The Master's program **Quantum Physics for Advanced Materials Engineering** is devoted to the study of new physical phenomena discovered in nanostructured materials and quantum devices created last 20-30 years in the search for components for quantum electronics. At the same time, the program addresses the basic physical principles of electronic systems and devices of quantum electronics, as well as some important manufacturing techniques and measurements of physical and chemical characteristics of quantum-sized structures and materials.

The program is designed for students trained in the number of university courses in general physics and introduction to theoretical physics for a Bachelors, which includes the courses: theoretical mechanics and the theory of elasticity, electrodynamics, quantum mechanics and statistical physics. The program does not involve a starting special training of students in the condensed matter physics, because it includes basic courses in:

1) modern quantum physics of solids,

2) electronic theory of metals,

3) technology and materials of quantum electronics,

4) spectroscopic methods of materials characterization.

The medium of instruction for this program is English.

A distinctive feature of this Master’s program is to focus on the study of new physical phenomena in quantum-sized materials and devices, all of which are overlooked in traditional courses of solid state physics. These objects of the study appeared in the last 20-30 years due to development of tools and methods of measurement and conversion of properties of materials in the nanometer range of distances.

Although the physical phenomena and processes observed in the new materials and nanostructures are described in the framework of well-established fundamental concepts of quantum and classical physics, they could not become an object of study of traditional training courses on condensed matter physics, which were created in the middle of the twentieth century, simply because most of these facilities and adequate measurement tools for their research were not yet developed.

The circle of new physical phenomena studied in special courses of this master's program includes the effects of size quantization in low-dimensional structures, in particular: the quantum Hall effect, quantum charge fluctuations, Coulomb blockade and Landauer quantum conductance of the contacts of atomic size, the Wigner-Dyson statistics of electronic energy levels in the nanoclusters, the Rabi oscillations in two-level systems, the spectra of quantum dots, wells and wires in a magnetic field, phonons in fractal structures, Einstein modes in thermoelectric semiconductor materials with complex crystal cell, etc.

This master's program enables students to orient themselves in the modern scientific and applied research and development of quantum-sized materials and devices through the acquisition of skills in both theoretical calculations in the field of quantum physics of nanosystems as well as experimental measurements using modern equipment in the field of electron and scanning probe microscopy and spectroscopy.

**Basic Courses**

- Modern quantum physics of solids (1 st semester) introduces into: different aspects of modern solid state physics, including phenomena in the objects of atomic size, including those considered in the following topics: quantum Hall effect, graphene and carbon nanotubes, Landauer quantum conductance of atomic size contacts, quantum magnets (spin chains), magnetism of frustrated systems, magnetic semiconductors, including silicon doped with manganese, colossal magnetoresistance, quantum phase transitions, the low-energy excitations in disordered media and fractal structures, granular conductors, metals with heavy fermions, the Kondo semiconductors, quasicrystals and structurally complex alloys;
- Electron theory of metals (1 st semester) introduces into basic methods and results of the electron theory of metals, that are in the focus of the current research of quantum properties of solids and use the concept of Landau quasi-particles and Fermi-liquid theory to describe the properties of normal metals; description of phenomena in superconductors, based on the concept of spontaneous symmetry breaking and Bose-condensation of Cooper pairs in the framework of the theory of Bardeen, Cooper and Schrieffer, with application of the equations of the Ginzburg and Landau; foundations of the Green's functions technique and its applications for prediction and interpretation of experiments involving the scattering of photons, neutrons, muons and measuring the current-voltage characteristics of the tunneling microcontacts;
- Technologies and Materials of Quantum Electronics (2 nd semester) introduces into: physical properties of basic semiconductor materials and methods of nanotechnology in relation to the creation of the base elements of nanoelectronics, optoelectronics, quantum devices, in particular, including the study of changes in the electrical and optical properties of bulk materials when they are produced in the form of low-dimensional structures (quantum wells, wires, and dots) due to the effects of quantum-size effect; with the emphasis on C, Si, solid solutions GeXSi1 -X , compounds and solid solutions А2В6 and A3B5; also considered are basic technologies of manufacturing of quantum-sized structures: liquid phase epitaxy, molecular beam epitaxy, vapor phase epitaxy of organometallic compounds, nanolithography, self-organisation of quantum wires and dots; outline of the use of low-dimensional structures in the devices of micro-and nanoelectronics; also considered are emitting diodes and lasers for the infrared, visible and ultraviolet spectral regions, photodetectors and transistors;
- Spectroscopic methods for analysis of materials (1 st semester) introduces into: the fundamentals of modern spectroscopic methods of analysis of materials, such as Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XRF), secondary ion mass spectrometry (SIMS), transmission electron microscopy (TEM), scanning ion microscopy (SIM), i.e. methods that allow us to investigate elemental, chemical composition, atomic structure, structural perfection of the surfaces of solids, surface layers, interphase boundaries and nanostructures.

**Special Courses** familiarize students with basic modern areas of theoretical physics research in nanosystems, in including low-dimensional systems.

- Quantum electronic properties of nanosystems (3rd semester) introduces into theory of electronic quantum phenomena in nanosystems: random Hamiltonian matrices of Wigner-Dyson and thermodynamics of nanoclusters, Peierls transitions in quasi-one-dimensional conductors, transitions of Ising and Berezinskii Kosterlitz-Thouless in two-dimensional lattice systems, the theory of spin fluctuations in one-dimensional Ising chain, the theory of Landauer quantum conductance of quantum point contact;
- Physics of liquid-crystal membranes (3rd semester) introduces into physics of liquid crystals and its applications to the theory of lipid membranes, in particular, into fundamentals of elasticity of liquid crystals adapted to describe bilayer membranes, thermodynamics and kinetics of phase transitions in multicomponent systems, Gibbs phase diagrams and various two-dimensional lattice models; basic theory of wetting, adapted to biomembranes, mechanisms of protein-lipid interactions and conditions of formation of macroscopic wetting films, the dependence of the rate of cellular processes on the energy of forming membrane structures using exo-and endocytosis as example;
- Physics of Low-Dimensional Systems (2 nd semester) introduces into low-dimensional systems - quasi-two-dimensional quantum wells, one-dimensional quantum wires and quasi zero-dimensional quantum dots, in particular, with the quantum-mechanical phenomena in such systems and the influence of external electric and magnetic fields, methods of computer modelling and calculations from first principles of parameters of the low-dimensional systems: resonant frequencies, the energy spectra and wave functions of electronic and excitonic systems with carriers incoupled quantum wells and coupled quantum dots; evolution of the spectrum and restructuring of the spin states of molecules consisting of horizontally and vertically coupled quantum dots;
- Experimental Methods in the physics of low-dimensional systems (2-nd semester) introduces into: methods of experimental studies of transport and magnetic properties of solids, including: galvanomagnetic effects (magnetoresistance, Hall effect, de Haas-van Alphen effect, Shubnikov - de Haas effect), electrodynamics of metals, nuclear magnetic resonance, nuclear gamma resonance; equipment and experimental techniques of measurement of weak signals in the presence of noise, resistance measurement, thermometery, application of high magnetic fields; methods of choice of appropriate measurement technology for research, experimental design, design scheme of the experimental setup, processing and interpretation of the results of the experiment, the course also teaches methods of analysis of surfaces of solids, including classification of methods of analysis of materials surface, ion-beam probe (inverse Rutherford scattering, channeling, mass spectroscopy of secondary ions), electron-beam probe (characteristic loss spectroscopy, secondary electron emission, Auger spectroscopy), electromagnetic radiation probe, tunneling microscopy;
- Phase diagrams of multicomponent systems (3rd semester) introduces into: analysis of phase diagrams of multicomponent systems, including applied to real materials and processes based on software packet calculation methods “Thermo-Calc”, as well as the original techniques focused on the use of widespread program EXCEL; methods of solution of the following tasks: analysis of phase composition of multicomponent materials at different temperatures; graphical estimate and calculation of the liquidus, solidus, and other critical temperatures of phase transformations; construction of insulated and polythermal cuts of triple, quadruple and five fingers systems using both graphical and computational methods; calculation of the mass and volume fractions of phases in multicomponent systems, a critical analysis of information on phase diagrams and finding errors in the prediction of phase equilibria in unexplored multicomponent systems.
- Electronic properties of quantum confined semiconductor heterostructures (2–nd semester) introduces into physics of low dimensional quantum confined heterostructures, that are the structures where the carrier motion is restricted in one or more directions at the distances of the order of de Broglie wavelength; electron transport and optical transitions in low dimensional electronic systems, and the difference between the electronic properties of low dimensional structures and those of bulk semiconductors; applications of quantum dots and wells in photovoltaics and laser techniques.
- Introduction to path integral methods in condensed matter physics (2–nd semester)motivation and contents: The idea of the course is to get students acquainted with path integral approach to problems of contemporary condensed matter physics. The aim is to give students firm command of this approach via carefully selected examples and problems. The course contains mathematical digression into complex calculus, the basics of second quantization, field quantization, path integral description of quantum statistical mechanics, finite temperature perturbation theory, theory of linear response, basics of renormalization group analysis and effective field theory. The final project consists of the theoretical description of single electron transistor via effective Ambegaokar-Eckern-Schoen action.

Courses in experimental research methods help students to get an idea of materials for a prospective elementary base of quantum electronics, as well as on the possibilities of measurement methods:

- spectroscopy,
- tunneling microscopy,
- scanning ion microscopy,
- the accuracy, sensitivity, locality, and applicability of different measurement methods for the study of nanomaterials. Focus of lecture courses is new materials and modern quantum devices.

List of new materials studied in the course of the program includes:

- graphene and carbon nanotubes;
- quantum magnets - atomic spin chain;
- magnetic semiconductors - silicon doped with manganese;
- semiconductor materials based on solid solutions of germanium in silicon
- disordered media and fractal structures – aerogels, granular conductors;
- heavy fermionic metals, the Kondo semiconductors;
- quasicrystals and structurally complex thermionic materials based on bismuth telluride.

Studied electronic devices and appliances include:

- tunnel contact of atomic size;
- magnetic switches on the basis of manganites with colossal magnetoresistance;
- Josephson junctions;
- emitting diodes and lasers for the infrared, visible and ultraviolet, photodetectors, transistors.

Studied manufacturing technologies of quantum-sized materials:

- liquid-phase epitaxy;
- molecular-beam epitaxy;
- vapor-phase epitaxy from organometallic compounds;
- nanolithography;
- self-organisation of quantum wires and dots.

**Admission**

Admission to International Master’s Programs at MISiS is open to both Russian and international students. Given that all classes will be conducted in English, we recommend that non-native speakers of English achieve a TOEFL score of at least 525 (paper-based) or 200 (computer-based) prior to admission. To apply for a two-year Master’s program at MISiS, the applicant must hold a Bachelor’s degree in a related field. Upon the completion of the program of study at MISiS, the applicant will receive a Russian State diploma and a European Diploma Supplement.

**Admission Deadline**

The deadline to submit the application for **Fall 2018** is **August 10, 2018**, however, we encourage international students to submit applications by **July 20, 2018**.

** Program taught in:**

- English

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