Chimie Théorique » QMX

import numpy as np

from numpy import linalg

from ase.transport.selfenergy import LeadSelfEnergy, BoxProbe

from ase.transport.greenfunction import GreenFunction

from ase.transport.tools import subdiagonalize, cutcoupling, tri2full, dagger,\

    rotate_matrix

class TransportCalculator:

    """Determine transport properties of a device sandwiched between

    two semi-infinite leads using a Green function method.

    """

    def __init__(self, **kwargs):

        """Create the transport calculator.

        Parameters

        ==========

        h : (N, N) ndarray

            Hamiltonian matrix for the central region. 

        s : {None, (N, N) ndarray}, optional

            Overlap matrix for the central region. 

            Use None for an orthonormal basis.

        h1 : (N1, N1) ndarray

            Hamiltonian matrix for lead1.

        h2 : {None, (N2, N2) ndarray}, optional

            Hamiltonian matrix for lead2. You may use None if lead1 and lead2 

            are identical.

        s1 : {None, (N1, N1) ndarray}, optional

            Overlap matrix for lead1. Use None for an orthonomormal basis.

        hc1 : {None, (N1, N) ndarray}, optional

            Hamiltonian coupling matrix between the first principal

            layer in lead1 and the central region.

        hc2 : {None, (N2, N} ndarray), optional

            Hamiltonian coupling matrix between the first principal

            layer in lead2 and the central region.

        sc1 : {None, (N1, N) ndarray}, optional  

            Overlap coupling matrix between the first principal

            layer in lead1 and the central region.

        sc2 : {None, (N2, N) ndarray}, optional  

            Overlap coupling matrix between the first principal

            layer in lead2 and the central region.

        energies : {None, array_like}, optional

            Energy points for which calculated transport properties are

            evaluated.

        eta : {1.0e-5, float}, optional

            Infinitesimal for the central region Green function. 

        eta1/eta2 : {1.0e-5, float}, optional

            Infinitesimal for lead1/lead2 Green function.

        align_bf : {None, int}, optional

            Use align_bf=m to shift the central region 

            by a constant potential such that the m'th onsite element

            in the central region is aligned to the m'th onsite element

            in lead1 principal layer.

        logfile : {None, str}, optional 

            Write a logfile to file with name `logfile`.

            Use '-' to write to std out.

        eigenchannels: {0, int}, optional

            Number of eigenchannel transmission coefficients to 

            calculate. 

        pdos : {None, (N,) array_like}, optional

            Specify which basis functions to calculate the

            projected density of states for.

        dos : {False, bool}, optional

            The total density of states of the central region.

        box: XXX

            YYY

        If hc1/hc2 are None, they are assumed to be identical to

        the coupling matrix elements between neareste neighbor 

        principal layers in lead1/lead2.

        Examples

        ========

        >>> import numpy as np

        >>> h = np.array((0,)).reshape((1,1))

        >>> h1 = np.array((0, -1, -1, 0)).reshape(2,2)

        >>> energies = np.arange(-3, 3, 0.1)

        >>> calc = TransportCalculator(h=h, h1=h1, energies=energies)

        >>> T = calc.get_transmission()

        """

        # The default values for all extra keywords

        self.input_parameters = {'energies': None,

                                 'h': None,

                                 'h1': None,

                                 'h2': None,

                                 's': None,

                                 's1': None,

                                 's2': None,

                                 'hc1': None,

                                 'hc2': None,

                                 'sc1': None,

                                 'sc2': None,

                                 'box': None,

                                 'align_bf': None,

                                 'eta1': 1e-5,

                                 'eta2': 1e-5,

                                 'eta': 1e-5,

                                 'logfile': None, # '-',

                                 'eigenchannels': 0,

                                 'dos': False,

                                 'pdos': [],

                                 }

        self.initialized = False # Changed Hamiltonians?

        self.uptodate = False # Changed energy grid?

        self.set(**kwargs)

    def set(self, **kwargs):

        for key in kwargs:

            if key in ['h', 'h1', 'h2', 'hc1', 'hc2',

                       's', 's1', 's2', 'sc1', 'sc2',

                       'eta', 'eta1', 'eta2', 'align_bf', 'box']:

                self.initialized = False

                self.uptodate = False

                break

            elif key in ['energies', 'eigenchannels', 'dos', 'pdos']:

                self.uptodate = False

            elif key not in self.input_parameters:

                raise KeyError, '\'%s\' not a vaild keyword' % key

        self.input_parameters.update(kwargs)

        log = self.input_parameters['logfile']

        if log is None:

            class Trash:

                def write(self, s):

                    pass

                def flush(self):

                    pass

            self.log = Trash()

        elif log == '-':

            from sys import stdout

            self.log = stdout

        elif 'logfile' in kwargs:

            self.log = open(log, 'w')

    def initialize(self):

        if self.initialized:

            return

        print >> self.log, '# Initializing calculator...'

        p = self.input_parameters

        if p['s'] == None:

            p['s'] = np.identity(len(p['h']))

        identical_leads = False

        if p['h2'] == None:   

            p['h2'] = p['h1'] # Lead2 is idendical to lead1

            identical_leads = True

        if p['s1'] == None: 

            p['s1'] = np.identity(len(p['h1']))

        if p['s2'] == None and not identical_leads:

            p['s2'] = np.identity(len(p['h2'])) # Orthonormal basis for lead 2

        else: # Lead2 is idendical to lead1

            p['s2'] = p['s1']

        h_mm = p['h']

        s_mm = p['s']

        pl1 = len(p['h1']) / 2

        pl2 = len(p['h2']) / 2

        h1_ii = p['h1'][:pl1, :pl1]

        h1_ij = p['h1'][:pl1, pl1:2 * pl1]

        s1_ii = p['s1'][:pl1, :pl1]

        s1_ij = p['s1'][:pl1, pl1:2 * pl1]

        h2_ii = p['h2'][:pl2, :pl2]

        h2_ij = p['h2'][pl2: 2 * pl2, :pl2]

        s2_ii = p['s2'][:pl2, :pl2]

        s2_ij = p['s2'][pl2: 2 * pl2, :pl2]

        if p['hc1'] is None:

            nbf = len(h_mm)

            h1_im = np.zeros((pl1, nbf), complex)

            s1_im = np.zeros((pl1, nbf), complex)

            h1_im[:pl1, :pl1] = h1_ij

            s1_im[:pl1, :pl1] = s1_ij

            p['hc1'] = h1_im

            p['sc1'] = s1_im

        else:

            h1_im = p['hc1']

            if p['sc1'] is not None:

                s1_im = p['sc1']

            else:

                s1_im = np.zeros(h1_im.shape, complex)

                p['sc1'] = s1_im

        if p['hc2'] is None:

            h2_im = np.zeros((pl2, nbf), complex)

            s2_im = np.zeros((pl2, nbf), complex)

            h2_im[-pl2:, -pl2:] = h2_ij

            s2_im[-pl2:, -pl2:] = s2_ij

            p['hc2'] = h2_im

            p['sc2'] = s2_im

        else:

            h2_im = p['hc2']

            if p['sc2'] is not None:

                s2_im = p['sc2']

            else:

                s2_im = np.zeros(h2_im.shape, complex)

                p['sc2'] = s2_im

        align_bf = p['align_bf']

        if align_bf != None:

            diff = (h_mm[align_bf, align_bf] - h1_ii[align_bf, align_bf]) \

                   / s_mm[align_bf, align_bf]

            print >> self.log, '# Aligning scat. H to left lead H. diff=', diff

            h_mm -= diff * s_mm

        # Setup lead self-energies

        # All infinitesimals must be > 0 

        assert np.all(np.array((p['eta'], p['eta1'], p['eta2'])) > 0.0)

        self.selfenergies = [LeadSelfEnergy((h1_ii, s1_ii), 

                                            (h1_ij, s1_ij),

                                            (h1_im, s1_im),

                                            p['eta1']),

                             LeadSelfEnergy((h2_ii, s2_ii), 

                                            (h2_ij, s2_ij),

                                            (h2_im, s2_im),

                                            p['eta2'])]

        box = p['box']

        if box is not None:

            print 'Using box probe!'

            self.selfenergies.append(

                BoxProbe(eta=box[0], a=box[1], b=box[2], energies=box[3],

                         S=s_mm, T=0.3))

        #setup scattering green function

        self.greenfunction = GreenFunction(selfenergies=self.selfenergies,

                                           H=h_mm,

                                           S=s_mm,

                                           eta=p['eta'])

        self.initialized = True

    def update(self):

        if self.uptodate:

            return

        p = self.input_parameters

        self.energies = p['energies']

        nepts = len(self.energies)

        nchan = p['eigenchannels']

        pdos = p['pdos']

        self.T_e = np.empty(nepts)

        if p['dos']:

            self.dos_e = np.empty(nepts)

        if pdos != []:

            self.pdos_ne = np.empty((len(pdos), nepts))

        if nchan > 0:

            self.eigenchannels_ne = np.empty((nchan, nepts))

        for e, energy in enumerate(self.energies):

            Ginv_mm = self.greenfunction.retarded(energy, inverse=True)

            lambda1_mm = self.selfenergies[0].get_lambda(energy)

            lambda2_mm = self.selfenergies[1].get_lambda(energy)

            a_mm = linalg.solve(Ginv_mm, lambda1_mm)

            b_mm = linalg.solve(dagger(Ginv_mm), lambda2_mm)

            T_mm = np.dot(a_mm, b_mm)

            if nchan > 0:

                t_n = linalg.eigvals(T_mm).real

                self.eigenchannels_ne[:, e] = np.sort(t_n)[-nchan:]

                self.T_e[e] = np.sum(t_n)

            else:

                self.T_e[e] = np.trace(T_mm).real

            print >> self.log, energy, self.T_e[e]

            self.log.flush()

            if p['dos']:

                self.dos_e[e] = self.greenfunction.dos(energy)

            if pdos != []:

                self.pdos_ne[:, e] = np.take(self.greenfunction.pdos(energy),

                                             pdos)

        self.uptodate = True

    def print_pl_convergence(self):

        self.initialize()

        pl1 = len(self.input_parameters['h1']) / 2

        h_ii = self.selfenergies[0].h_ii

        s_ii = self.selfenergies[0].s_ii

        ha_ii = self.greenfunction.H[:pl1, :pl1]

        sa_ii = self.greenfunction.S[:pl1, :pl1]

        c1 = np.abs(h_ii - ha_ii).max()

        c2 = np.abs(s_ii - sa_ii).max()

        print 'Conv (h,s)=%.2e, %2.e' % (c1, c2)

    def plot_pl_convergence(self):

        self.initialize()

        pl1 = len(self.input_parameters['h1']) / 2       

        hlead = self.selfenergies[0].h_ii.real.diagonal()

        hprincipal = self.greenfunction.H.real.diagonal[:pl1]

        import pylab as pl

        pl.plot(hlead, label='lead')

        pl.plot(hprincipal, label='principal layer')

        pl.axis('tight')

        pl.show()

    def get_transmission(self):

        self.initialize()

        self.update()

        return self.T_e

    def get_dos(self):

        self.initialize()

        self.update()

        return self.dos_e

    def get_eigenchannels(self, n=None):

        """Get ``n`` first eigenchannels."""

        self.initialize()

        self.update()

        if n is None:

            n = self.input_parameters['eigenchannels']

        return self.eigenchannels_ne[:n]

    def get_pdos(self):

        self.initialize()

        self.update()

        return self.pdos_ne

    def subdiagonalize_bfs(self, bfs, apply=False):

        self.initialize()

        bfs = np.array(bfs)

        p = self.input_parameters

        h_mm = p['h']

        s_mm = p['s']

        ht_mm, st_mm, c_mm, e_m = subdiagonalize(h_mm, s_mm, bfs)

        if apply:

            self.uptodate = False

            h_mm[:] = ht_mm 

            s_mm[:] = st_mm 

            # Rotate coupling between lead and central region

            for alpha, sigma in enumerate(self.selfenergies):

                sigma.h_im[:] = np.dot(sigma.h_im, c_mm)

                sigma.s_im[:] = np.dot(sigma.s_im, c_mm)

        c_mm = np.take(c_mm, bfs, axis=0)

        c_mm = np.take(c_mm, bfs, axis=1)

        return ht_mm, st_mm, e_m, c_mm

    def cutcoupling_bfs(self, bfs, apply=False):

        self.initialize()

        bfs = np.array(bfs)

        p = self.input_parameters

        h_pp = p['h'].copy()

        s_pp = p['s'].copy()

        cutcoupling(h_pp, s_pp, bfs)

        if apply:

            self.uptodate = False

            p['h'][:] = h_pp

            p['s'][:] = s_pp

            for alpha, sigma in enumerate(self.selfenergies):

                for m in bfs:

                    sigma.h_im[:, m] = 0.0

                    sigma.s_im[:, m] = 0.0

        return h_pp, s_pp

    def lowdin_rotation(self, apply=False):

        p = self.input_parameters

        h_mm = p['h']

        s_mm = p['s']

        eig, rot_mm = linalg.eigh(s_mm)

        eig = np.abs(eig)

        rot_mm = np.dot(rot_mm / np.sqrt(eig), dagger(rot_mm))

        if apply:

            self.uptodate = False

            h_mm[:] = rotate_matrix(h_mm, rot_mm) # rotate C region

            s_mm[:] = rotate_matrix(s_mm, rot_mm)

            for alpha, sigma in enumerate(self.selfenergies):

                sigma.h_im[:] = np.dot(sigma.h_im, rot_mm) # rotate L-C coupl.

                sigma.s_im[:] = np.dot(sigma.s_im, rot_mm)

        return rot_mm

    def get_left_channels(self, energy, nchan=1):

        self.initialize()

        g_s_ii = self.greenfunction.retarded(energy)

        lambda_l_ii = self.selfenergies[0].get_lambda(energy)

        lambda_r_ii = self.selfenergies[1].get_lambda(energy)

        if self.greenfunction.S is None:

            s_s_qsrt_ii = s_s_isqrt = np.identity(len(g_s_ii))

        else:

            s_mm = self.greenfunction.S

            s_s_i, s_s_ii = linalg.eig(s_mm)

            s_s_i = np.abs(s_s_i)

            s_s_sqrt_i = np.sqrt(s_s_i) # sqrt of eigenvalues  

            s_s_sqrt_ii = np.dot(s_s_ii * s_s_sqrt_i, dagger(s_s_ii))

            s_s_isqrt_ii = np.dot(s_s_ii / s_s_sqrt_i, dagger(s_s_ii))

        lambdab_r_ii = np.dot(np.dot(s_s_isqrt_ii, lambda_r_ii),s_s_isqrt_ii)

        a_l_ii = np.dot(np.dot(g_s_ii, lambda_l_ii), dagger(g_s_ii))

        ab_l_ii = np.dot(np.dot(s_s_sqrt_ii, a_l_ii), s_s_sqrt_ii)

        lambda_i, u_ii = linalg.eig(ab_l_ii)

        ut_ii = np.sqrt(lambda_i / (2.0 * np.pi)) * u_ii

        m_ii = 2 * np.pi * np.dot(np.dot(dagger(ut_ii), lambdab_r_ii),ut_ii)

        T_i,c_in = linalg.eig(m_ii)

        T_i = np.abs(T_i)

        channels = np.argsort(-T_i)[:nchan]

        c_in = np.take(c_in, channels, axis=1)

        T_n = np.take(T_i, channels)

        v_in = np.dot(np.dot(s_s_isqrt_ii, ut_ii), c_in)

        return T_n, v_in