R. Bhatt - Academia.edu (original) (raw)
Papers by R. Bhatt
Computer Simulation Studies in Condensed-Matter Physics XVI
Philosophical Magazine B, 1980
A phenomenological model of donor clusters is found to describe the optical and magnetic properti... more A phenomenological model of donor clusters is found to describe the optical and magnetic properties well at donor densities below the Mott density. The effects of clustering on the single-particle density of states is discussed. Microscopic calculations lead to the conclusion that in multi-valley semiconductors large clusters are sufficiently electronegative to attract an electron from isolated donors or donor pairs and as a result, there is no Mott-Hubbard gap due to correlation. The insulating property is ascribed to Anderson localization at the Fermi level.
Physical Review B, 1979
A theory is developed of optical absorption in mercury fluid which is correct in the atomic limit... more A theory is developed of optical absorption in mercury fluid which is correct in the atomic limit and describes densities up to 4-5 gcm '. The model takes density fluctuations into account explicitly, and shows that the steep, near-exponential absorption edge observed in mercury can be explained quantitatively in terms of absorption by excitonic states of large randomly distributed clusters. This removes the discrepancy between optical-absorption measurements which indicated the band gap closes around 5 gcm ' and transport and Knight-shift measurements which showed a metal-insulator transition around 8.5 gcm '. The model predicts, in qualitative agreement with results of recent reflectivity measurements, that the excitonic absorption is separate at densities even up to-5 gcm
Physical Review B, 1979
It is pointed out that the fine structure in the density of states in the R-point model of A-15 c... more It is pointed out that the fine structure in the density of states in the R-point model of A-15 compounds proposed by Lee, Birman, and Williamson to fit the anomalous properties of Nb3Sn and V3Si is (i) based on bands which are-100 times flatter than calculated band structures, and (ii) sensitive to cutoff procedures adopted to determine the density of states. Thus the model in its present form does not appear to be a viable picture of the anomalies present in these materials.
Physical Review B, 1977
Coherence lengths and phonon softening in A-15 compounds are investigated on the' basis of existi... more Coherence lengths and phonon softening in A-15 compounds are investigated on the' basis of existing onedimensional models and a recent three-dimensional tight-binding model. Results are found to depend sensitively on the band structure near the Fermi surface, and the tight-binding model is found to give a very short coherence length ((Ja & EF/T,), in agreement with the extensive softening of finite-wave-vector phonons seen by neutron scattering. General remarks on phonon softening in models with three-dimensional peaked density of states and on some consequences of the short coherence length are made. I, INTRODUCTION One of the major difficulties of theories of the martensitic transition in A.-15 compounds Nb, Sn and V, Si has been in attempts to explain the rather marked softening of the [110] polarized phonon' ' (see Fig. 1). The softening of this phonon, whose k-0 limit corresponds to the mode that becomes almost totally soft at the transiti'on, extends in k space almost halfway to the zone boundary. An explanation based on a two-dimensional square lattice which was inherently unstable, but stabilized by defects, has been proposed by Varma, Phillips, and Chui. On the other hand for electronic models, the large softening implies a low-temperature correlation length $, which is not much larger than 16 4288
Physical Review B, 1976
Based on Gorkov's physical model of a Peierls-like charge-density-eave-driven transition, a Landa... more Based on Gorkov's physical model of a Peierls-like charge-density-eave-driven transition, a Landau theory has been formulated for the structural phase transition in the A-15 compounds. Pretransition elastic anomalies, softening of the [110) transverse ([110]polarized) phonon, sublattice distortions, variation of transition temperature with stress, and alloying and other effects have been accurately predicted, and a detailed comparison is made with experimental results. Central peaks in neutron scattering are shown to be nondynamic in nature and no pretransition forbidden (300}reflection is predicted. The I » optic mode does not go soft at the transition, though its frequency is expected to be temperature dependent right up to room temperature.
Journal of Physics C: Solid State Physics, 1988
The authors use Monte Carlo simulations to investigate the possibility of obtaining equilibrium v... more The authors use Monte Carlo simulations to investigate the possibility of obtaining equilibrium values of quantities which relax slowly to equilibrium by studying the evolution of their non-equilibrium behaviour. As an example they study the order parameter distribution P(q) for the infinite-range Ising spin glass during the approach to equilibrium. This is evaluated both by computing the overlap between two initially uncorrelated copies of the system and from the correlation between the same set of spins at two different times. They find that the value of the most slowly relaxing part of the distribution, P(q=0), decreases monotonically with time from the first method, while a monotonically increasing result is obtained from the second technique. Consequently they expect that one could obtain the equilibrium value of P(q=0) for larger sizes by extrapolation of non-equilibrium data.
Physical Review B, 1987
We have measured and modeled the far-infrared reflectivity of La/sub 2-//sub x/Sr/sub x/CuO/sub 4... more We have measured and modeled the far-infrared reflectivity of La/sub 2-//sub x/Sr/sub x/CuO/sub 4/ for x = 0.175 in the normal and superconducting states in the frequency range 20 to 350 cm/sup -1/. We find a much stronger drop of the reflectivity with increasing frequency below 100 cm/sup -1/ than is implied by the dc conductivity. In addition, we observe a resonance of large spectral weight at ..omega..approx. =250 cm/sup -1/ which is absent or much weaker in the insulating x = 0 compound. Below the superconducting temperature of the x = 0.175 sample we observe an additional sharp feature at approx. =80 cm/sup -1/, which can be accounted for in terms of the unusual normal-state properties of the material.
Condensed Matter Theories, 2008
While ferromagnetism has been obtained above 100 K in doped semiconductors with magnetic ions suc... more While ferromagnetism has been obtained above 100 K in doped semiconductors with magnetic ions such as Ga 1−x Mn x As , bulk doped semiconductors in the absence of magnetic ions have shown no tendency towards ferromagnetism. We re-examine the nonmagnetic doped semiconductor system at low carrier densities in terms of a generalized Hubbard model. Using exact diagonalization of the many-body Hamiltonian for finite clusters, we find that the system exhibits significant ferromagnetic tendencies at nanoscales, in a region of parameter space not accessible to bulk systems, but achievable in quantum dots and heterostructures. Implications for studying these effects in experimentally realizable systems, as well as the possibility of true (macroscopic) ferromagnetism in these systems is discussed.
We report results of numerical studies of the fractional quantum Hall effect in the cylindrical g... more We report results of numerical studies of the fractional quantum Hall effect in the cylindrical geometry using exact diagonalization as well as density-matrix renormalization group techniques. We provide convergence benchmarks that illustrate the advantage of the cylinder over the sphere, based on the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy for the ground state at ν=5/2 filling [1]. Further, we address several issues of interest that can be studied more directly using the cylindrical geometry. These include (i) transitions between the hierarchy of fractional quantum Hall states as a function of the confining potential; (ii) quasiparticle tunneling between the two edges of the cylinder; and (iii) generalized off-diagonal long-range order as a probe of the local geometry fluctuations in fractional quantum Hall liquids due to confinement potential or mass anisotropy.[4pt] [1] Zi-Xiang Hu, Z. Papic, S. Johri, R. N. Bhatt, Peter S...
It remains a puzzle how a non-interacting two-dimensional electron system evolves from a series o... more It remains a puzzle how a non-interacting two-dimensional electron system evolves from a series of quantum Hall phases in strong magnetic fields to an insulating phase, as commonly believed, in zero magnetic field. Experiments (D. Shahar et al.), Phys. Rev. B 52, R14372 (1995); S. H. Song et al., Phys. Rev. Lett. 78, 2200 (1997). and subsequent numerical calculations (D. N. Sheng and Z. Y. Weng, Phys. Rev. Lett. 80), 580 (1998). have raised the possibility that direct quantum phase transitions can occur from various quantum Hall phases to the insulating phase, with Hall conductance change of multiples of the fundamental unit of conductance e^2/h. We report results of a numerical study, using a tight-binding model on a square lattice, which reveal a quantum to classical crossover in finite size systems. Such crossover behavior may be relevant to the experimental results measured at finite temperatures. This research was supported by NSF DMR 9809483.
Recent experiments(S. H. Song et al.), Phys. Rev. Lett. 78, 2200 (1997). suggest that the transit... more Recent experiments(S. H. Song et al.), Phys. Rev. Lett. 78, 2200 (1997). suggest that the transition from quantum Hall plateaus to the insulator at low magnetic fields may involve steps in the Hall conductance that are multiples of the fundamental unit of conductance e^2/h, which do not fit the proposed ``universal'' phase diagramfootnote S. Kivelson et al., Phys. Rev. B 46, 2223 (1992).. We have examined the possibility of multiple step quantum Hall transitions for noninteracting electrons in the presence of a random potential and perpendicular magnetic field, using a tight-binding model on a square lattice with 1/(2n+1) flux quanta per unit cell, for a sequence of integers n. By studying the behavior of the Thouless conductance, and topological quantum (Chern) numbers characterizing eigenstates, we find conditions under which multiple quantum Hall transitions can be obtained, and obtain the critical exponent for the localization length near quantum Hall steps under differe...
Physical Review B, 2002
We investigate the effect of mass anisotropy on the Wigner crystallization transition in a twodim... more We investigate the effect of mass anisotropy on the Wigner crystallization transition in a twodimensional (2D) electron gas. The static and dynamical properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais lattices in the presence of anisotropic mass, as may be obtainable in Si MOSFETs with (110) surface. By studying the stability of all possible lattices, we find significant change in the crystal structure and melting density of the electron lattice with the lowest ground state energy.
Physical Review Letters, 1980
Zero-temperature metallic conductivities have been measured above and below Mott's minimum value ... more Zero-temperature metallic conductivities have been measured above and below Mott's minimum value o~j" in bulk crystals of P-doped Si. Conductivities below O~jp increase by over 103 as the density is raised by less than 1"/o, and do not rule out a discontinuous transition. However, over a wider density range the data can be fitted with a scaling form with a characteristic length that tends to diverge with the same exponent in the metal and insulator.
Physical Review Letters, 1983
Physica B: Condensed Matter, 1999
ABSTRACT
Journal of Applied Physics, 1981
Low temperature properties of random antiferromagnetic Heisenberg spin-1/2 systems with a wide di... more Low temperature properties of random antiferromagnetic Heisenberg spin-1/2 systems with a wide distribution of exchange couplings are examined using a scaling technique. The method iteratively discards the irrelevant high energy excitations of strongly coupled clusters, while retaining the low lying states which are reproduced by an equivalent smaller cluster. The method is applied to n-doped semiconductors, a spatially random three dimensional system of spin-1/2 donors with Heisenberg exchange varying exponentially with separation. It shows how the system does not order down to temperatures well below the median nearest neighbor exchange. Comparison is made with the corresponding system in two dimensions and the one-dimensional random antiferromagnetic chain (applicable to certain organic charge transfer salts), as well as with the case of Ising spins in three dimensions.
Journal of Applied Physics, 1991
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions ... more We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.
Computer Simulation Studies in Condensed-Matter Physics XVI
Philosophical Magazine B, 1980
A phenomenological model of donor clusters is found to describe the optical and magnetic properti... more A phenomenological model of donor clusters is found to describe the optical and magnetic properties well at donor densities below the Mott density. The effects of clustering on the single-particle density of states is discussed. Microscopic calculations lead to the conclusion that in multi-valley semiconductors large clusters are sufficiently electronegative to attract an electron from isolated donors or donor pairs and as a result, there is no Mott-Hubbard gap due to correlation. The insulating property is ascribed to Anderson localization at the Fermi level.
Physical Review B, 1979
A theory is developed of optical absorption in mercury fluid which is correct in the atomic limit... more A theory is developed of optical absorption in mercury fluid which is correct in the atomic limit and describes densities up to 4-5 gcm '. The model takes density fluctuations into account explicitly, and shows that the steep, near-exponential absorption edge observed in mercury can be explained quantitatively in terms of absorption by excitonic states of large randomly distributed clusters. This removes the discrepancy between optical-absorption measurements which indicated the band gap closes around 5 gcm ' and transport and Knight-shift measurements which showed a metal-insulator transition around 8.5 gcm '. The model predicts, in qualitative agreement with results of recent reflectivity measurements, that the excitonic absorption is separate at densities even up to-5 gcm
Physical Review B, 1979
It is pointed out that the fine structure in the density of states in the R-point model of A-15 c... more It is pointed out that the fine structure in the density of states in the R-point model of A-15 compounds proposed by Lee, Birman, and Williamson to fit the anomalous properties of Nb3Sn and V3Si is (i) based on bands which are-100 times flatter than calculated band structures, and (ii) sensitive to cutoff procedures adopted to determine the density of states. Thus the model in its present form does not appear to be a viable picture of the anomalies present in these materials.
Physical Review B, 1977
Coherence lengths and phonon softening in A-15 compounds are investigated on the' basis of existi... more Coherence lengths and phonon softening in A-15 compounds are investigated on the' basis of existing onedimensional models and a recent three-dimensional tight-binding model. Results are found to depend sensitively on the band structure near the Fermi surface, and the tight-binding model is found to give a very short coherence length ((Ja & EF/T,), in agreement with the extensive softening of finite-wave-vector phonons seen by neutron scattering. General remarks on phonon softening in models with three-dimensional peaked density of states and on some consequences of the short coherence length are made. I, INTRODUCTION One of the major difficulties of theories of the martensitic transition in A.-15 compounds Nb, Sn and V, Si has been in attempts to explain the rather marked softening of the [110] polarized phonon' ' (see Fig. 1). The softening of this phonon, whose k-0 limit corresponds to the mode that becomes almost totally soft at the transiti'on, extends in k space almost halfway to the zone boundary. An explanation based on a two-dimensional square lattice which was inherently unstable, but stabilized by defects, has been proposed by Varma, Phillips, and Chui. On the other hand for electronic models, the large softening implies a low-temperature correlation length $, which is not much larger than 16 4288
Physical Review B, 1976
Based on Gorkov's physical model of a Peierls-like charge-density-eave-driven transition, a Landa... more Based on Gorkov's physical model of a Peierls-like charge-density-eave-driven transition, a Landau theory has been formulated for the structural phase transition in the A-15 compounds. Pretransition elastic anomalies, softening of the [110) transverse ([110]polarized) phonon, sublattice distortions, variation of transition temperature with stress, and alloying and other effects have been accurately predicted, and a detailed comparison is made with experimental results. Central peaks in neutron scattering are shown to be nondynamic in nature and no pretransition forbidden (300}reflection is predicted. The I » optic mode does not go soft at the transition, though its frequency is expected to be temperature dependent right up to room temperature.
Journal of Physics C: Solid State Physics, 1988
The authors use Monte Carlo simulations to investigate the possibility of obtaining equilibrium v... more The authors use Monte Carlo simulations to investigate the possibility of obtaining equilibrium values of quantities which relax slowly to equilibrium by studying the evolution of their non-equilibrium behaviour. As an example they study the order parameter distribution P(q) for the infinite-range Ising spin glass during the approach to equilibrium. This is evaluated both by computing the overlap between two initially uncorrelated copies of the system and from the correlation between the same set of spins at two different times. They find that the value of the most slowly relaxing part of the distribution, P(q=0), decreases monotonically with time from the first method, while a monotonically increasing result is obtained from the second technique. Consequently they expect that one could obtain the equilibrium value of P(q=0) for larger sizes by extrapolation of non-equilibrium data.
Physical Review B, 1987
We have measured and modeled the far-infrared reflectivity of La/sub 2-//sub x/Sr/sub x/CuO/sub 4... more We have measured and modeled the far-infrared reflectivity of La/sub 2-//sub x/Sr/sub x/CuO/sub 4/ for x = 0.175 in the normal and superconducting states in the frequency range 20 to 350 cm/sup -1/. We find a much stronger drop of the reflectivity with increasing frequency below 100 cm/sup -1/ than is implied by the dc conductivity. In addition, we observe a resonance of large spectral weight at ..omega..approx. =250 cm/sup -1/ which is absent or much weaker in the insulating x = 0 compound. Below the superconducting temperature of the x = 0.175 sample we observe an additional sharp feature at approx. =80 cm/sup -1/, which can be accounted for in terms of the unusual normal-state properties of the material.
Condensed Matter Theories, 2008
While ferromagnetism has been obtained above 100 K in doped semiconductors with magnetic ions suc... more While ferromagnetism has been obtained above 100 K in doped semiconductors with magnetic ions such as Ga 1−x Mn x As , bulk doped semiconductors in the absence of magnetic ions have shown no tendency towards ferromagnetism. We re-examine the nonmagnetic doped semiconductor system at low carrier densities in terms of a generalized Hubbard model. Using exact diagonalization of the many-body Hamiltonian for finite clusters, we find that the system exhibits significant ferromagnetic tendencies at nanoscales, in a region of parameter space not accessible to bulk systems, but achievable in quantum dots and heterostructures. Implications for studying these effects in experimentally realizable systems, as well as the possibility of true (macroscopic) ferromagnetism in these systems is discussed.
We report results of numerical studies of the fractional quantum Hall effect in the cylindrical g... more We report results of numerical studies of the fractional quantum Hall effect in the cylindrical geometry using exact diagonalization as well as density-matrix renormalization group techniques. We provide convergence benchmarks that illustrate the advantage of the cylinder over the sphere, based on the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy for the ground state at ν=5/2 filling [1]. Further, we address several issues of interest that can be studied more directly using the cylindrical geometry. These include (i) transitions between the hierarchy of fractional quantum Hall states as a function of the confining potential; (ii) quasiparticle tunneling between the two edges of the cylinder; and (iii) generalized off-diagonal long-range order as a probe of the local geometry fluctuations in fractional quantum Hall liquids due to confinement potential or mass anisotropy.[4pt] [1] Zi-Xiang Hu, Z. Papic, S. Johri, R. N. Bhatt, Peter S...
It remains a puzzle how a non-interacting two-dimensional electron system evolves from a series o... more It remains a puzzle how a non-interacting two-dimensional electron system evolves from a series of quantum Hall phases in strong magnetic fields to an insulating phase, as commonly believed, in zero magnetic field. Experiments (D. Shahar et al.), Phys. Rev. B 52, R14372 (1995); S. H. Song et al., Phys. Rev. Lett. 78, 2200 (1997). and subsequent numerical calculations (D. N. Sheng and Z. Y. Weng, Phys. Rev. Lett. 80), 580 (1998). have raised the possibility that direct quantum phase transitions can occur from various quantum Hall phases to the insulating phase, with Hall conductance change of multiples of the fundamental unit of conductance e^2/h. We report results of a numerical study, using a tight-binding model on a square lattice, which reveal a quantum to classical crossover in finite size systems. Such crossover behavior may be relevant to the experimental results measured at finite temperatures. This research was supported by NSF DMR 9809483.
Recent experiments(S. H. Song et al.), Phys. Rev. Lett. 78, 2200 (1997). suggest that the transit... more Recent experiments(S. H. Song et al.), Phys. Rev. Lett. 78, 2200 (1997). suggest that the transition from quantum Hall plateaus to the insulator at low magnetic fields may involve steps in the Hall conductance that are multiples of the fundamental unit of conductance e^2/h, which do not fit the proposed ``universal'' phase diagramfootnote S. Kivelson et al., Phys. Rev. B 46, 2223 (1992).. We have examined the possibility of multiple step quantum Hall transitions for noninteracting electrons in the presence of a random potential and perpendicular magnetic field, using a tight-binding model on a square lattice with 1/(2n+1) flux quanta per unit cell, for a sequence of integers n. By studying the behavior of the Thouless conductance, and topological quantum (Chern) numbers characterizing eigenstates, we find conditions under which multiple quantum Hall transitions can be obtained, and obtain the critical exponent for the localization length near quantum Hall steps under differe...
Physical Review B, 2002
We investigate the effect of mass anisotropy on the Wigner crystallization transition in a twodim... more We investigate the effect of mass anisotropy on the Wigner crystallization transition in a twodimensional (2D) electron gas. The static and dynamical properties of a 2D Wigner crystal have been calculated for arbitrary 2D Bravais lattices in the presence of anisotropic mass, as may be obtainable in Si MOSFETs with (110) surface. By studying the stability of all possible lattices, we find significant change in the crystal structure and melting density of the electron lattice with the lowest ground state energy.
Physical Review Letters, 1980
Zero-temperature metallic conductivities have been measured above and below Mott's minimum value ... more Zero-temperature metallic conductivities have been measured above and below Mott's minimum value o~j" in bulk crystals of P-doped Si. Conductivities below O~jp increase by over 103 as the density is raised by less than 1"/o, and do not rule out a discontinuous transition. However, over a wider density range the data can be fitted with a scaling form with a characteristic length that tends to diverge with the same exponent in the metal and insulator.
Physical Review Letters, 1983
Physica B: Condensed Matter, 1999
ABSTRACT
Journal of Applied Physics, 1981
Low temperature properties of random antiferromagnetic Heisenberg spin-1/2 systems with a wide di... more Low temperature properties of random antiferromagnetic Heisenberg spin-1/2 systems with a wide distribution of exchange couplings are examined using a scaling technique. The method iteratively discards the irrelevant high energy excitations of strongly coupled clusters, while retaining the low lying states which are reproduced by an equivalent smaller cluster. The method is applied to n-doped semiconductors, a spatially random three dimensional system of spin-1/2 donors with Heisenberg exchange varying exponentially with separation. It shows how the system does not order down to temperatures well below the median nearest neighbor exchange. Comparison is made with the corresponding system in two dimensions and the one-dimensional random antiferromagnetic chain (applicable to certain organic charge transfer salts), as well as with the case of Ising spins in three dimensions.
Journal of Applied Physics, 1991
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions ... more We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.