Papers by Selman Hershfield
APS March Meeting Abstracts, Mar 1, 2001
Physical review, Apr 1, 2000
A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the t... more A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green function, the impurity-free surface Green function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance lineshapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, ∼ 10Å, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhancement. The formalism for tunneling into small clusters of magnetic adatoms is developed.
Bulletin of the American Physical Society, Mar 17, 2016
Submitted for the MAR16 Meeting of The American Physical Society Thermal Conductivity of Quantum ... more Submitted for the MAR16 Meeting of The American Physical Society Thermal Conductivity of Quantum Wires with Surface Roughness SELMAN HERSHFIELD, KHANDKER MUTTALIB, Dept. of Physics, University of Florida-Quantum wires have been shown to have greatly reduced thermal conductivity compared to bulk systems because of the increased role of surface scattering. The lattice thermal conductance and conductivity is calculated in the harmonic approximation for a long quantum wire placed between two heat baths using the Landauer formula for phonons and a recursive Green function technique to compute the transmission probabilities. The width of the wires is varied in the transverse direction so as to have a root mean square value σ and correlation length L. As observed experimentally, we find that the thermal conductance is decreased with increasing σ and increased as L increases. The full scaling of the thermal conductance as a function of σ, L, the width and the length of the sample is discussed. The simulations are also compared to approximate techniques such as modeling the surfaces as having diffusive scattering.
Bulletin of the American Physical Society, Mar 14, 2016
Submitted for the MAR16 Meeting of The American Physical Society Lattice thermal conductance of q... more Submitted for the MAR16 Meeting of The American Physical Society Lattice thermal conductance of quantum wires with disorder ERIK VYHMEISTER, Andrews University, SELMAN HERSHFIELD, University of Florida-We model the lattice thermal conductance in long quantum wires connected to two large heat baths at different temperatures in the harmonic approximation. The thermal conductance is computed with the Landauer formula for phonons, where it is related to the sum over all transmission probabilities for phonons through the wire. The net transmission probability is computed using a recursive Green function technique, which allows one to study long wires efficiently. We consider several different kinds of disorder to reduce the lattice thermal conductivity: periodic rectangular holes of varying sizes and shapes, periodic triangular holes, and narrow bands, averaged over randomness to account for variance in manufacturing. Depending on the model, the thermal conductance was reduced by 80 percent or more from the perfectly ordered wire case. Funded by NSF grant DMR-1461019.
Bulletin of the American Physical Society, 2017
Submitted for the MAR17 Meeting of The American Physical Society Non-linear thermoelectric nano-d... more Submitted for the MAR17 Meeting of The American Physical Society Non-linear thermoelectric nano-device with electron-phonon interactions BRADLEY NARTOWT, SELMAN HERSHFIELD, KHANDKER MUTTALIB, University of Florida-We consider electron transport through a single (tight-binding Hamiltonian) site and a localized phonon, about which are placed two leads at disparate chemical potentials due to being at disparate temperatures (the usual thermoelectric regime). In a calculation patterned after the large body of zero-temperature work done in the driven regime (where an external agent maintains the chemical potential difference), non-equilibrium Green functions are used to obtain the nonlinear current-voltage characteristics. The Green functions are calculated using the self-consistent Born approximation to incorporate (at the Hartree-Fock-diagram level) interactions between the itinerant electrons and localized phonon-mode. In the thermoelectric regime, we evaluate the power and efficiency of the device as a function of the electron-phonon coupling at various temperature differences. In addition, we will report studies of a new regime where an external driving agent and a temperature-difference are both responsible for the chemical potential difference: the partially-driven thermoelectric regime.
Bulletin of the American Physical Society, 2013
Physical Review B, 1993
We have used nonequilibrium quantum statistical mechanics to derive an exact expression for the c... more We have used nonequilibrium quantum statistical mechanics to derive an exact expression for the current and a rate equation for a simple model of a resonant-tunneling diode including scattering within the resonant state. The rate equation is identical to the classical rate equation for resonant tunneling provided that two conditions are met. First, the driving frequency must be slow compared with the Fermi energy of incoming electrons; the lifetime of the resonance does not set a scale. Second, the resonance must be narrow compared with the range of incoming energies and on a scale set by the variation in energy of the tunneling rates of the individual barriers. Our derivation shows that the rate equation holds both in the coherent limit, in which transport can be described by elementary wave mechanics alone, and in the limit where scattering within the resonant state makes a classical "sequential" picture more appropriate; all information about coherence is lost in the averaging required to deduce the rate equation. The current through the resonant state is independent of scattering provided that the rate equation holds. We also examine the current when the rate equation does not hold, and show how strongly inelastic processes enter the quantum kinetic description through scattering-out and scattering-in processes at di8'erent energies.
Journal of undergraduate research, Dec 1, 2022
Ternary organic solar cells were simulated as a 3D grid of resistors and photodiodes to study how... more Ternary organic solar cells were simulated as a 3D grid of resistors and photodiodes to study how a secondary acceptor as a third material affects the overall blend to optimize for power output. The voltage at zero current, VOC, of the donor and secondary acceptor interfaces should be at least that of the primary system. When the thickness and secondary acceptor conductivity are high, it is better for a secondary acceptor to stick to the main acceptor due to an asymmetry in current pathways. Otherwise, it is better to place the secondary acceptor next to the donor to increase the amount of donor : acceptor interfaces. These results are likely most applicable to the addition of fullerene acceptors into donor : non-fullerene acceptor blends, since their potential benefits come from an increased conductance and morphology as opposed to increasing the absorption spectra.
Bulletin of the American Physical Society, 2020
Physical Review B
The magnetization of graphene flakes as a function of size, shape, boundary type, and edge defect... more The magnetization of graphene flakes as a function of size, shape, boundary type, and edge defects is computed in a tight-binding model. Flakes with Klein boundaries exhibit a smaller orbital magnetization than flakes with other boundaries. The difference in magnitude is significant for flakes with a few hundred to a few thousand atoms. One can tune the magnetization of a zigzag or Klein flake quasicontinuously by adding atoms, one by one, to the edges of the zigzag flake, or removing atoms from a Klein flake. Flakes with an odd number of atoms show a paramagnetic spin response due to particle-hole symmetry. The addition of a next-nearest neighbor term to the Hamiltonian, which breaks particle-hole symmetry, does not destroy this effect as long as there is approximate particle-hole symmetry. Other defects that affect the chemical potential, such as edge atoms with an onsite potential, or doping, can affect the paramagnetism but preserve the difference in magnetization between Klein and non-Klein flakes. These results are consistent with experiments which see paramagnetic response at low magnetic fields crossing over to diamagnetic response at higher fields.
American Physical Society, Mar 16, 2006
Submitted for the MAR06 Meeting of The American Physical Society Periodic time dependent problems... more Submitted for the MAR06 Meeting of The American Physical Society Periodic time dependent problems in nonequilibrium quantum statistical mechanics SELMAN HERSHFIELD, Univ. of Florida-The usual Kadanoff-Baym or Keldysh formulation of nonequilibrium quantum statistical mechanics can be reformulated for steady state problems in terms of a nonequilibrium density matrix of the form exp(−(H − Y)/k B T), where H is the hamiltonian and Y contains the information about how the system is driven out of equilibrium. * This approach has now been used to solve exactly solvable models as well as in approximate techniques. Here we show that for a periodic time dependent hamiltonian there is a similar formulation in terms of a nonequilibrium density matrix, where the density matrix acts in one higher dimension than in the original problem. Thus, a time dependent nonequilibrum problem is mapped onto a time independent nonequilibrium problem in one higher dimension. This is true for interacting as well as noninteracting problems. The approach is illustrated by applying it to some exactly solvable time dependent nonequilibrium problems such as tunneling through a resonant level where the level and/or the voltage applied are time dependent.
We compute the zero frequency current noise numerically and in several limits analytically for th... more We compute the zero frequency current noise numerically and in several limits analytically for the coulomb blockade problem consisting of two tunnel junctions connected in series. At low temperatures over a wide range of voltages, capacitances, and resistances it is shown that the noise measures the variance in the number of electrons in the region between the two tunnel junctions. The average current, on the other hand, only measures the mean number of electrons. Thus, the noise provides additional information about transport in these devices which is not available from measuring the current alone.
The low energy Dirac and Weyl spectra are allowed to violate the Lorentz symmetry and thereby hav... more The low energy Dirac and Weyl spectra are allowed to violate the Lorentz symmetry and thereby have a tilted energy dispersion. The tilt in the energy dispersion induces a Hall voltage in the plane spanned by the electric field and the tilt velocity. In the presence of a magnetic field the planar Hall conductivity and resistivity show Shubnikov de Haas oscillations. The oscillations in the planar Hall effect can become a fingerprint to spot the anomalous transport in Dirac and Weyl semimetals.
A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the t... more A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green function, the impurity-free surface Green function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance lineshapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, \sim 10\AA, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhan...
Calculations are presented of a superlattice effect, observable in samples where most of the scat... more Calculations are presented of a superlattice effect, observable in samples where most of the scattering is at sharp interfaces. As the layer thicknesses change, oscillations in the resistivity of up to 100% are found. These oscillations are due to interface disorder breaking the degeneracy of certain states, causing them to have nodes at the interfaces. The states with nodes have high conductivities, leading to a "short-circuit" effect. Only for special thicknesses is it possible for a state to have nodes at all the interfaces. Hence, the oscillations occur as a function of layer thickness. Spreading the width of the interfaces or increasing the ratio of bulk disorder to interface disorder reduces the effect.
Bulletin of the American Physical Society, 2016
The usual Kadanoff-Baym or Keldysh formulation of nonequilibrium quantum statistical mechanics ca... more The usual Kadanoff-Baym or Keldysh formulation of nonequilibrium quantum statistical mechanics can be reformulated for steady state problems in terms of a nonequilibrium density matrix of the form (-(H - Y)/kBT), where H is the hamiltonian and Y contains the information about how the system is driven out of equilibrium.^* This approach has now been used to solve exactly solvable models as well as in approximate techniques. Here we show that for a periodic time dependent hamiltonian there is a similar formulation in terms of a nonequilibrium density matrix, where the density matrix acts in one higher dimension than in the original problem. Thus, a time dependent nonequilibrum problem is mapped onto a time independent nonequilibrium problem in one higher dimension. This is true for interacting as well as noninteracting problems. The approach is illustrated by applying it to some exactly solvable time dependent nonequilibrium problems such as tunneling through a resonant level where the level and/or the voltage applied are time dependent.* S. Hershfield, PRL 70, 2134 (1993).
Bulletin of the American Physical Society, 2015
Bulletin of the American Physical Society, 2016
Bulletin of the American Physical Society, 2018
Uploads
Papers by Selman Hershfield