Current-density functional theory of the response of solids

Abstract

The response of an extended periodic system to a homogeneous field (of wave-vector q = 0) cannot be obtained from a q = 0 time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply. Time-dependent current-density functional theory is needed and demonstrates that one key ingredient missing from TDDFT is the macroscopic current. In the low-frequency limit, in certain cases, density polarization functional theory is recovered and a formally exact expression for the polarization functional is given.PACS numbers: 71.15. Mb,78.20.Ci, Density functional theory[1, 2] is a standard approach for calculating ground-state properties of solids [3] and molecules [4]. Time-dependent density functional theory (TDDFT) is an extension of the ground-state formalism based on the Runge-Gross theorem [5]; this establishes a one-to-one correspondence between time-dependent densities and time-dependent one-body potentials. When a time-dependent electric field is applied to a system, this formalism provides a route to its optical response [6]. The response equations of TDDFT have been encoded in standard quantum chemical packages [7], and results for molecules are appearing (see Ref.[8] for many examples). As in the ground-state case, the accuracy depends on the quality of the approximate functional used.There is great interest in applying the same technique to extended systems. While these can be treated well within existing wavefunction technology, using, e.g., the GW approximation and then solving the BetheSalpeter equation for the optical response[9], the allure of a TDDFT approach is its far lower computational cost. Calculations already show that excitonic effects appear to be treatable by going beyond the usual local and semi-local approximations of standard DFT calculations [10,11].There is also a version of the time-dependent theory, called time-dependent current-density functional theory (TDCDFT), that uses the current-density as the basic variable: As the choice of variable (charge density versus current density) appears a matter of convenience, TDCDFT and TDDFT appear to be equivalent (for non-magnetic systems). The time-dependent exchange-correlation potential has been argued to be more amenable to local and semilocal approximation in terms of the current-density [12] and this framework has been used in recent response calculations of solids [13,14] and conjugated polymers [15]. Initial work towards a matrix formulation of the current-density response equations has been presented in Ref. [16].In this paper, we demonstrate a difference in principle between the two approaches when applied to bulk solids. The basic theorems of DFT, ground-state or timedependent, are proven for finite electronic systems (i.e. systems with a boundary). We consider the response of periodic systems (such as the bulk of an insulator or metal) to time-varying electric fields which have a spatially uniform component. We show that TDDFT fails in this case: there is no one-to-one correspondence between ...

Density functional calculations of nanoscale conductance

“…beyond adiabatic) effects are important. Most importantly, it often yields finite corrections where ALDA gives nothing, such as to the (0,0) component needed for the optical response of solids [105,108], or the over-polarizability of long-chain conjugated polymers [73,109]. But, given that it is a simple gradient expansion, its quantitative accuracy in any given situation is open to question [109,110,111].…”

Time-dependent density-functional theory for ultrafast interband excitations

“…Strictly speaking, for external homogeneous fields, one needs to use current TDDFT in order to study the response of the system. 22,23 One then gets the macroscopic current, which allows one to satisfy the periodicity condition. In this paper, however, we use the usual approximation 4 where the external homogeneous electric field is described by the following scalar potential:…”

Dielectrics in a time-dependent electric field: A real-time approach based on density-polarization functional theory

“…However, for periodic systems in a time-dependent homogeneous electric field only the one-to-one correspondence between the time-dependent currents and potentials (scalar and vector) can be established and time-dependent current density functional theory (TD-CDFT) is then the correct theoretical framework. 3,4 In particular it is the optical limit, i.e. the case in which the transferred momentum q → 0, which cannot be described starting from the density only.…”

“…In particular here we consider an effective electric field which is a functional of the macroscopic polarization. We employ simple local functionals of the polarization 3,11,12 either fitted to reproduce the linear optical spectra 13 or derived from the jellium with gap model kernel.…”