kwant.system.
InfiniteSystem
[source]¶Abstract infinite low-level system.
An infinite system consists of an infinite series of identical cells. Adjacent cells are connected by identical inter-cell hoppings.
Notes
The system graph of an infinite systems contains a single cell, as well as
the part of the previous cell which is connected to it. The first
cell_size sites form one complete single cell. The remaining N
sites
of the graph (N
equals graph.num_nodes - cell_size
) belong to the
previous cell. They are included so that hoppings between cells can be
represented. The N sites of the previous cell correspond to the first
N
sites of the fully included cell. When an InfiniteSystem
is used
as a lead, N
acts also as the number of interface sites to which it
must be connected.
The drawing shows three cells of an infinite system. Each cell consists of three sites. Numbers denote sites which are included into the system graph. Stars denote sites which are not included. Hoppings are included in the graph if and only if they occur between two sites which are part of the graph:
* 2 *
... | | | ...
* 0 3
|/|/|
*-1-4
<-- order of cells
The numbering of sites in the drawing is one of the two valid ones for that infinite system. The other scheme has the numbers of site 0 and 1 exchanged, as well as of site 3 and 4.
The number of sites in a single cell of the system.
Methods
cell_hamiltonian
(args=(), sparse=False, *, params=None)[source]¶Hamiltonian of a single cell of the infinite system.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
discrete_symmetry
(args, *, params=None)[source]¶Return the discrete symmetry of the system.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
hamiltonian
(i, j, *args, params=None)[source]¶Return the hamiltonian matrix element for sites i
and j
.
If i == j
, return the on-site Hamiltonian of site i
.
if i != j
, return the hopping between site i
and j
.
Hamiltonians may depend (optionally) on positional and keyword arguments.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
hamiltonian_submatrix
(self, args=(), to_sites=None, from_sites=None, sparse=False, return_norb=False, *, params=None)[source]¶Return a submatrix of the system Hamiltonian.
Positional arguments to pass to the hamiltonian
method. Mutually
exclusive with ‘params’.
Whether to return a sparse or a dense matrix. Defaults to False
.
Whether to return arrays of numbers of orbitals. Defaults to False
.
Dictionary of parameter names and their values. Mutually exclusive with ‘args’.
Submatrix of Hamiltonian of the system.
Numbers of orbitals on each site in to_sites. Only returned when
return_norb
is true.
Numbers of orbitals on each site in from_sites. Only returned when
return_norb
is true.
Notes
The returned submatrix contains all the Hamiltonian matrix elements
from from_sites
to to_sites
. The default for from_sites
and
to_sites
is None
which means to use all sites of the system in the
order in which they appear.
inter_cell_hopping
(args=(), sparse=False, *, params=None)[source]¶Hopping Hamiltonian between two cells of the infinite system.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
modes
(energy=0, args=(), *, params=None)[source]¶Return mode decomposition of the lead
See documentation of PropagatingModes
and
StabilizedModes
for the return format details.
The wave functions of the returned modes are defined over the
unit cell of the system, which corresponds to the degrees of
freedom on the first cell_sites
sites of the system
(recall that infinite systems store first the sites in the unit
cell, then connected sites in the neighboring unit cell).
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
selfenergy
(energy=0, args=(), *, params=None)[source]¶Return self-energy of a lead.
The returned matrix has the shape (s, s), where s is
sum(len(self.hamiltonian(i, i)) for i in range(self.graph.num_nodes -
self.cell_size))
.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.
validate_symmetries
(args=(), *, params=None)[source]¶Check that the Hamiltonian satisfies discrete symmetries.
Returns validate
applied
to the onsite matrix and the hopping. See its documentation for
details on the return format.
Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.