate Magnetic Fields

Orion Ciftja, Chidera Ozurumba, Francis Ujeyah

Journal of Low Temperature PhysicsSep 15, 20124 citations

Liquid crystalline states for two-dimensional electrons in strong magnetic fields

Orion Ciftja, Cintia Mariela Lapilli, Carlos Wexler

Based on the Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma, we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wave functions that are translationally invariant but possess twofold (i.e., nematic), fourfold (tetratic), or sixfold (hexatic) broken rotational symmetry at respective filling factors $\ensuremath{\nu}=1/3,$ 1/5, and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge-density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L=0,1),$ whereas the nematic is favorable at the second excited LL $(L=2).$ Based on the Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma, we investigate the possibility of liquid crystalline states in a single Landau level (LL). We introduce many-body trial wave functions that are translationally invariant but possess twofold (i.e., nematic), fourfold (tetratic), or sixfold (hexatic) broken rotational symmetry at respective filling factors $\ensuremath{\nu}=1/3,$ 1/5, and 1/7 of the valence LL. We find that the above liquid crystalline states exhibit a soft charge-density wave (CDW) which underlies the translationally invariant state but which is destroyed by quantum fluctuations. By means of Monte Carlo simulations, we determine that, for a considerable variety of interaction potentials, the anisotropic states are energetically unfavorable for the lowest and first excited LL's (with index $L=0,1),$ whereas the nematic is favorable at the second excited LL $(L=2).$

arXiv:cond-mat/0311144Physical Review BMar 17, 200422 citations

Monte Carlo study of anisotropic quantum Hall liquid phases

Orion Ciftja, LeDarion Escamilla, Giancarlo Paredes +1 more

Bulletin of the American Physical SocietyMar 3, 20140 citations

On the quantum phase transition of a quantum Hall liquid

Adriaan M. J. Schakel

Nuclear Physics BOct 1, 19954 citations

Liquid crystalline states in quantum Hall systems

Carlos Wexler, Orion Ciftja

We investigate liquid crystalline phases with nematic order at (1/3)-filling of the valence Landau level (LL). We generalize Laughlin's fractional quantum Hall (QH) effect wavefunction at ν = (1/3) to include anisotropic nodal distribution by modifying the Jastrow factors. Lengthy Monte Carlo simulations are then used to determine with unprecedented accuracy the (anisotropic) pair distribution function g ( r ) and static structure factor S ( q ) for various degrees of anisotropy. The determination of the correlation energies at (1/3)-filling of an arbitrary LL is then performed by using standard mappings of g ( r ) and S ( q ) to higher LLs. Our results indicate that while Laughlin's state is stable in the lowest LL, there are regions of instability towards nematic order in higher LLs. Possible connections to the recently discovered QH liquid crystals are discussed.We investigate liquid crystalline phases with nematic order at (1/3)-filling of the valence Landau level (LL). We generalize Laughlin's fractional quantum Hall (QH) effect wavefunction at ν = (1/3) to include anisotropic nodal distribution by modifying the Jastrow factors. Lengthy Monte Carlo simulations are then used to determine with unprecedented accuracy the (anisotropic) pair distribution function g ( r ) and static structure factor S ( q ) for various degrees of anisotropy. The determination of the correlation energies at (1/3)-filling of an arbitrary LL is then performed by using standard mappings of g ( r ) and S ( q ) to higher LLs. Our results indicate that while Laughlin's state is stable in the lowest LL, there are regions of instability towards nematic order in higher LLs. Possible connections to the recently discovered QH liquid crystals are discussed.

Journal of Physics Condensed MatterMar 28, 200215 citations

L=0,1),

whereas the nematic is favorable at the second excited LL

(L=2).